TSTP Solution File: ITP204^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP204^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:50 EDT 2024
% Result : Theorem 64.08s 47.85s
% Output : Refutation 65.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 305
% Syntax : Number of formulae : 567 ( 186 unt; 45 typ; 0 def)
% Number of atoms : 2943 ( 638 equ; 2 cnn)
% Maximal formula atoms : 68 ( 5 avg)
% Number of connectives : 10100 ( 223 ~; 50 |; 92 &;9165 @)
% ( 0 <=>; 570 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 1801 (1801 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 13 con; 0-5 aty)
% Number of variables : 2103 ( 504 ^1543 !; 28 ?;2103 :)
% ( 28 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(variable_type,type,
variable: $tType ).
thf(game_type,type,
game: $tType ).
thf(char_type,type,
char: $tType ).
thf(trm_type,type,
trm: $tType ).
thf(fml_type,type,
fml: $tType ).
thf(bounded_lattice_type,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : $o ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_type,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(none_type,type,
none:
!>[TA: $tType] : ( option @ TA ) ).
thf(some_type,type,
some:
!>[TA: $tType] : ( TA > ( option @ TA ) ) ).
thf(case_option_type,type,
case_option:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > TB ) > ( option @ TA ) > TB ) ).
thf(the_type,type,
the:
!>[TA: $tType] : ( ( option @ TA ) > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_case_prod_type,type,
product_case_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(static_FVF_type,type,
static_FVF: fml > ( set @ variable ) ).
thf(static_FVT_type,type,
static_FVT: trm > ( set @ variable ) ).
thf(geq_type,type,
geq: trm > trm > fml ).
thf(pred_type,type,
pred: char > trm > fml ).
thf(const_type,type,
const: char > trm ).
thf(func_type,type,
func: char > trm > trm ).
thf(uSubst1556497037e_Geqo_type,type,
uSubst1556497037e_Geqo: ( option @ trm ) > ( option @ trm ) > ( option @ fml ) ).
thf(uSubst969145931substt_type,type,
uSubst969145931substt: trm > ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) ).
thf(uSubst1138577137pconst_type,type,
uSubst1138577137pconst: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > char > ( option @ trm ) ).
thf(uSubst95898978stappf_type,type,
uSubst95898978stappf: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > fml > ( option @ fml ) ).
thf(uSubst95898992stappt_type,type,
uSubst95898992stappt: ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ) > ( set @ variable ) > trm > ( option @ trm ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(ua_type,type,
ua: set @ variable ).
thf(va_type,type,
va: set @ variable ).
thf(sigma_type,type,
sigma: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) ).
thf(theta_type,type,
theta: trm ).
thf(p_type,type,
p: char ).
thf(vv_type,type,
vv: ( set @ variable ) > ( set @ variable ) > variable ).
thf(vva_type,type,
vva: ( set @ variable ) > ( set @ variable ) > variable ).
thf(185,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( ( some @ TA @ ( the @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_option_Ocollapse) ).
thf(809,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( ( some @ TA @ ( the @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(237,axiom,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: trm] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( ( uSubst95898992stappt @ C @ B @ D )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ C @ B @ D )
= ( uSubst95898992stappt @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_usubstappt__antimon) ).
thf(1024,plain,
! [A: set @ variable,B: set @ variable,C: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),D: trm] :
( ( ord_less_eq @ ( set @ variable ) @ A @ B )
=> ( ( ( uSubst95898992stappt @ C @ B @ D )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ C @ B @ D )
= ( uSubst95898992stappt @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(171,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_set__eq__subset) ).
thf(760,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(74,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bot__set__def) ).
thf(479,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(36,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_inf__commute) ).
thf(352,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(128,axiom,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( geq @ A @ B )
= ( geq @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_fml_Oinject_I2_J) ).
thf(645,plain,
! [A: trm,B: trm,C: trm,D: trm] :
( ( ( geq @ A @ B )
= ( geq @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(211,axiom,
! [A: variable > ( option @ fml ) > $o,B: variable,C: option @ fml] :
( ! [D: variable,E: fml] : ( A @ D @ ( some @ fml @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ fml ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Existso_Oinduct) ).
thf(892,plain,
! [A: variable > ( option @ fml ) > $o,B: variable,C: option @ fml] :
( ! [D: variable,E: fml] : ( A @ D @ ( some @ fml @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ fml ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(28,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_inf__left__commute) ).
thf(333,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Collect__restrict) ).
thf(628,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_inf__le2) ).
thf(408,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(105,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inf__set__def) ).
thf(582,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(231,axiom,
! [A: option @ fml] :
( ! [B: fml] :
( A
!= ( some @ fml @ B ) )
=> ( A
= ( none @ fml ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Testo_Ocases) ).
thf(1005,plain,
! [A: option @ fml] :
( ! [B: fml] :
( A
!= ( some @ fml @ B ) )
=> ( A
= ( none @ fml ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(276,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_inf_Oidem) ).
thf(308,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inf__mono) ).
thf(440,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ ( inf_inf @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(110,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( some @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_option_Osel) ).
thf(597,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( some @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(204,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable,E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( func @ B @ E ) )
= ( none @ trm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_usubstappt__func2) ).
thf(873,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable,E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( func @ B @ E ) )
= ( none @ trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(63,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inf_OboundedE) ).
thf(449,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(248,axiom,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_split__option__all) ).
thf(1078,plain,
! [TA: $tType] :
( ( '!' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
& ! [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(90,axiom,
bounded_lattice_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__bot_11) ).
thf(533,plain,
bounded_lattice_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(97,axiom,
~ ! [A: ( set @ variable ) > ( set @ variable ) > variable] :
~ ! [B: set @ variable,C: set @ variable] :
( ( ( ( inf_inf @ ( set @ variable ) @ B @ C )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [D: variable] :
( ~ ( member @ variable @ D @ B )
| ! [E: variable] :
( ~ ( member @ variable @ E @ C )
| ( D != E ) ) ) )
& ( ( ( inf_inf @ ( set @ variable ) @ B @ C )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable @ ( vv @ C @ B ) @ B )
& ( member @ variable @ ( A @ C @ B ) @ C )
& ( ( vv @ C @ B )
= ( A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(550,plain,
~ ! [A: ( set @ variable ) > ( set @ variable ) > variable] :
~ ! [B: set @ variable,C: set @ variable] :
( ( ( ( inf_inf @ ( set @ variable ) @ B @ C )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [D: variable] :
( ~ ( member @ variable @ D @ B )
| ! [E: variable] :
( ~ ( member @ variable @ E @ C )
| ( D != E ) ) ) )
& ( ( ( inf_inf @ ( set @ variable ) @ B @ C )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable @ ( vv @ C @ B ) @ B )
& ( member @ variable @ ( A @ C @ B ) @ C )
& ( ( vv @ C @ B )
= ( A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(155,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( uSubst95898992stappt @ A @ B @ ( const @ C ) )
= ( uSubst1138577137pconst @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_usubstappt_Osimps_I3_J) ).
thf(715,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( uSubst95898992stappt @ A @ B @ ( const @ C ) )
= ( uSubst1138577137pconst @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_subset__CollectI) ).
thf(472,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(217,axiom,
~ ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
= ( none @ fml ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062) ).
thf(913,plain,
~ ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
= ( none @ fml ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_pred__subset__eq) ).
thf(670,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(191,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( pred @ C @ D ) )
!= ( none @ fml ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
& ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : G ) )
@ A
@ C )
= ( none @ fml ) )
| ? [E: fml] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ C )
= ( some @ fml @ E ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ E ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_usubstappf__pred__conv) ).
thf(829,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( pred @ C @ D ) )
!= ( none @ fml ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
& ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : G ) )
@ A
@ C )
= ( none @ fml ) )
| ? [E: fml] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ C )
= ( some @ fml @ E ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ E ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(213,axiom,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_option_OdiscI) ).
thf(898,plain,
! [TA: $tType,A: option @ TA,B: TA] :
( ( A
= ( some @ TA @ B ) )
=> ( A
!= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(194,axiom,
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_f8) ).
thf(841,plain,
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(17,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_inf__right__idem) ).
thf(301,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(98,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_inf__sup__ord_I2_J) ).
thf(565,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_IntD2) ).
thf(651,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(100,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(570,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(44,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_linorder__wlog) ).
thf(372,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_inf__idem) ).
thf(357,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(67,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_inf_OcoboundedI1) ).
thf(460,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_subset__iff) ).
thf(619,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(193,axiom,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_not__Some__eq) ).
thf(838,plain,
! [TA: $tType,A: option @ TA] :
( ( ! [B: TA] :
( A
!= ( some @ TA @ B ) ) )
= ( A
= ( none @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(149,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__eq__set__def) ).
thf(702,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_bot_Oextremum__uniqueI) ).
thf(751,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(183,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: set @ variable] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ C )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ A @ B @ C )
= ( uSubst95898992stappt @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_usubstappt__det) ).
thf(802,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: set @ variable] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ C )
!= ( none @ trm ) )
=> ( ( uSubst95898992stappt @ A @ B @ C )
= ( uSubst95898992stappt @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(33,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_5) ).
thf(344,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(214,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
!= ( none @ fml ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
& ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_usubstappf__geq__conv) ).
thf(902,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
!= ( none @ fml ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
& ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_ex__in__conv) ).
thf(638,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(113,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Collect__mono) ).
thf(606,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inf__absorb2) ).
thf(416,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(25,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_7) ).
thf(325,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__bot_3) ).
thf(289,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inf_Oabsorb__iff2) ).
thf(591,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc2004651681e_prod @ TA @ TB @ TC )
= ( product_case_prod @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_internal__case__prod__def) ).
thf(806,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc2004651681e_prod @ TA @ TB @ TC )
= ( product_case_prod @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TA > $o,C: option @ TA,D: TB > $o,E: TB,F: TA > TB] :
( ( case_option @ $o @ TA @ A @ B @ C )
=> ( ( A
=> ( D @ E ) )
=> ( ! [G: TA] :
( ( B @ G )
=> ( D @ ( F @ G ) ) )
=> ( D @ ( case_option @ TB @ TA @ E @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_disjE__realizer2) ).
thf(397,plain,
! [TA: $tType,TB: $tType,A: $o,B: TA > $o,C: option @ TA,D: TB > $o,E: TB,F: TA > TB] :
( ( case_option @ $o @ TA @ A @ B @ C )
=> ( ( A
=> ( D @ E ) )
=> ( ! [G: TA] :
( ( B @ G )
=> ( D @ ( F @ G ) ) )
=> ( D @ ( case_option @ TB @ TA @ E @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(8,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_4) ).
thf(280,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_inf_Ocommute) ).
thf(293,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(201,axiom,
! [A: option @ game] :
( ( A
!= ( none @ game ) )
= ( ? [B: game] :
( A
= ( some @ game @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_undefg__equiv) ).
thf(866,plain,
! [A: option @ game] :
( ( A
!= ( none @ game ) )
= ( ? [B: game] :
( A
= ( some @ game @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(258,axiom,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_option_Oexpand) ).
thf(1119,plain,
! [TA: $tType,A: option @ TA,B: option @ TA] :
( ( ( A
= ( none @ TA ) )
= ( B
= ( none @ TA ) ) )
=> ( ( ( A
!= ( none @ TA ) )
=> ( ( B
!= ( none @ TA ) )
=> ( ( the @ TA @ A )
= ( the @ TA @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(133,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_inf_Oorder__iff) ).
thf(660,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( A
= ( inf_inf @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(51,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_empty__iff) ).
thf(411,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_equalityE) ).
thf(428,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(205,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( case_option @ $o @ TA @ $false
@ ^ [B: TA] : $true
@ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_option_Odisc__eq__case_I2_J) ).
thf(877,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( case_option @ $o @ TA @ $false
@ ^ [B: TA] : $true
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(145,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_predicate1D) ).
thf(692,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(247,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: fml,D: set @ variable,E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ B )
= ( some @ fml @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ C ) @ D )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ A @ D @ ( pred @ B @ E ) )
= ( none @ fml ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_usubstappf__pred2) ).
thf(1074,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: fml,D: set @ variable,E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ B )
= ( some @ fml @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ C ) @ D )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ A @ D @ ( pred @ B @ E ) )
= ( none @ fml ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(64,axiom,
! [A: char,B: char] :
( ( ( const @ A )
= ( const @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_trm_Oinject_I3_J) ).
thf(452,plain,
! [A: char,B: char] :
( ( ( const @ A )
= ( const @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(139,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_empty__def) ).
thf(678,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(270,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(95,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_inf__greatest) ).
thf(546,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(91,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_inf_Oabsorb1) ).
thf(534,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(245,axiom,
! [A: option @ fml] :
( ( A
!= ( none @ fml ) )
= ( ? [B: fml] :
( A
= ( some @ fml @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_undeff__equiv) ).
thf(1067,plain,
! [A: option @ fml] :
( ( A
!= ( none @ fml ) )
= ( ? [B: fml] :
( A
= ( some @ fml @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(244,axiom,
( ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [A: variable] :
( ~ ( member @ variable @ A
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) ) ) )
| ! [B: variable] :
( ~ ( member @ variable @ B @ va )
| ( A != B ) ) ) )
& ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable
@ ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
& ( member @ variable
@ ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ va )
& ( ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
= ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f10) ).
thf(1057,plain,
( ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [A: variable] :
( ~ ( member @ variable @ A
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) ) ) )
| ! [B: variable] :
( ~ ( member @ variable @ B @ va )
| ( A != B ) ) ) )
& ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable
@ ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
& ( member @ variable
@ ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ va )
& ( ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
= ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(216,axiom,
( ~ ( member @ variable
@ ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
| ~ ( member @ variable
@ ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ va )
| ( ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
!= ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062) ).
thf(910,plain,
( ~ ( member @ variable
@ ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
| ~ ( member @ variable
@ ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
@ va )
| ( ( vv @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) )
!= ( vva @ va
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(166,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Int__def) ).
thf(746,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(190,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: fml,D: set @ variable] :
( ( ( uSubst95898978stappf @ A @ B @ C )
!= ( none @ fml ) )
=> ( ( ( uSubst95898978stappf @ A @ D @ C )
!= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ A @ B @ C )
= ( uSubst95898978stappf @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_usubstappf__det) ).
thf(825,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: fml,D: set @ variable] :
( ( ( uSubst95898978stappf @ A @ B @ C )
!= ( none @ fml ) )
=> ( ( ( uSubst95898978stappf @ A @ D @ C )
!= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ A @ B @ C )
= ( uSubst95898978stappf @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(240,axiom,
! [A: char,B: trm,C: char,D: trm] :
( ( ( pred @ A @ B )
= ( pred @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_fml_Oinject_I1_J) ).
thf(1042,plain,
! [A: char,B: trm,C: char,D: trm] :
( ( ( pred @ A @ B )
= ( pred @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(349,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(122,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_conj__subset__def) ).
thf(630,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(187,axiom,
! [A: option @ trm,B: option @ trm] :
( ( ( uSubst1556497037e_Geqo @ A @ B )
= ( none @ fml ) )
= ( ( A
= ( none @ trm ) )
| ( B
= ( none @ trm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Geqo__undef) ).
thf(815,plain,
! [A: option @ trm,B: option @ trm] :
( ( ( uSubst1556497037e_Geqo @ A @ B )
= ( none @ fml ) )
= ( ( A
= ( none @ trm ) )
| ( B
= ( none @ trm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_equalityD2) ).
thf(729,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(236,axiom,
( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
!= ( none @ fml ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Pred_Oprems_I2_J) ).
thf(1021,plain,
( ( uSubst95898978stappf @ sigma @ ua @ ( pred @ p @ theta ) )
!= ( none @ fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_subset__Collect__iff) ).
thf(778,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(40,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_inf_Oassoc) ).
thf(361,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_bot__apply) ).
thf(625,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(58,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_emptyE) ).
thf(435,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType] :
( ( case_option @ TA @ TB )
= ( ^ [A: TA,B: TB > TA,C: option @ TB] :
( if @ TA
@ ( C
= ( none @ TB ) )
@ A
@ ( B @ ( the @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_option_Ocase__eq__if) ).
thf(889,plain,
! [TA: $tType,TB: $tType] :
( ( case_option @ TA @ TB )
= ( ^ [A: TA,B: TB > TA,C: option @ TB] :
( if @ TA
@ ( C
= ( none @ TB ) )
@ A
@ ( B @ ( the @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(79,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_14) ).
thf(493,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(757,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(259,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( uSubst95898978stappf @ A @ B @ ( pred @ C @ D ) )
= ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [E: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ C @ E ) )
@ ^ [F: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ E ) @ ( bot_bot @ ( set @ variable ) ) @ F )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ C ) )
@ ( uSubst95898992stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_usubstappf_Osimps_I1_J) ).
thf(1128,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( uSubst95898978stappf @ A @ B @ ( pred @ C @ D ) )
= ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [E: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ C @ E ) )
@ ^ [F: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ F ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ E ) @ ( bot_bot @ ( set @ variable ) ) @ F )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : H ) )
@ A
@ C ) )
@ ( uSubst95898992stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(152,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(710,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(233,axiom,
! [A: trm,B: trm] :
( ( uSubst1556497037e_Geqo @ ( some @ trm @ A ) @ ( some @ trm @ B ) )
= ( some @ fml @ ( geq @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Geqo_Osimps_I1_J) ).
thf(1012,plain,
! [A: trm,B: trm] :
( ( uSubst1556497037e_Geqo @ ( some @ trm @ A ) @ ( some @ trm @ B ) )
= ( some @ fml @ ( geq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(10,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_le__cases) ).
thf(285,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(196,axiom,
! [A: trm] :
( ( uSubst1556497037e_Geqo @ ( some @ trm @ A ) @ ( none @ trm ) )
= ( none @ fml ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Geqo_Osimps_I3_J) ).
thf(847,plain,
! [A: trm] :
( ( uSubst1556497037e_Geqo @ ( some @ trm @ A ) @ ( none @ trm ) )
= ( none @ fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_le__infE) ).
thf(484,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(164,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_inf_OboundedI) ).
thf(742,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(22,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_order__refl) ).
thf(317,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_IntD1) ).
thf(615,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(202,axiom,
! [A: ( option @ game ) > ( option @ game ) > $o,B: option @ game,C: option @ game] :
( ! [D: game,E: game] : ( A @ ( some @ game @ D ) @ ( some @ game @ E ) )
=> ( ! [D: option @ game] : ( A @ D @ ( none @ game ) )
=> ( ! [D: game] : ( A @ ( none @ game ) @ ( some @ game @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Composeo_Oinduct) ).
thf(869,plain,
! [A: ( option @ game ) > ( option @ game ) > $o,B: option @ game,C: option @ game] :
( ! [D: game,E: game] : ( A @ ( some @ game @ D ) @ ( some @ game @ E ) )
=> ( ! [D: option @ game] : ( A @ D @ ( none @ game ) )
=> ( ! [D: game] : ( A @ ( none @ game ) @ ( some @ game @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA] :
( ( case_option @ TA @ TB @ A @ B @ ( none @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_option_Osimps_I4_J) ).
thf(857,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA] :
( ( case_option @ TA @ TB @ A @ B @ ( none @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(208,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
= ( none @ TA ) )
= ( case_option @ $o @ TA @ $true
@ ^ [B: TA] : $false
@ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_option_Odisc__eq__case_I1_J) ).
thf(884,plain,
! [TA: $tType,A: option @ TA] :
( ( A
= ( none @ TA ) )
= ( case_option @ $o @ TA @ $true
@ ^ [B: TA] : $false
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(238,axiom,
! [A: ( option @ trm ) > $o,B: option @ trm] :
( ! [C: trm] : ( A @ ( some @ trm @ C ) )
=> ( ( A @ ( none @ trm ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Differentialo_Oinduct) ).
thf(1028,plain,
! [A: ( option @ trm ) > $o,B: option @ trm] :
( ! [C: trm] : ( A @ ( some @ trm @ C ) )
=> ( ( A @ ( none @ trm ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(92,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Set_Ois__empty__def) ).
thf(537,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_bot__fun__def) ).
thf(476,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_inf__Int__eq) ).
thf(622,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(254,axiom,
! [A: char,B: trm,C: trm,D: trm] :
( ( pred @ A @ B )
!= ( geq @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_fml_Odistinct_I1_J) ).
thf(1099,plain,
! [A: char,B: trm,C: trm,D: trm] :
( ( pred @ A @ B )
!= ( geq @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(260,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( uSubst95898992stappt @ A @ B @ ( func @ C @ D ) )
= ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
@ ^ [E: trm] :
( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ C @ E ) )
@ ^ [F: trm] :
( if @ ( option @ trm )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ F ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898992stappt @ ( uSubst969145931substt @ E ) @ ( bot_bot @ ( set @ variable ) ) @ F )
@ ( none @ trm ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ C ) )
@ ( uSubst95898992stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_usubstappt_Osimps_I4_J) ).
thf(1131,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( uSubst95898992stappt @ A @ B @ ( func @ C @ D ) )
= ( case_option @ ( option @ trm ) @ trm @ ( none @ trm )
@ ^ [E: trm] :
( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( func @ C @ E ) )
@ ^ [F: trm] :
( if @ ( option @ trm )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ F ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898992stappt @ ( uSubst969145931substt @ E ) @ ( bot_bot @ ( set @ variable ) ) @ F )
@ ( none @ trm ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ C ) )
@ ( uSubst95898992stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(66,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Int__left__commute) ).
thf(457,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(157,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_bot_Oextremum) ).
thf(721,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(84,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(503,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(47,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_eq__refl) ).
thf(393,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(257,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( ( uSubst95898992stappt @ A @ B @ ( const @ C ) )
!= ( none @ trm ) )
=> ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C )
= ( none @ trm ) )
| ? [D: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ C )
= ( some @ trm @ D ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_usubstappt__const__conv) ).
thf(1114,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( ( uSubst95898992stappt @ A @ B @ ( const @ C ) )
!= ( none @ trm ) )
=> ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C )
= ( none @ trm ) )
| ? [D: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ C )
= ( some @ trm @ D ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(86,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Int__emptyI) ).
thf(508,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(20,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_boolean__algebra__cancel_Oinf1) ).
thf(311,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(173,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_bot__empty__eq) ).
thf(765,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(89,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inf_Oabsorb2) ).
thf(530,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(182,axiom,
! [TA: $tType,A: $o,B: TA > $o,C: option @ TA] :
( ( case_option @ $o @ TA @ A @ B @ C )
=> ( ( ( C
= ( none @ TA ) )
=> ~ A )
=> ~ ! [D: TA] :
( ( C
= ( some @ TA @ D ) )
=> ~ ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_case__optionE) ).
thf(794,plain,
! [TA: $tType,A: $o,B: TA > $o,C: option @ TA] :
( ( case_option @ $o @ TA @ A @ B @ C )
=> ( ( ( C
= ( none @ TA ) )
=> ~ A )
=> ~ ! [D: TA] :
( ( C
= ( some @ TA @ D ) )
=> ~ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(156,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Collect__mono__iff) ).
thf(718,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(220,axiom,
! [A: ( option @ game ) > ( option @ fml ) > $o,B: option @ game,C: option @ fml] :
( ! [D: game,E: fml] : ( A @ ( some @ game @ D ) @ ( some @ fml @ E ) )
=> ( ! [D: option @ fml] : ( A @ ( none @ game ) @ D )
=> ( ! [D: game] : ( A @ ( some @ game @ D ) @ ( none @ fml ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Diamondo_Oinduct) ).
thf(926,plain,
! [A: ( option @ game ) > ( option @ fml ) > $o,B: option @ game,C: option @ fml] :
( ! [D: game,E: fml] : ( A @ ( some @ game @ D ) @ ( some @ fml @ E ) )
=> ( ! [D: option @ fml] : ( A @ ( none @ game ) @ D )
=> ( ! [D: game] : ( A @ ( some @ game @ D ) @ ( none @ fml ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(123,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Int__greatest) ).
thf(633,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(39,axiom,
lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_15) ).
thf(360,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_subset__empty) ).
thf(425,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(513,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(255,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
=> ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ C ) ) @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_usubstappf__geq) ).
thf(1103,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
=> ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ C ) ) @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inf_Oleft__idem) ).
thf(296,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(161,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_inf_Oabsorb__iff1) ).
thf(733,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Int__lower2) ).
thf(694,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(175,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_inf__absorb1) ).
thf(772,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( inf_inf @ TA @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Int__absorb1) ).
thf(413,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(103,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_le__infI) ).
thf(577,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Int__lower1) ).
thf(711,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Int__absorb2) ).
thf(579,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(13,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_10) ).
thf(291,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_subset__trans) ).
thf(641,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(391,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Int__Collect__mono) ).
thf(445,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(180,axiom,
! [A: option @ trm] :
( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ A )
= ( none @ fml ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Geqo_Osimps_I2_J) ).
thf(787,plain,
! [A: option @ trm] :
( ( uSubst1556497037e_Geqo @ ( none @ trm ) @ A )
= ( none @ fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(256,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ ( func @ C @ D ) )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
& ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : F ) )
@ A
@ C )
= ( none @ trm ) )
| ? [E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ C )
= ( some @ trm @ E ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ E ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_usubstappt__func__conv) ).
thf(1107,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char,D: trm] :
( ( ( uSubst95898992stappt @ A @ B @ ( func @ C @ D ) )
!= ( none @ trm ) )
=> ( ( ( uSubst95898992stappt @ A @ B @ D )
!= ( none @ trm ) )
& ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : F ) )
@ A
@ C )
= ( none @ trm ) )
| ? [E: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ fml ),I: char > ( option @ game )] : G ) )
@ A
@ C )
= ( some @ trm @ E ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ E ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(70,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Collect__empty__eq) ).
thf(466,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(251,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst1138577137pconst @ A @ D @ B )
= ( some @ trm @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_usappconst__simp) ).
thf(1090,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst1138577137pconst @ A @ D @ B )
= ( some @ trm @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_case__prod__app) ).
thf(919,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(93,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_all__not__in__conv) ).
thf(540,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(154,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_le__infI1) ).
thf(713,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_IntE) ).
thf(498,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(140,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Collect__empty__eq__bot) ).
thf(681,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_subset__antisym) ).
thf(784,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Int__Collect) ).
thf(419,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_le__cases3) ).
thf(377,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(99,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_empty__Collect__eq) ).
thf(567,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(242,axiom,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_option_Oinducts) ).
thf(1048,plain,
! [TA: $tType,A: ( option @ TA ) > $o,B: option @ TA] :
( ( A @ ( none @ TA ) )
=> ( ! [C: TA] : ( A @ ( some @ TA @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(162,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_inf_Obounded__iff) ).
thf(736,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(206,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_not__None__eq) ).
thf(880,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
= ( ? [B: TA] :
( A
= ( some @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(130,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__infI2) ).
thf(649,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(80,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_inf1I) ).
thf(494,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( C @ B )
=> ( inf_inf @ ( TA > $o ) @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(42,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_inf__sup__aci_I1_J) ).
thf(367,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(114,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_inf__bot__left) ).
thf(609,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_subset__eq) ).
thf(594,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Int__absorb) ).
thf(726,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(212,axiom,
! [A: ( option @ fml ) > ( option @ fml ) > $o,B: option @ fml,C: option @ fml] :
( ! [D: fml,E: fml] : ( A @ ( some @ fml @ D ) @ ( some @ fml @ E ) )
=> ( ! [D: option @ fml] : ( A @ ( none @ fml ) @ D )
=> ( ! [D: fml] : ( A @ ( some @ fml @ D ) @ ( none @ fml ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Ando_Oinduct) ).
thf(895,plain,
! [A: ( option @ fml ) > ( option @ fml ) > $o,B: option @ fml,C: option @ fml] :
( ! [D: fml,E: fml] : ( A @ ( some @ fml @ D ) @ ( some @ fml @ E ) )
=> ( ! [D: option @ fml] : ( A @ ( none @ fml ) @ D )
=> ( ! [D: fml] : ( A @ ( some @ fml @ D ) @ ( none @ fml ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_inf__fun__def) ).
thf(330,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(68,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_inf1D1) ).
thf(462,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(222,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_option_Oexhaust) ).
thf(932,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( some @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(142,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Int__commute) ).
thf(685,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_equalityD1) ).
thf(768,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(278,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(234,axiom,
! [A: variable > ( option @ trm ) > $o,B: variable,C: option @ trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Assigno_Oinduct) ).
thf(1015,plain,
! [A: variable > ( option @ trm ) > $o,B: variable,C: option @ trm] :
( ! [D: variable,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: variable] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(229,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
!= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ C ) ) @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_usubstappf__geqr) ).
thf(1000,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
!= ( none @ fml ) )
=> ( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( some @ fml @ ( geq @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ C ) ) @ ( the @ trm @ ( uSubst95898992stappt @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(299,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inf_Oright__idem) ).
thf(267,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_option_Oinject) ).
thf(505,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( some @ TA @ A )
= ( some @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(132,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inf__unique) ).
thf(653,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA > TA > TA,B: TA,C: TA] :
( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ D )
=> ( ! [D: TA,E: TA] : ( ord_less_eq @ TA @ ( A @ D @ E ) @ E )
=> ( ! [D: TA,E: TA,F: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( ( ord_less_eq @ TA @ D @ F )
=> ( ord_less_eq @ TA @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf @ TA @ B @ C )
= ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(219,axiom,
! [A: option @ trm] :
( ! [B: trm] :
( A
!= ( some @ trm @ B ) )
=> ( A
= ( none @ trm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Differentialo_Ocases) ).
thf(922,plain,
! [A: option @ trm] :
( ! [B: trm] :
( A
!= ( some @ trm @ B ) )
=> ( A
= ( none @ trm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_subsetD) ).
thf(455,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(207,axiom,
ord_less_eq @ ( set @ variable ) @ va @ ua,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Pred_Oprems_I1_J) ).
thf(883,plain,
ord_less_eq @ ( set @ variable ) @ va @ ua,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(239,axiom,
! [A: option @ fml,B: fml > ( option @ fml ),C: option @ fml] :
( ( ( C
= ( none @ fml ) )
=> ( ( case_option @ ( option @ fml ) @ fml @ A @ B @ C )
= A ) )
& ( ( C
!= ( none @ fml ) )
=> ( ( case_option @ ( option @ fml ) @ fml @ A @ B @ C )
= ( B @ ( the @ fml @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_f2) ).
thf(1034,plain,
! [A: option @ fml,B: fml > ( option @ fml ),C: option @ fml] :
( ( ( C
= ( none @ fml ) )
=> ( ( case_option @ ( option @ fml ) @ fml @ A @ B @ C )
= A ) )
& ( ( C
!= ( none @ fml ) )
=> ( ( case_option @ ( option @ fml ) @ fml @ A @ B @ C )
= ( B @ ( the @ fml @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(186,axiom,
! [A: char > ( option @ trm ) > $o,B: char,C: option @ trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: char] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ODEo_Oinduct) ).
thf(812,plain,
! [A: char > ( option @ trm ) > $o,B: char,C: option @ trm] :
( ! [D: char,E: trm] : ( A @ D @ ( some @ trm @ E ) )
=> ( ! [D: char] : ( A @ D @ ( none @ trm ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__bot) ).
thf(342,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( none @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
=> ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_option_Osplit__sel) ).
thf(1018,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( none @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
=> ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(355,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(169,axiom,
! [A: set @ variable,B: set @ variable] :
( ( ? [C: variable] :
( ( member @ variable @ C @ B )
& ? [D: variable] :
( ( member @ variable @ D @ A )
& ( C = D ) ) ) )
= ( ( member @ variable @ ( vv @ A @ B ) @ B )
& ? [C: variable] :
( ( member @ variable @ C @ A )
& ( ( vv @ A @ B )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062) ).
thf(754,plain,
! [A: set @ variable,B: set @ variable] :
( ( ? [C: variable] :
( ( member @ variable @ C @ B )
& ? [D: variable] :
( ( member @ variable @ D @ A )
& ( C = D ) ) ) )
= ( ( member @ variable @ ( vv @ A @ B ) @ B )
& ? [C: variable] :
( ( member @ variable @ C @ A )
& ( ( vv @ A @ B )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(192,axiom,
! [A: variable] :
( ~ ( member @ variable @ A @ va )
| ( member @ variable @ A @ ua ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f1) ).
thf(836,plain,
! [A: variable] :
( ~ ( member @ variable @ A @ va )
| ( member @ variable @ A @ ua ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(78,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_inf__bot__right) ).
thf(490,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_subsetI) ).
thf(675,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(134,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_equals0D) ).
thf(663,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_subset__emptyI) ).
thf(548,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(261,axiom,
( ( none @ trm )
= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_undeft__None) ).
thf(1134,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(129,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(648,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Int__empty__left) ).
thf(487,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(249,axiom,
! [A: ( option @ trm ) > ( option @ trm ) > $o,B: option @ trm,C: option @ trm] :
( ! [D: trm,E: trm] : ( A @ ( some @ trm @ D ) @ ( some @ trm @ E ) )
=> ( ! [D: option @ trm] : ( A @ ( none @ trm ) @ D )
=> ( ! [D: trm] : ( A @ ( some @ trm @ D ) @ ( none @ trm ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Timeso_Oinduct) ).
thf(1081,plain,
! [A: ( option @ trm ) > ( option @ trm ) > $o,B: option @ trm,C: option @ trm] :
( ! [D: trm,E: trm] : ( A @ ( some @ trm @ D ) @ ( some @ trm @ E ) )
=> ( ! [D: option @ trm] : ( A @ ( none @ trm ) @ D )
=> ( ! [D: trm] : ( A @ ( some @ trm @ D ) @ ( none @ trm ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_prop__restrict) ).
thf(749,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(117,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Int__mono) ).
thf(617,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(88,axiom,
! [A: set @ variable,B: set @ variable] :
( ( ( ( inf_inf @ ( set @ variable ) @ A @ B )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [C: variable] :
( ~ ( member @ variable @ C @ A )
| ! [D: variable] :
( ~ ( member @ variable @ D @ B )
| ( C != D ) ) ) )
& ( ( ( inf_inf @ ( set @ variable ) @ A @ B )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable @ ( vv @ B @ A ) @ A )
& ( member @ variable @ ( vva @ B @ A ) @ B )
& ( ( vv @ B @ A )
= ( vva @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_f9) ).
thf(516,plain,
! [A: set @ variable,B: set @ variable] :
( ( ( ( inf_inf @ ( set @ variable ) @ A @ B )
!= ( bot_bot @ ( set @ variable ) ) )
| ! [C: variable] :
( ~ ( member @ variable @ C @ A )
| ! [D: variable] :
( ~ ( member @ variable @ D @ B )
| ( C != D ) ) ) )
& ( ( ( inf_inf @ ( set @ variable ) @ A @ B )
= ( bot_bot @ ( set @ variable ) ) )
| ( ( member @ variable @ ( vv @ B @ A ) @ A )
& ( member @ variable @ ( vva @ B @ A ) @ B )
& ( ( vv @ B @ A )
= ( vva @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(230,axiom,
( uSubst1138577137pconst
= ( ^ [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ C ) )
@ ^ [D: trm] :
( if @ ( option @ trm )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( some @ trm @ D )
@ ( none @ trm ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_usappconst__def) ).
thf(1003,plain,
( uSubst1138577137pconst
= ( ^ [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( case_option @ ( option @ trm ) @ trm @ ( some @ trm @ ( const @ C ) )
@ ^ [D: trm] :
( if @ ( option @ trm )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) )
@ ( some @ trm @ D )
@ ( none @ trm ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(144,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inf_Ocobounded1) ).
thf(690,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(209,axiom,
( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [A: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ A ) )
@ ^ [B: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ B ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ A ) @ ( bot_bot @ ( set @ variable ) ) @ B )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) )
@ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
= ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
@ ^ [A: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ A ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ A )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_f6) ).
thf(887,plain,
( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [A: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ A ) )
@ ^ [B: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ B ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ A ) @ ( bot_bot @ ( set @ variable ) ) @ B )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) )
@ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
= ( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) )
@ ^ [A: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ A ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ ua @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) ) @ A )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(225,axiom,
( ~ ( ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
& ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( none @ fml )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062) ).
thf(971,plain,
( ~ ( ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898978stappf @ ( uSubst969145931substt @ ( the @ trm @ ( uSubst95898992stappt @ sigma @ va @ theta ) ) ) @ ( bot_bot @ ( set @ variable ) )
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) )
& ( ( ( inf_inf @ ( set @ variable )
@ ( static_FVF
@ ( the @ fml
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p ) ) )
@ va )
!= ( bot_bot @ ( set @ variable ) ) )
=> ( ( none @ fml )
= ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) )
=> ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(26,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_inf__sup__aci_I2_J) ).
thf(327,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(163,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_predicate1I) ).
thf(739,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(246,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( const @ B ) )
= ( some @ trm @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_usubstappt__const) ).
thf(1070,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( const @ B ) )
= ( some @ trm @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(203,axiom,
( ( some @ trm )
= ( some @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Aterm__Some) ).
thf(872,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(150,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Int__subset__iff) ).
thf(705,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(9,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inf_Oleft__commute) ).
thf(282,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(243,axiom,
! [A: option @ game] :
( ! [B: game] :
( A
!= ( some @ game @ B ) )
=> ( A
= ( none @ game ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Loopo_Ocases) ).
thf(1053,plain,
! [A: option @ game] :
( ! [B: game] :
( A
!= ( some @ game @ B ) )
=> ( A
= ( none @ game ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(137,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_rev__predicate1D) ).
thf(673,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_inf__apply) ).
thf(338,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(127,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_inf_OcoboundedI2) ).
thf(643,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(215,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ A @ B @ C ) @ ( uSubst95898992stappt @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_usubstappf_Osimps_I2_J) ).
thf(907,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: trm,D: trm] :
( ( uSubst95898978stappf @ A @ B @ ( geq @ C @ D ) )
= ( uSubst1556497037e_Geqo @ ( uSubst95898992stappt @ A @ B @ C ) @ ( uSubst95898992stappt @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inf_OorderI) ).
thf(585,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_linear) ).
thf(370,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(165,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_inf1D2) ).
thf(744,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Int__assoc) ).
thf(600,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(252,axiom,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( A
= ( some @ TA @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_option_Oexhaust__sel) ).
thf(1094,plain,
! [TA: $tType,A: option @ TA] :
( ( A
!= ( none @ TA ) )
=> ( A
= ( some @ TA @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(101,axiom,
! [A: char,B: char,C: trm] :
( ( const @ A )
!= ( func @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_trm_Odistinct_I23_J) ).
thf(571,plain,
! [A: char,B: char,C: trm] :
( ( const @ A )
!= ( func @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( case_option @ TB @ TA @ A @ B @ ( some @ TA @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_option_Osimps_I5_J) ).
thf(612,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( case_option @ TB @ TA @ A @ B @ ( some @ TA @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(250,axiom,
! [A: ( option @ fml ) > $o,B: option @ fml] :
( ! [C: fml] : ( A @ ( some @ fml @ C ) )
=> ( ( A @ ( none @ fml ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Testo_Oinduct) ).
thf(1084,plain,
! [A: ( option @ fml ) > $o,B: option @ fml] :
( ! [C: fml] : ( A @ ( some @ fml @ C ) )
=> ( ( A @ ( none @ fml ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_subset__refl) ).
thf(482,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( none @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
& ~ ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_option_Osplit__sel__asm) ).
thf(844,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( none @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( some @ TA @ ( the @ TA @ D ) ) )
& ~ ( A @ ( C @ ( the @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_combine__options__cases) ).
thf(976,plain,
! [TA: $tType,TB: $tType,A: option @ TB,B: ( option @ TB ) > ( option @ TA ) > $o,C: option @ TA] :
( ( ( A
= ( none @ TB ) )
=> ( B @ A @ C ) )
=> ( ( ( C
= ( none @ TA ) )
=> ( B @ A @ C ) )
=> ( ! [D: TB,E: TA] :
( ( A
= ( some @ TB @ D ) )
=> ( ( C
= ( some @ TA @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_IntI) ).
thf(688,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(224,axiom,
! [A: option @ fml,B: trm > ( option @ fml ),C: option @ trm] :
( ( ( C
= ( none @ trm ) )
=> ( ( case_option @ ( option @ fml ) @ trm @ A @ B @ C )
= A ) )
& ( ( C
!= ( none @ trm ) )
=> ( ( case_option @ ( option @ fml ) @ trm @ A @ B @ C )
= ( B @ ( the @ trm @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_f4) ).
thf(963,plain,
! [A: option @ fml,B: trm > ( option @ fml ),C: option @ trm] :
( ( ( C
= ( none @ trm ) )
=> ( ( case_option @ ( option @ fml ) @ trm @ A @ B @ C )
= A ) )
& ( ( C
!= ( none @ trm ) )
=> ( ( case_option @ ( option @ fml ) @ trm @ A @ B @ C )
= ( B @ ( the @ trm @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(23,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_inf__sup__aci_I4_J) ).
thf(319,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_boolean__algebra__cancel_Oinf2) ).
thf(304,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(178,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_disjoint__iff__not__equal) ).
thf(781,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(228,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( ( uSubst1138577137pconst @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C )
= ( none @ trm ) )
| ? [D: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ C )
= ( some @ trm @ D ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_usappconst__conv) ).
thf(995,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: set @ variable,C: char] :
( ( ( uSubst1138577137pconst @ A @ B @ C )
!= ( none @ trm ) )
=> ( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [D: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ fml ),G: char > ( option @ game )] : D ) )
@ A
@ C )
= ( none @ trm ) )
| ? [D: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [E: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [F: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ fml ),H: char > ( option @ game )] : E ) )
@ A
@ C )
= ( some @ trm @ D ) )
& ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ D ) @ B )
= ( bot_bot @ ( set @ variable ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(107,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Int__iff) ).
thf(588,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(148,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_le__iff__inf) ).
thf(699,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(135,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inf_OorderE) ).
thf(667,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( A
= ( inf_inf @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_prod_Ocase__distrib) ).
thf(929,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(172,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_in__mono) ).
thf(763,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(141,axiom,
order_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_13) ).
thf(684,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_inf__assoc) ).
thf(346,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(241,axiom,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_split__option__ex) ).
thf(1045,plain,
! [TA: $tType] :
( ( '?' @ ( option @ TA ) )
= ( ^ [A: ( option @ TA ) > $o] :
( ( A @ ( none @ TA ) )
| ? [B: TA] : ( A @ ( some @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(11,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_6) ).
thf(287,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_order__trans) ).
thf(315,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(50,axiom,
bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_18) ).
thf(410,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(188,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable,E: trm,F: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [I: char > ( option @ fml ),J: char > ( option @ game )] : H ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ E )
= ( some @ trm @ F ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( func @ B @ E ) )
= ( uSubst95898992stappt @ ( uSubst969145931substt @ F ) @ ( bot_bot @ ( set @ variable ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_usubstappt__func) ).
thf(818,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: trm,D: set @ variable,E: trm,F: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ trm ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ trm ) )
@ ^ [H: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ trm ) )
@ ^ [I: char > ( option @ fml ),J: char > ( option @ game )] : H ) )
@ A
@ B )
= ( some @ trm @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVT @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ E )
= ( some @ trm @ F ) )
=> ( ( uSubst95898992stappt @ A @ D @ ( func @ B @ E ) )
= ( uSubst95898992stappt @ ( uSubst969145931substt @ F ) @ ( bot_bot @ ( set @ variable ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(198,axiom,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_option_Odistinct_I1_J) ).
thf(854,plain,
! [TA: $tType,A: TA] :
( ( none @ TA )
!= ( some @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inf__left__idem) ).
thf(273,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(112,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Collect__conj__eq) ).
thf(603,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(253,axiom,
( ( uSubst95898992stappt @ sigma @ ua @ theta )
= ( uSubst95898992stappt @ sigma @ va @ theta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_f7) ).
thf(1097,plain,
( ( uSubst95898992stappt @ sigma @ ua @ theta )
= ( uSubst95898992stappt @ sigma @ va @ theta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1,conjecture,
( ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( none @ fml ) )
| ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( none @ fml ) )
| ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(262,plain,
~ ( ( ( uSubst95898978stappf @ sigma @ va @ ( pred @ p @ theta ) )
!= ( none @ fml ) )
| ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [A: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ fml ),D: char > ( option @ game )] : C ) )
@ sigma
@ p )
= ( none @ fml ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_bot_Oextremum__unique) ).
thf(422,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(181,axiom,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: fml,D: set @ variable,E: trm,F: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [I: char > ( option @ fml ),J: char > ( option @ game )] : I ) )
@ A
@ B )
= ( some @ fml @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ E )
= ( some @ trm @ F ) )
=> ( ( uSubst95898978stappf @ A @ D @ ( pred @ B @ E ) )
= ( uSubst95898978stappf @ ( uSubst969145931substt @ F ) @ ( bot_bot @ ( set @ variable ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_usubstappf__pred) ).
thf(790,plain,
! [A: product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ),B: char,C: fml,D: set @ variable,E: trm,F: trm] :
( ( ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [G: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [H: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [I: char > ( option @ fml ),J: char > ( option @ game )] : I ) )
@ A
@ B )
= ( some @ fml @ C ) )
=> ( ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ C ) @ D )
= ( bot_bot @ ( set @ variable ) ) )
=> ( ( ( uSubst95898992stappt @ A @ D @ E )
= ( some @ trm @ F ) )
=> ( ( uSubst95898978stappf @ A @ D @ ( pred @ B @ E ) )
= ( uSubst95898978stappf @ ( uSubst969145931substt @ F ) @ ( bot_bot @ ( set @ variable ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(31,axiom,
semilattice_inf @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_12) ).
thf(341,plain,
semilattice_inf @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Int__left__absorb) ).
thf(437,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(124,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_inf1E) ).
thf(635,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( inf_inf @ ( TA > $o ) @ A @ B @ C )
=> ~ ( ( A @ C )
=> ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Int__empty__right) ).
thf(696,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(69,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_inf__le1) ).
thf(464,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(102,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inf__sup__ord_I1_J) ).
thf(575,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(200,axiom,
! [A: ( option @ game ) > $o,B: option @ game] :
( ! [C: game] : ( A @ ( some @ game @ C ) )
=> ( ( A @ ( none @ game ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Loopo_Oinduct) ).
thf(860,plain,
! [A: ( option @ game ) > $o,B: option @ game] :
( ! [C: game] : ( A @ ( some @ game @ C ) )
=> ( ( A @ ( none @ game ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(227,axiom,
( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [A: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ A ) )
@ ^ [B: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ B ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ A ) @ ( bot_bot @ ( set @ variable ) ) @ B )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) )
@ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
!= ( none @ fml ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_f3) ).
thf(992,plain,
( ( case_option @ ( option @ fml ) @ trm @ ( none @ fml )
@ ^ [A: trm] :
( case_option @ ( option @ fml ) @ fml @ ( some @ fml @ ( pred @ p @ A ) )
@ ^ [B: fml] :
( if @ ( option @ fml )
@ ( ( inf_inf @ ( set @ variable ) @ ( static_FVF @ B ) @ ua )
= ( bot_bot @ ( set @ variable ) ) )
@ ( uSubst95898978stappf @ ( uSubst969145931substt @ A ) @ ( bot_bot @ ( set @ variable ) ) @ B )
@ ( none @ fml ) )
@ ( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) ) @ ( char > ( option @ fml ) )
@ ^ [B: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ trm ) ) @ ( product_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) ) @ ( char > ( option @ fml ) )
@ ^ [C: char > ( option @ trm )] :
( product_case_prod @ ( char > ( option @ fml ) ) @ ( char > ( option @ game ) ) @ ( char > ( option @ fml ) )
@ ^ [D: char > ( option @ fml ),E: char > ( option @ game )] : D ) )
@ sigma
@ p ) )
@ ( uSubst95898992stappt @ sigma @ ua @ theta ) )
!= ( none @ fml ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(158,axiom,
! [A: char,B: trm,C: char,D: trm] :
( ( ( func @ A @ B )
= ( func @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_trm_Oinject_I4_J) ).
thf(723,plain,
! [A: char,B: trm,C: char,D: trm] :
( ( ( func @ A @ B )
= ( func @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(189,axiom,
! [A: option @ trm] :
( ( A
!= ( none @ trm ) )
= ( ? [B: trm] :
( A
= ( some @ trm @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_undeft__equiv) ).
thf(822,plain,
! [A: option @ trm] :
( ( A
!= ( none @ trm ) )
= ( ? [B: trm] :
( A
= ( some @ trm @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(197,axiom,
! [A: product_prod @ ( option @ game ) @ ( option @ fml )] :
( ! [B: game,C: fml] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ B ) @ ( some @ fml @ C ) ) )
=> ( ! [B: option @ fml] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ B ) )
=> ~ ! [B: game] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ B ) @ ( none @ fml ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Diamondo_Ocases) ).
thf(850,plain,
! [A: product_prod @ ( option @ game ) @ ( option @ fml )] :
( ! [B: game,C: fml] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ B ) @ ( some @ fml @ C ) ) )
=> ( ! [B: option @ fml] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( none @ game ) @ B ) )
=> ~ ! [B: game] :
( A
!= ( product_Pair @ ( option @ game ) @ ( option @ fml ) @ ( some @ game @ B ) @ ( none @ fml ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_disjoint__iff) ).
thf(442,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_empty__subsetI) ).
thf(501,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(24,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_inf__sup__aci_I3_J) ).
thf(322,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( case_option @ TC @ TA @ ( A @ B )
@ ^ [E: TA] : ( A @ ( C @ E ) )
@ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_option_Ocase__distrib) ).
thf(469,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TB,C: TA > TB,D: option @ TA] :
( ( A @ ( case_option @ TB @ TA @ B @ C @ D ) )
= ( case_option @ TC @ TA @ ( A @ B )
@ ^ [E: TA] : ( A @ ( C @ E ) )
@ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equals0I) ).
thf(543,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(176,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__inf__iff) ).
thf(775,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Collect__subset) ).
thf(496,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(364,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(151,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_inf_Ocobounded2) ).
thf(708,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( inf_inf @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(223,axiom,
! [A: option @ trm,B: option @ trm,C: option @ fml] :
( ( ( uSubst1556497037e_Geqo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some @ trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some @ trm @ E ) )
=> ( C
!= ( some @ fml @ ( geq @ D @ E ) ) ) ) )
=> ( ( ( A
= ( none @ trm ) )
=> ( C
!= ( none @ fml ) ) )
=> ~ ( ? [D: trm] :
( A
= ( some @ trm @ D ) )
=> ( ( B
= ( none @ trm ) )
=> ( C
!= ( none @ fml ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Geqo_Oelims) ).
thf(935,plain,
! [A: option @ trm,B: option @ trm,C: option @ fml] :
( ( ( uSubst1556497037e_Geqo @ A @ B )
= C )
=> ( ! [D: trm] :
( ( A
= ( some @ trm @ D ) )
=> ! [E: trm] :
( ( B
= ( some @ trm @ E ) )
=> ( C
!= ( some @ fml @ ( geq @ D @ E ) ) ) ) )
=> ( ( ( A
= ( none @ trm ) )
=> ( C
!= ( none @ fml ) ) )
=> ~ ( ? [D: trm] :
( A
= ( some @ trm @ D ) )
=> ( ( B
= ( none @ trm ) )
=> ( C
!= ( none @ fml ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(232,axiom,
( ( uSubst95898992stappt @ sigma @ ua @ theta )
!= ( none @ trm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_f5) ).
thf(1009,plain,
( ( uSubst95898992stappt @ sigma @ ua @ theta )
!= ( none @ trm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1135,plain,
$false,
inference(e,[status(thm)],[809,1024,760,479,352,645,892,333,628,408,582,1005,276,308,440,597,873,449,1078,533,550,715,472,913,670,829,898,841,301,565,651,570,372,357,460,619,838,702,751,802,344,902,638,606,416,325,289,591,806,397,280,293,866,1119,660,411,428,877,692,1074,452,678,270,546,534,1067,1057,910,746,825,1042,349,630,815,729,1021,778,361,625,435,889,493,757,1128,710,1012,285,847,484,742,317,615,869,857,884,1028,537,476,622,1099,1131,457,721,503,393,1114,508,311,765,530,794,718,926,633,360,425,513,1103,296,733,694,772,413,577,711,579,291,641,391,445,787,1107,466,1090,919,540,713,498,681,784,419,377,567,1048,736,880,649,494,367,609,594,726,895,330,462,932,685,768,278,1015,1000,299,267,505,653,922,455,883,1034,812,342,1018,355,754,836,490,675,663,548,1134,648,487,1081,749,617,516,1003,690,887,971,327,739,1070,872,705,282,1053,673,338,643,907,585,370,744,336,600,1094,571,612,1084,482,844,976,688,963,319,304,781,995,588,699,667,929,763,684,346,1045,287,315,410,818,854,273,603,1097,262,422,790,341,437,635,696,464,575,860,992,723,822,850,442,501,322,469,543,775,496,364,708,935,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP204^2 : TPTP v8.1.2. Released v7.5.0.
% 0.16/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:37:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.00/1.15 % [INFO] Parsing done (278ms).
% 2.00/1.16 % [INFO] Running in sequential loop mode.
% 2.82/1.37 % [INFO] eprover registered as external prover.
% 2.82/1.38 % [INFO] cvc4 registered as external prover.
% 2.82/1.38 % [INFO] Scanning for conjecture ...
% 3.26/1.51 % [INFO] Found a conjecture and 286 axioms. Running axiom selection ...
% 3.57/1.63 % [INFO] Axiom selection finished. Selected 259 axioms (removed 27 axioms).
% 4.64/1.87 % [INFO] Problem is higher-order (TPTP THF).
% 4.64/1.89 % [INFO] Type checking passed.
% 4.64/1.89 % [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 ...
% 63.87/47.85 % External prover 'e' found a proof!
% 63.87/47.85 % [INFO] Killing All external provers ...
% 63.87/47.85 % Time passed: 47314ms (effective reasoning time: 46688ms)
% 64.08/47.85 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 64.08/47.85 % Axioms used in derivation (259): tcon_fun___Orderings_Obot, fact_88_option_Odisc__eq__case_I2_J, fact_223_usubstappf__geq__conv, fact_38_option_Ocase__eq__if, fact_140_inf_Oorder__iff, fact_28_usubstappt__det, fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062, fact_35_option_Oexhaust, fact_177_bot_Oextremum__unique, fact_126_IntD2, fact_190_Loopo_Oinduct, fact_182_inf1I, fact_22_option_Ocollapse, fact_120_inf__sup__aci_I4_J, tcon_Set_Oset___Lattices_Obounded__lattice__bot_3, fact_42_Testo_Oinduct, fact_136_inf_Oabsorb__iff2, fact_27_option_Osplit__sel__asm, fact_111_inf_Ocommute, fact_104_subset__eq, fact_253_conj__subset__def, fact_139_inf_Ocobounded1, fact_132_Int__Collect, fact_251_subset__Collect__iff, fact_1_Pred_Oprems_I2_J, fact_10_f1, fact_180_fml_Oinject_I2_J, fact_184_inf1D1, fact_148_le__iff__inf, fact_208_le__cases3, fact_243_usappconst__simp, fact_154_inf__mono, fact_157_inf__le2, fact_185_inf1D2, fact_76_IntI, fact_67_subsetI, tcon_HOL_Obool___Lattices_Obounded__lattice__bot_11, tcon_Set_Oset___Orderings_Opreorder_6, fact_97_set__eq__subset, fact_77_usubstappf__pred, fact_100_subset__refl, fact_221_prop__restrict, fact_245_usappconst__def, fact_155_le__infI, fact_158_inf__le1, fact_15_Pred_Oprems_I1_J, fact_246_usubstappt__const, tcon_HOL_Obool___Orderings_Olinorder, fact_43_Testo_Ocases, fact_114_boolean__algebra__cancel_Oinf2, fact_72_inf__idem, fact_205_eq__refl, fact_87_less__eq__set__def, fact_230_Geqo_Osimps_I3_J, fact_250_usubstappt__const__conv, fact_52_f3, fact_8_f7, tcon_HOL_Obool___Orderings_Obot_18, fact_109_inf_Oleft__commute, fact_240_usubstappt__func2, fact_163_Int__empty__left, fact_94_equals0D, fact_181_predicate1I, fact_23_option_Osimps_I5_J, fact_130_Collect__subset, fact_178_bot_Oextremum, fact_5_f8, fact_106_subsetD, fact_249_trm_Odistinct_I23_J, fact_9_case__prod__app, fact_173_bot__apply, fact_107_in__mono, fact_175_subset__emptyI, fact_108_inf__left__commute, fact_34_option_Oinducts, fact_138_inf_Ocobounded2, fact_4_usubstappf__det, fact_188_Aterm__Some, tcon_HOL_Obool___Lattices_Olattice_15, tcon_Set_Oset___Orderings_Obot_10, fact_228_Geqo_Osimps_I2_J, fact_128_IntE, fact_98_subset__trans, fact_0__092_060open_062_092_060forall_062x0_Ax1_O_A_I_092_060exists_062v2_O_Av2_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Av2_A_061_Av3_J_J_A_061_A_Ivv_Ax0_Ax1_A_092_060in_062_Ax1_A_092_060and_062_A_I_092_060exists_062v3_O_Av3_A_092_060in_062_Ax0_A_092_060and_062_Avv_Ax0_Ax1_A_061_Av3_J_J_092_060close_062, fact_37_option_Odistinct_I1_J, fact_166_Int__Collect__mono, fact_134_inf_OcoboundedI2, fact_68_inf__right__idem, fact_26_option_Ocase__distrib, fact_89_option_Odisc__eq__case_I1_J, fact_64_all__not__in__conv, tcon_fun___Lattices_Obounded__lattice_2, fact_96_Collect__mono__iff, fact_113_inf_Oassoc, fact_129_empty__def, fact_234_pred__subset__eq, help_If_1_1_T, fact_237_internal__case__prod__def, tcon_Set_Oset___Orderings_Oorder__bot_5, fact_191_undefg__equiv, fact_143_inf_OboundedE, fact_227_inf__Int__eq, fact_24_option_Osel, fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062, fact_231_Geqo_Osimps_I1_J, fact_222_Collect__restrict, fact_112_inf__assoc, fact_11_f10, fact_12_prod_Ocase__distrib, fact_238_usubstappt_Osimps_I4_J, fact_144_inf__absorb2, fact_119_inf__sup__aci_I3_J, fact_160_inf__sup__ord_I2_J, fact_41_undeff__equiv, fact_145_inf__absorb1, fact_192_Composeo_Oinduct, fact_51_f6, tcon_fun___Lattices_Osemilattice__inf, fact_49_option_Oexpand, fact_232_usubstappf_Osimps_I2_J, fact_224_usubstappf__geq, fact_156_le__infE, fact_204_linear, fact_56_inf__bot__right, fact_236_Set_Ois__empty__def, fact_239_trm_Oinject_I4_J, fact_85_bot__set__def, fact_63_Collect__empty__eq, fact_116_inf__fun__def, fact_168_Int__absorb2, fact_95_emptyE, fact_105_equalityE, fact_101_subset__iff, fact_247_trm_Oinject_I3_J, fact_131_Int__def, fact_103_equalityD1, fact_70_inf__left__idem, fact_137_inf_Oabsorb__iff1, fact_186_predicate1D, fact_248_usubstappt_Osimps_I3_J, fact_36_option_OdiscI, fact_235_Collect__empty__eq__bot, fact_93_equals0I, fact_225_disjE__realizer2, fact_91_case__optionE, fact_102_equalityD2, fact_135_inf_OcoboundedI1, tcon_fun___Lattices_Obounded__lattice__bot, fact_86_inf__set__def, fact_150_inf_OorderI, fact_58_empty__subsetI, fact_65_empty__iff, fact_7_fml_Oinject_I1_J, fact_54_Int__subset__iff, fact_151_inf_OorderE, fact_164_disjoint__iff, fact_125_Int__assoc, tcon_fun___Orderings_Oorder__bot, help_If_2_1_T, tcon_Set_Oset___Lattices_Olattice_7, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_161_disjoint__iff__not__equal, fact_167_Int__greatest, fact_220_bot__fun__def, fact_133_Collect__conj__eq, fact_33_split__option__ex, help_If_3_1_T, fact_19_f5, fact_73_inf_Oidem, fact_80_undeft__equiv, fact_214_order__trans, fact_30_option_Oexhaust__sel, fact_117_inf__sup__aci_I1_J, fact_183_inf1E, fact_75_Int__iff, fact_20_not__Some__eq, fact_31_combine__options__cases, tcon_HOL_Obool___Orderings_Oorder__bot_13, fact_110_inf__commute, fact_171_Int__lower1, fact_252_subset__CollectI, fact_226_Geqo_Oelims, fact_122_Int__left__absorb, fact_55_inf__bot__left, fact_25_option_Osplit__sel, fact_189_Loopo_Ocases, fact_216_linorder__wlog, tcon_fun___Orderings_Opreorder, fact_39_option_Osimps_I4_J, fact_45_Collect__mem__eq, fact_62_empty__Collect__eq, tcon_HOL_Obool___Lattices_Osemilattice__inf_12, fact_152_le__infI2, fact_244_usappconst__conv, fact_229_Geqo__undef, fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062, fact_83_Differentialo_Ocases, fact_74_inf__apply, fact_169_Int__absorb1, fact_170_Int__lower2, fact_81_Timeso_Oinduct, fact_124_Int__absorb, fact_66_subset__antisym, fact_48_Ando_Oinduct, fact_187_rev__predicate1D, fact_13_usubstappf__pred2, fact_59_le__inf__iff, fact_254_Diamondo_Ocases, fact_50_usubstappf__pred__conv, fact_69_inf_Oright__idem, fact_153_le__infI1, fact_21_not__None__eq, tcon_HOL_Obool___Orderings_Opreorder_14, fact_18_option_Oinject, fact_206_le__cases, fact_159_inf__sup__ord_I1_J, fact_142_inf_OboundedI, fact_29_usubstappt__antimon, fact_141_inf__greatest, fact_115_boolean__algebra__cancel_Oinf1, fact_82_Assigno_Oinduct, fact_176_bot_Oextremum__uniqueI, fact_121_Int__left__commute, fact_242_usubstappt__func__conv, fact_17__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062vva_O_A_092_060forall_062V_AVa_O_A_IV_A_092_060inter_062_AVa_A_092_060noteq_062_A_123_125_A_092_060or_062_A_I_092_060forall_062v_O_Av_A_092_060notin_062_AV_A_092_060or_062_A_I_092_060forall_062va_O_Ava_A_092_060notin_062_AVa_A_092_060or_062_Av_A_092_060noteq_062_Ava_J_J_J_A_092_060and_062_A_IV_A_092_060inter_062_AVa_A_061_A_123_125_A_092_060or_062_Avv_AVa_AV_A_092_060in_062_AV_A_092_060and_062_Avva_AVa_AV_A_092_060in_062_AVa_A_092_060and_062_Avv_AVa_AV_A_061_Avva_AVa_AV_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_241_usubstappt__func, fact_179_usubstappf__geqr, fact_146_inf_Oabsorb2, fact_162_Int__empty__right, fact_60_inf_Obounded__iff, fact_79_undeft__None, fact_78_ODEo_Oinduct, fact_123_Int__commute, fact_165_Int__emptyI, fact_71_inf_Oleft__idem, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_40_Existso_Oinduct, fact_57_subset__empty, fact_174_order__refl, fact_193_fml_Odistinct_I1_J, fact_16_f9, fact_172_Int__mono, fact_99_Collect__mono, fact_149_inf__unique, fact_32_split__option__all, tcon_Set_Oset___Lattices_Osemilattice__inf_4, fact_90_Diamondo_Oinduct, fact_92_ex__in__conv, fact_14_f2, fact_46_Collect__cong, fact_118_inf__sup__aci_I2_J, fact_44_mem__Collect__eq, fact_61_f4, fact_127_IntD1, fact_233_bot__empty__eq, fact_53_usubstappf_Osimps_I1_J, fact_84_Differentialo_Oinduct, tcon_fun___Lattices_Olattice, fact_147_inf_Oabsorb1
% 64.08/47.85 % No. of inferences in proof: 522
% 64.08/47.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 47314 ms resp. 46688 ms w/o parsing
% 65.00/48.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 65.00/48.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------