%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:31 AM UTC 2026
% Result : Theorem 18.89s 7.85s
% Output : Refutation 19.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 1071 ( 128 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 4443 ( 49 ~; 16 |; 46 &;4146 @)
% ( 22 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 9 con; 0-6 aty)
% Number of variables : 619 ( 0 ^; 609 !; 10 ?; 619 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(cl_Groups_Ominus_decl,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(arrow_1985332922le_Lin_decl,type,
arrow_1985332922le_Lin: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(order_1409979114der_on_decl,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_915043626der_on_decl,type,
order_915043626der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_preorder_on_decl,type,
order_preorder_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_215145569der_on_decl,type,
order_215145569der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ fun ) ) ) ).
thf(order_well_order_on_decl,type,
order_well_order_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(domain_decl,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) ) > ( bool @ ( TB @ fun ) ) ) ).
thf(id_decl,type,
id:
!>[TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ).
thf(id_on_decl,type,
id_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(range_decl,type,
range:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(antisym_decl,type,
antisym:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(irrefl_decl,type,
irrefl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(trans_decl,type,
trans:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(lex_prod_decl,type,
lex_prod:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ fun ) ) ) ).
thf(measure_decl,type,
measure:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(wf_decl,type,
wf:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(r_decl,type,
r: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(84,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(371,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(120,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_empty__Diff) ).
thf(482,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(76,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_empty__def) ).
thf(347,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_double__diff) ).
thf(352,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(110,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_empty__iff) ).
thf(449,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(88,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_equalityI) ).
thf(379,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(107,axiom,
arrow_411405190le_alt @ id @ ( r @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ minus_minus ) ) @ ( arrow_411405190le_alt @ wf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(440,plain,
arrow_411405190le_alt @ id @ ( r @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ minus_minus ) ) @ ( arrow_411405190le_alt @ wf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(90,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_iso__tuple__UNIV__I) ).
thf(384,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
? [B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( B @ ( A @ ( TA @ order_well_order_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_well__order__on) ).
thf(142,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
? [B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( B @ ( A @ ( TA @ order_well_order_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_915043626der_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_partial__order__on__empty) ).
thf(288,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_915043626der_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_in__mono) ).
thf(301,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(45,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Diff__empty) ).
thf(257,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(18,axiom,
! [TA: $tType] : ( TA @ id @ ( TA @ antisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_antisym__Id) ).
thf(184,plain,
! [TA: $tType] : ( TA @ id @ ( TA @ antisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ id @ ( TA @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Domain__Id) ).
thf(344,plain,
! [TA: $tType] :
( ( TA @ id @ ( TA @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(102,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_well_order_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_well__order__on__empty) ).
thf(421,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_well_order_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(100,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(416,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(35,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ antisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_antisym__empty) ).
thf(228,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ antisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_bot__empty__eq) ).
thf(216,plain,
! [TA: $tType,A: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
<=> ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_preorder__on__def) ).
thf(179,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_preorder_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
=> ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(321,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(121,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_strict__linear__order__on__diff__Id) ).
thf(485,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(119,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(480,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_order__refl) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(132,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
<=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_set__eq__subset) ).
thf(428,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(265,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(63,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Collect__empty__eq) ).
thf(307,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(57,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ total_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_total__on__empty) ).
thf(292,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ total_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(37,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_empty__Collect__eq) ).
thf(233,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Diff__idemp) ).
thf(248,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ id @ ( TA @ ( TA @ range ) ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Range__Id) ).
thf(270,plain,
! [TA: $tType] :
( ( TA @ id @ ( TA @ ( TA @ range ) ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(201,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_bot__fun__def) ).
thf(220,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_minus__apply) ).
thf(260,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ id_on ) @ ( TA @ ( TA @ domain ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Domain__Id__on) ).
thf(160,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ id_on ) @ ( TA @ ( TA @ domain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TB @ ( TA @ range ) ) )
= ( bool @ ( TB @ fun ) @ bot_bot ) )
<=> ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Range__empty__iff) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) )
=> ( ( A @ ( TB @ ( TA @ range ) ) )
= ( bool @ ( TB @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TB @ ( TA @ range ) ) )
= ( bool @ ( TB @ fun ) @ bot_bot ) )
=> ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(59,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_set__rev__mp) ).
thf(297,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__bot) ).
thf(192,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_set__mp) ).
thf(275,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(43,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_1409979114der_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_lnear__order__on__empty) ).
thf(252,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_1409979114der_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
bool @ top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(197,plain,
bool @ top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_bot__apply) ).
thf(361,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TB @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Domain__empty__iff) ).
thf(324,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) )
=> ( ( A @ ( TB @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TB @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( A
= ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(317,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ trans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_trans__Id__on) ).
thf(156,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_empty__subsetI) ).
thf(403,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_subset__UNIV) ).
thf(388,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(127,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( B @ ( TA @ total_on ) ) )
<=> ( A @ ( B @ ( TA @ total_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_total__on__diff__Id) ).
thf(499,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ total_on ) ) )
=> ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( B @ ( TA @ total_on ) ) ) )
& ( ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( B @ ( TA @ total_on ) ) )
=> ( A @ ( B @ ( TA @ total_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(123,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_DiffI) ).
thf(488,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(33,axiom,
bool @ cl_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(225,plain,
bool @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_subsetD) ).
thf(212,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,conjecture,
? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( A @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( A @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( A @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(81,axiom,
bool @ bot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(360,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TB @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Domain__empty) ).
thf(205,plain,
! [TA: $tType,TB: $tType] :
( ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TB @ ( TA @ domain ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_bot__least) ).
thf(149,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(86,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(375,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(16,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(176,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(423,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(89,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_preorder_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_preorder__on__empty) ).
thf(382,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ order_preorder_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_DiffD2) ).
thf(313,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(144,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(115,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_UNIV__not__empty) ).
thf(466,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(77,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_DiffD1) ).
thf(350,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] : ( TA @ top_top @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_top__greatest) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] : ( TA @ top_top @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_predicate1D) ).
thf(377,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(36,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ top_top )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_UNIV__eq__I) ).
thf(230,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ top_top )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(111,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_set__diff__eq) ).
thf(451,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(40,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_UNIV__def) ).
thf(245,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(62,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_equalityD2) ).
thf(303,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(26,axiom,
! [TA: $tType] : ( TA @ id @ ( bool @ ( TA @ fun ) @ top_top @ ( TA @ refl_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_refl__Id) ).
thf(208,plain,
! [TA: $tType] : ( TA @ id @ ( bool @ ( TA @ fun ) @ top_top @ ( TA @ refl_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_fun__diff__def) ).
thf(477,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_top__le) ).
thf(494,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(69,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(323,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(251,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ id_on ) )
= ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Id__on__empty) ).
thf(198,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ id_on ) )
= ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,axiom,
! [TA: $tType] : ( TA @ id @ ( TA @ trans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_trans__Id) ).
thf(130,plain,
! [TA: $tType] : ( TA @ id @ ( TA @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(95,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(399,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(32,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_UNIV__I) ).
thf(223,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_bot__unique) ).
thf(135,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( ( A
= ( TA @ bot_bot ) )
=> ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,axiom,
( arrow_1985332922le_Lin
= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Lin__def) ).
thf(299,plain,
( arrow_1985332922le_Lin
= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(34,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ wf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_wf__empty) ).
thf(226,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( TA @ wf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(106,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_emptyE) ).
thf(438,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_equals0D) ).
thf(473,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(124,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_equalityD1) ).
thf(490,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(426,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(122,axiom,
r @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_1409979114der_on ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(487,plain,
r @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_1409979114der_on ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_equals0I) ).
thf(355,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_strict__linear__order__on__def) ).
thf(282,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) )
=> ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
<=> ( A
= ( TA @ top_top ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_top__unique) ).
thf(409,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( ( A
= ( TA @ top_top ) )
=> ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(263,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Diff__iff) ).
thf(331,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(108,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(441,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(338,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(72,axiom,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ refl_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_refl__on__empty) ).
thf(336,plain,
! [TA: $tType] : ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ refl_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(91,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rev__predicate1D) ).
thf(386,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(126,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ trans ) )
=> ( ( A @ ( TA @ antisym ) )
=> ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ trans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_trans__diff__Id) ).
thf(497,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ trans ) )
=> ( ( A @ ( TA @ antisym ) )
=> ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ trans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(319,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(12,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] : ( A @ ( TA @ measure ) @ ( TA @ wf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_wf__measure) ).
thf(158,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] : ( A @ ( TA @ measure ) @ ( TA @ wf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(93,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(390,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_diff__eq__diff__less__eq) ).
thf(186,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( D @ ( TA @ ord_less_eq ) ) ) )
& ( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__refl) ).
thf(401,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(15,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
<=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_linear__order__on__def) ).
thf(171,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( C @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( A @ ( D @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Diff__mono) ).
thf(290,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( C @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( A @ ( D @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(29,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ irrefl ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_irrefl__diff__Id) ).
thf(214,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ irrefl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_915043626der_on ) ) )
<=> ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_partial__order__on__def) ).
thf(151,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_915043626der_on ) ) )
=> ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ wf ) )
=> ( ( A @ ( TA @ wf ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ wf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_wf__lex__prod) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ wf ) )
=> ( ( A @ ( TA @ wf ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ wf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_DiffE) ).
thf(405,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Diff__subset) ).
thf(273,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TB @ ( TA @ domain ) ) @ ( B @ ( TB @ ( TA @ domain ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Domain__mono) ).
thf(373,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TB @ ( TA @ domain ) ) @ ( B @ ( TB @ ( TA @ domain ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( ( A @ ( TA @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ trans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_trans__lex__prod) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( ( A @ ( TA @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ trans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(294,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ bot_bot @ ( TA @ ( TB @ range ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Range__empty) ).
thf(341,plain,
! [TA: $tType,TB: $tType] :
( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ bot_bot @ ( TA @ ( TB @ range ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(49,axiom,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_top1I) ).
thf(268,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(80,axiom,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_UNIV__witness) ).
thf(358,plain,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] : ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ range ) ) @ ( A @ ( TB @ ( TA @ range ) ) @ ( B @ ( TB @ ( TA @ range ) ) @ ( bool @ ( TB @ fun ) @ minus_minus ) ) @ ( bool @ ( TB @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Range__Diff__subset) ).
thf(195,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] : ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ range ) ) @ ( A @ ( TB @ ( TA @ range ) ) @ ( B @ ( TB @ ( TA @ range ) ) @ ( bool @ ( TB @ fun ) @ minus_minus ) ) @ ( bool @ ( TB @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_top__apply) ).
thf(239,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Diff__UNIV) ).
thf(242,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_subset__empty) ).
thf(459,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_diff__eq__diff__eq) ).
thf(163,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_well_order_on ) ) )
<=> ( ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ wf ) )
& ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_well__order__on__def) ).
thf(277,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ wf ) )
& ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_well_order_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_well_order_on ) ) )
=> ( ( TA @ id @ ( A @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TA @ wf ) )
& ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(109,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_ex__in__conv) ).
thf(442,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(44,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Diff__cancel) ).
thf(254,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_in__inv__imagep) ).
thf(469,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] : ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ domain ) ) @ ( A @ ( TB @ ( TA @ domain ) ) @ ( B @ ( TB @ ( TA @ domain ) ) @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Domain__Diff__subset) ).
thf(454,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] : ( A @ ( B @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ domain ) ) @ ( A @ ( TB @ ( TA @ domain ) ) @ ( B @ ( TB @ ( TA @ domain ) ) @ ( bool @ ( TA @ fun ) @ minus_minus ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(83,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_all__not__in__conv) ).
thf(364,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(610,plain,
$false,
inference(e,[status(thm)],[371,482,347,352,449,379,440,384,142,288,301,257,184,344,421,416,228,216,179,321,485,480,147,132,428,265,307,292,233,248,270,201,220,260,160,392,297,192,275,252,197,361,456,324,317,156,403,388,499,488,225,212,128,360,205,149,375,176,423,382,313,144,466,350,419,377,230,451,245,303,208,477,494,323,251,198,130,399,223,135,299,226,438,473,490,426,487,355,282,409,263,331,441,338,336,386,497,319,158,390,186,401,171,290,214,151,315,405,273,373,210,294,341,268,358,195,239,242,459,163,277,442,254,469,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT179_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 06:38:51 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.31 % [INFO] Parsing done (322ms).
% 1.92/1.32 % [INFO] Running in sequential loop mode.
% 2.70/1.71 % [INFO] eprover registered as external prover.
% 2.70/1.71 % [INFO] Scanning for conjecture ...
% 2.89/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 3.09/2.02 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 4.10/2.23 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.10/2.26 % [INFO] Type checking passed.
% 4.10/2.27 % [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 ...
% 4.92/2.55 % [INFO] [Domain constraints] Detected constraint on bool
% 4.92/2.56 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 5.13/2.65 % [INFO] [Domain constraints] Detected constraint on bool
% 5.13/2.65 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 18.89/7.85 % External prover 'e' found a proof!
% 18.89/7.85 % [INFO] Killing All external provers ...
% 18.89/7.85 % Time passed: 7306ms (effective reasoning time: 6520ms)
% 18.89/7.85 % 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)>
% 18.89/7.85 % Axioms used in derivation (125): arity_HOL_Obool___Groups_Ominus, fact_9_well__order__on__def, fact_92_set__eq__subset, fact_21_diff__eq__diff__eq, fact_99_set__mp, fact_23_well__order__on, fact_70_subsetD, fact_60_trans__diff__Id, fact_1_Lin__def, fact_10_fun__diff__def, fact_18_UNIV__witness, fact_78_trans__Id__on, fact_52_Domain__empty__iff, fact_56_partial__order__on__empty, help_COMBS_1_1_U, fact_61_antisym__empty, arity_HOL_Obool___Orderings_Opreorder, arity_fun___Orderings_Obot, fact_42_Diff__empty, help_fconj_3_1_U, fact_38_total__on__empty, fact_3_Diff__idemp, fact_41_UNIV__not__empty, fact_27_empty__iff, fact_32_bot__empty__eq, help_fTrue_1_1_T, fact_91_subset__refl, fact_94_equalityD1, fact_51_Range__empty, fact_8_iso__tuple__UNIV__I, fact_25_all__not__in__conv, fact_65_preorder__on__empty, fact_44_linear__order__on__def, fact_2_Diff__iff, fact_74_Domain__Id__on, help_fNot_2_1_U, help_fTrue_1_1_U, fact_30_empty__Diff, fact_47_Range__Id, fact_54_refl__on__empty, help_fNot_1_1_U, fact_7_UNIV__I, fact_37_bot__fun__def, fact_97_predicate1D, help_fFalse_1_1_T, fact_87_subset__UNIV, fact_73_empty__subsetI, fact_33_empty__def, fact_4_DiffI, fact_64_preorder__on__def, fact_40_well__order__on__empty, fact_85_top__unique, fact_88_double__diff, fact_95_equalityD2, help_COMBB_1_1_U, fact_45_strict__linear__order__on__def, fact_93_rev__predicate1D, fact_5_DiffE, fact_96_in__mono, fact_46_equals0I, arity_fun___Orderings_Opreorder, fact_17_UNIV__eq__I, help_fconj_2_1_U, fact_80_bot__least, fact_62_antisym__Id, fact_86_top__greatest, fact_39_lnear__order__on__empty, fact_58_wf__lex__prod, fact_84_top__le, fact_13_DiffD2, fact_79_Domain__mono, fact_63_partial__order__on__def, fact_24_Diff__UNIV, fact_72_subset__empty, fact_67_Range__Diff__subset, fact_35_equals0D, fact_20_total__on__diff__Id, fact_81_bot__unique, arity_HOL_Obool___Orderings_Otop, fact_50_Domain__empty, fact_71_equalityI, fact_55_trans__Id, fact_59_wf__measure, fact_22_in__inv__imagep, fact_28_Collect__empty__eq, fact_90_Diff__subset, fact_82_le__bot, fact_76_mem__def, fact_6_top1I, fact_36_bot__apply, help_COMBK_1_1_U, fact_83_diff__eq__diff__less__eq, fact_89_Diff__mono, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, conj_1, fact_98_set__rev__mp, fact_31_Diff__cancel, fact_29_emptyE, help_fconj_1_1_U, fact_15_set__diff__eq, fact_0_strict__linear__order__on__diff__Id, fact_16_top__apply, fact_66_Id__on__empty, fact_14_DiffD1, help_fFalse_1_1_U, fact_43_wf__empty, fact_77_Collect__def, fact_12_UNIV__def, fact_19_irrefl__diff__Id, help_pp_1_1_U, fact_11_minus__apply, fact_34_ex__in__conv, fact_48_Domain__Id, fact_57_trans__lex__prod, fact_75_ext, fact_53_Range__empty__iff, arity_fun___Orderings_Otop, fact_49_refl__Id, conj_0, fact_26_empty__Collect__eq, help_pp_2_1_U, arity_fun___Groups_Ominus, fact_68_Domain__Diff__subset, fact_69_order__refl
% 18.89/7.85 % No. of inferences in proof: 254
% 18.89/7.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7306 ms resp. 6520 ms w/o parsing
% 19.32/7.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.32/7.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------