TSTP Solution File: COM191^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : COM191^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Mon May 20 19:09:20 EDT 2024
% Result : Theorem 147.60s 90.49s
% Output : Refutation 148.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 268
% Syntax : Number of formulae : 487 ( 174 unt; 51 typ; 0 def)
% Number of atoms : 1495 ( 438 equ; 2 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 6529 ( 178 ~; 24 |; 162 &;5561 @)
% ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 246 ( 246 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 16 con; 0-6 aty)
% Number of variables : 1700 ( 118 ^1437 !; 110 ?;1700 :)
% ( 29 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(dtree_type,type,
dtree: $tType ).
thf(t_type,type,
t: $tType ).
thf(n_type,type,
n: $tType ).
thf(bNF_Greatest_shift_type,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(bNF_Greatest_univ_type,type,
bNF_Greatest_univ:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(node_type,type,
node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).
thf(cont_type,type,
cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
thf(root_type,type,
root: dtree > n ).
thf(gram_L1580978439le_Itr_type,type,
gram_L1580978439le_Itr: ( set @ n ) > dtree > ( set @ n ) ).
thf(gram_L1905609002ubst_c_type,type,
gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).
thf(gram_L1905609017ubst_r_type,type,
gram_L1905609017ubst_r: dtree > n ).
thf(gram_L1333338417e_inFr_type,type,
gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
thf(gram_L805317441_inFr2_type,type,
gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
thf(gram_L830233218_inItr_type,type,
gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
thf(gram_L250615845e_path_type,type,
gram_L250615845e_path: ( n > dtree ) > ( list @ n ) > $o ).
thf(gram_L1918716148le_reg_type,type,
gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).
thf(gram_L646766332egular_type,type,
gram_L646766332egular: dtree > $o ).
thf(gram_L716654942_subtr_type,type,
gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
thf(gram_L1283001940subtr2_type,type,
gram_L1283001940subtr2: ( set @ n ) > dtree > dtree > $o ).
thf(gram_L1614515765ubtrOf_type,type,
gram_L1614515765ubtrOf: dtree > n > dtree ).
thf(gram_L864798063lle_wf_type,type,
gram_L864798063lle_wf: dtree > $o ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(coset_type,type,
coset:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(hd_type,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(set2_type,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(union_type,type,
union:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert2_type,type,
insert2:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(remove_type,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(sum_Inl_type,type,
sum_Inl:
!>[TA: $tType,TB: $tType] : ( TB > ( sum_sum @ TB @ TA ) ) ).
thf(sum_Inr_type,type,
sum_Inr:
!>[TA: $tType,TB: $tType] : ( TB > ( sum_sum @ TA @ TB ) ) ).
thf(sum_rec_sum_type,type,
sum_rec_sum:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TB ) > ( sum_sum @ TC @ TA ) > TB ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_type,type,
f: n > dtree ).
thf(nl_type,type,
nl: list @ n ).
thf(ns_type,type,
ns: set @ n ).
thf(nsa_type,type,
nsa: set @ n ).
thf(tr_type,type,
tr: dtree ).
thf(tr1_type,type,
tr1: dtree ).
thf(tr1a_type,type,
tr1a: dtree ).
thf(tr2_type,type,
tr2: dtree ).
thf(tra_type,type,
tra: dtree ).
thf(132,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_not__Cons__self2) ).
thf(645,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(127,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_rev__subsetD) ).
thf(629,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(210,axiom,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inFr__mono) ).
thf(941,plain,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inr @ TB @ TA @ A )
!= ( sum_Inl @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Inr__not__Inl) ).
thf(408,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inr @ TB @ TA @ A )
!= ( sum_Inl @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert2 @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_insert__Collect) ).
thf(276,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert2 @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(157,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( ( C = B )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ~ ( gram_L1283001940subtr2 @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subtr2_Ocases) ).
thf(741,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( ( C = B )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ~ ( gram_L1283001940subtr2 @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(188,axiom,
! [A: dtree,B: set @ n,C: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
=> ( gram_L1333338417e_inFr @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inFr_OBase) ).
thf(873,plain,
! [A: dtree,B: set @ n,C: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
=> ( gram_L1333338417e_inFr @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(11,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_137_set__eq__subset) ).
thf(247,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)],[11]) ).
thf(55,axiom,
member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ tr1a ) @ ( cont @ tra ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_tr1__tr) ).
thf(379,plain,
member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ tr1a ) @ ( cont @ tra ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_list_Oset__intros_I1_J) ).
thf(861,plain,
! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(92,axiom,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_subset__code_I1_J) ).
thf(523,plain,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(159,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_183_Collect__restrict) ).
thf(762,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)],[159]) ).
thf(72,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ( member @ n @ ( root @ B ) @ A )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
=> ~ ! [D: dtree,E: dtree,F: set @ n] :
( ( A
= ( insert2 @ n @ ( root @ E ) @ F ) )
=> ( ( B = E )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
=> ~ ( gram_L805317441_inFr2 @ F @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_inFr2_Ocases) ).
thf(440,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ( member @ n @ ( root @ B ) @ A )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
=> ~ ! [D: dtree,E: dtree,F: set @ n] :
( ( A
= ( insert2 @ n @ ( root @ E ) @ F ) )
=> ( ( B = E )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
=> ~ ( gram_L805317441_inFr2 @ F @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(136,axiom,
! [TA: $tType] :
( ( insert2 @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__compr) ).
thf(655,plain,
! [TA: $tType] :
( ( insert2 @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(58,axiom,
! [A: n > dtree,B: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( A @ ( root @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_reg__root) ).
thf(385,plain,
! [A: n > dtree,B: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( A @ ( root @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inr @ TB @ TA @ A )
!= ( sum_Inl @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_old_Osum_Odistinct_I2_J) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inr @ TB @ TA @ A )
!= ( sum_Inl @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_sumE) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(170,axiom,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L716654942_subtr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_subtr__mono) ).
thf(814,plain,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L716654942_subtr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(145,axiom,
( gram_L250615845e_path
= ( ^ [A: n > dtree,B: list @ n] :
( ? [C: n] :
( B
= ( cons @ n @ C @ ( nil @ n ) ) )
| ? [C: n,D: list @ n,E: n] :
( ( B
= ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
& ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_path_Osimps) ).
thf(698,plain,
( gram_L250615845e_path
= ( ^ [A: n > dtree,B: list @ n] :
( ? [C: n] :
( B
= ( cons @ n @ C @ ( nil @ n ) ) )
| ? [C: n,D: list @ n,E: n] :
( ( B
= ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
& ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(212,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_124_in__mono) ).
thf(945,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)],[212]) ).
thf(207,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_insertCI) ).
thf(930,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(175,axiom,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ? [C: list @ n] :
( ( gram_L250615845e_path @ A @ C )
& ( ( hd @ n @ C )
= ( hd @ n @ B ) )
& ( ( last @ n @ C )
= ( last @ n @ B ) )
& ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ C ) @ ( set2 @ n @ B ) )
& ( distinct @ n @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_path__distinct) ).
thf(829,plain,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ? [C: list @ n] :
( ( gram_L250615845e_path @ A @ C )
& ( ( hd @ n @ C )
= ( hd @ n @ B ) )
& ( ( last @ n @ C )
= ( last @ n @ B ) )
& ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ C ) @ ( set2 @ n @ B ) )
& ( distinct @ n @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(24,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_139_Collect__mono__iff) ).
thf(288,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)],[24]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
( ( sum_rec_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Osum_Osimps_I8_J) ).
thf(565,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
( ( sum_rec_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Inl__inject) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(153,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_List_Oinsert__def) ).
thf(719,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(46,axiom,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ! [E: set @ n,F: dtree] : ( D @ E @ F @ F )
=> ( ! [E: set @ n,F: dtree,G: dtree,H: dtree] :
( ( member @ n @ ( root @ F ) @ E )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ G ) )
=> ( ( gram_L716654942_subtr @ E @ G @ H )
=> ( ( D @ E @ G @ H )
=> ( D @ E @ F @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subtr__inductL) ).
thf(344,plain,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ! [E: set @ n,F: dtree] : ( D @ E @ F @ F )
=> ( ! [E: set @ n,F: dtree,G: dtree,H: dtree] :
( ( member @ n @ ( root @ F ) @ E )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ G ) )
=> ( ( gram_L716654942_subtr @ E @ G @ H )
=> ( ( D @ E @ G @ H )
=> ( D @ E @ F @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_insert__subsetI) ).
thf(587,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_list_Odistinct_I1_J) ).
thf(619,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(99,axiom,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
=> ( ( gram_L716654942_subtr @ B @ C @ D )
=> ( gram_L716654942_subtr @ B @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_subtr__StepL) ).
thf(542,plain,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
=> ( ( gram_L716654942_subtr @ B @ C @ D )
=> ( gram_L716654942_subtr @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
( ( f @ ( hd @ n @ nl ) )
= tr1a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_f__nl) ).
thf(460,plain,
( ( f @ ( hd @ n @ nl ) )
= tr1a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ @+[C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_univ__def) ).
thf(870,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ @+[C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(119,axiom,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L1283001940subtr2 @ B @ D @ C )
=> ( gram_L1283001940subtr2 @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_subtr2__StepR) ).
thf(606,plain,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L1283001940subtr2 @ B @ D @ C )
=> ( gram_L1283001940subtr2 @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(162,axiom,
gram_L1918716148le_reg @ f @ tr1a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_tr1) ).
thf(770,plain,
gram_L1918716148le_reg @ f @ tr1a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(67,axiom,
! [A: set @ n,B: dtree,C: n,D: ( set @ n ) > dtree > n > $o] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ ( root @ E ) ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
=> ( ( gram_L830233218_inItr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inItr_Oinducts) ).
thf(416,plain,
! [A: set @ n,B: dtree,C: n,D: ( set @ n ) > dtree > n > $o] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ ( root @ E ) ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
=> ( ( gram_L830233218_inItr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_sum_Oinject_I1_J) ).
thf(325,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(171,axiom,
! [TA: $tType,A: set @ TA,B: list @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ~ ( member @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_subset__code_I2_J) ).
thf(817,plain,
! [TA: $tType,A: set @ TA,B: list @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ B ) )
=> ~ ( member @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(199,axiom,
! [TA: $tType] :
~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_subset__code_I3_J) ).
thf(902,plain,
! [TA: $tType] :
~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_map__tailrec__rev_Oinduct) ).
thf(492,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(166,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subtr2__rootL__in) ).
thf(789,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(54,axiom,
! [A: n > dtree,B: n,C: list @ n,D: n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ B ) ) @ ( cont @ ( A @ D ) ) )
=> ( gram_L250615845e_path @ A @ ( cons @ n @ D @ ( cons @ n @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_path_OInd) ).
thf(376,plain,
! [A: n > dtree,B: n,C: list @ n,D: n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ B ) ) @ ( cont @ ( A @ D ) ) )
=> ( gram_L250615845e_path @ A @ ( cons @ n @ D @ ( cons @ n @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(8,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_180_conj__subset__def) ).
thf(238,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)],[8]) ).
thf(79,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list_Oinducts) ).
thf(475,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(204,axiom,
! [A: dtree,B: set @ n,C: t] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_not__root__inFr) ).
thf(924,plain,
! [A: dtree,B: set @ n,C: t] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(26,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_86_subset__antisym) ).
thf(293,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)],[26]) ).
thf(185,axiom,
gram_L1918716148le_reg @ f @ tr,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f) ).
thf(866,plain,
gram_L1918716148le_reg @ f @ tr,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(73,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_OdiscI) ).
thf(453,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(164,axiom,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ E ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ G ) )
=> ( ( gram_L1283001940subtr2 @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subtr2_Oinducts) ).
thf(774,plain,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ E ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ G ) )
=> ( ( gram_L1283001940subtr2 @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_contra__subsetD) ).
thf(411,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( A != B )
=> ( ( sum_Inr @ TA @ TB @ A )
!= ( sum_Inr @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_not__arg__cong__Inr) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( A != B )
=> ( ( sum_Inr @ TA @ TB @ A )
!= ( sum_Inr @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(62,axiom,
! [A: n > dtree,B: n,C: list @ n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
=> ( ( C
!= ( nil @ n ) )
=> ( gram_L250615845e_path @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_path__post) ).
thf(397,plain,
! [A: n > dtree,B: n,C: list @ n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
=> ( ( C
!= ( nil @ n ) )
=> ( gram_L250615845e_path @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert2 @ TA @ A @ B )
= ( insert2 @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_insert__ident) ).
thf(687,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert2 @ TA @ A @ B )
= ( insert2 @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(17,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_127_equalityE) ).
thf(265,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)],[17]) ).
thf(180,axiom,
! [A: dtree] :
( ( node @ ( root @ A ) @ ( cont @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Node__root__cont) ).
thf(849,plain,
! [A: dtree] :
( ( node @ ( root @ A ) @ ( cont @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(32,axiom,
gram_L1333338417e_inFr = gram_L805317441_inFr2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inFr__inFr2) ).
thf(307,plain,
gram_L1333338417e_inFr = gram_L805317441_inFr2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
gram_L1905609017ubst_r = root,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_hsubst__r__def) ).
thf(380,plain,
gram_L1905609017ubst_r = root,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(94,axiom,
( gram_L1905609002ubst_c
= ( ^ [A: dtree,B: dtree] :
( if @ ( set @ ( sum_sum @ t @ dtree ) )
@ ( ( root @ B )
= ( root @ A ) )
@ ( cont @ A )
@ ( cont @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_hsubst__c__def) ).
thf(529,plain,
( gram_L1905609002ubst_c
= ( ^ [A: dtree,B: dtree] :
( if @ ( set @ ( sum_sum @ t @ dtree ) )
@ ( ( root @ B )
= ( root @ A ) )
@ ( cont @ A )
@ ( cont @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(96,axiom,
( gram_L1580978439le_Itr
= ( ^ [A: set @ n,B: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Itr__def) ).
thf(534,plain,
( gram_L1580978439le_Itr
= ( ^ [A: set @ n,B: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert2 @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_insertI1) ).
thf(714,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert2 @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(89,axiom,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ? [D: dtree] :
( ( gram_L716654942_subtr @ A @ D @ B )
& ( ( root @ D )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inItr__subtr) ).
thf(512,plain,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ? [D: dtree] :
( ( gram_L716654942_subtr @ A @ D @ B )
& ( ( root @ D )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
gram_L1918716148le_reg @ f @ tra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_tr) ).
thf(439,plain,
gram_L1918716148le_reg @ f @ tra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(42,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_subset__insertI2) ).
thf(334,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(174,axiom,
! [A: dtree,B: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( ( gram_L1614515765ubtrOf @ A @ ( root @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_subtrOf__root) ).
thf(825,plain,
! [A: dtree,B: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( ( gram_L1614515765ubtrOf @ A @ ( root @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(215,axiom,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( gram_L716654942_subtr @ B @ C @ D )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ A ) )
=> ( gram_L716654942_subtr @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_subtr_OStep) ).
thf(952,plain,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( gram_L716654942_subtr @ B @ C @ D )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ A ) )
=> ( gram_L716654942_subtr @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_distinct__union) ).
thf(302,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct @ TA @ ( union @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [A: set @ n,B: dtree,C: dtree,D: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ C @ D )
=> ( gram_L716654942_subtr @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_subtr__trans) ).
thf(260,plain,
! [A: set @ n,B: dtree,C: dtree,D: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ C @ D )
=> ( gram_L716654942_subtr @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( set2 @ TA @ ( cons @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_list_Osimps_I15_J) ).
thf(598,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( set2 @ TA @ ( cons @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(172,axiom,
! [A: dtree,B: set @ n,C: dtree,D: n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L830233218_inItr @ B @ C @ D )
=> ( gram_L830233218_inItr @ B @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_inItr_OInd) ).
thf(820,plain,
! [A: dtree,B: set @ n,C: dtree,D: n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L830233218_inItr @ B @ C @ D )
=> ( gram_L830233218_inItr @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(28,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__insertI) ).
thf(297,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType] :
( ( '?' @ ( sum_sum @ TA @ TB ) )
= ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
( ? [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
| ? [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_split__sum__ex) ).
thf(693,plain,
! [TA: $tType,TB: $tType] :
( ( '?' @ ( sum_sum @ TA @ TB ) )
= ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
( ? [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
| ? [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(19,axiom,
gram_L716654942_subtr @ ns @ tr1 @ tr,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_n) ).
thf(275,plain,
gram_L716654942_subtr @ ns @ tr1 @ tr,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(125,axiom,
( gram_L805317441_inFr2
= ( ^ [A: set @ n,B: dtree,C: t] :
( ? [D: dtree,E: set @ n,F: t] :
( ( A = E )
& ( B = D )
& ( C = F )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
| ? [D: dtree,E: dtree,F: set @ n,G: t] :
( ( A
= ( insert2 @ n @ ( root @ E ) @ F ) )
& ( B = E )
& ( C = G )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
& ( gram_L805317441_inFr2 @ F @ D @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_inFr2_Osimps) ).
thf(625,plain,
( gram_L805317441_inFr2
= ( ^ [A: set @ n,B: dtree,C: t] :
( ? [D: dtree,E: set @ n,F: t] :
( ( A = E )
& ( B = D )
& ( C = F )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
| ? [D: dtree,E: dtree,F: set @ n,G: t] :
( ( A
= ( insert2 @ n @ ( root @ E ) @ F ) )
& ( B = E )
& ( C = G )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
& ( gram_L805317441_inFr2 @ F @ D @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(190,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inFr__root__in) ).
thf(879,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(181,axiom,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_inFr2__mono) ).
thf(852,plain,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(139,axiom,
( ( gram_L1918716148le_reg @ f @ tr1a )
=> ? [A: list @ n] :
( ( gram_L250615845e_path @ f @ A )
& ( ( f @ ( hd @ n @ A ) )
= tr1a )
& ( ( f @ ( last @ n @ A ) )
= tr2 )
& ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Step_Ohyps_I3_J) ).
thf(665,plain,
( ( gram_L1918716148le_reg @ f @ tr1a )
=> ? [A: list @ n] :
( ( gram_L250615845e_path @ f @ A )
& ( ( f @ ( hd @ n @ A ) )
= tr1a )
& ( ( f @ ( last @ n @ A ) )
= tr2 )
& ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(110,axiom,
gram_L250615845e_path @ f @ nl,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nl) ).
thf(583,plain,
gram_L250615845e_path @ f @ nl,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(194,axiom,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inItr_OBase) ).
thf(889,plain,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(102,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_set__rev__mp) ).
thf(551,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(23,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(285,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_old_Osum_Osimps_I7_J) ).
thf(229,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_last_Osimps) ).
thf(484,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(91,axiom,
! [A: n > dtree,B: list @ n] :
( ! [C: n] :
( ( root @ ( A @ C ) )
= C )
=> ( ( gram_L250615845e_path @ A @ B )
=> ( gram_L716654942_subtr @ ( set2 @ n @ B ) @ ( A @ ( last @ n @ B ) ) @ ( A @ ( hd @ n @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_path__subtr) ).
thf(519,plain,
! [A: n > dtree,B: list @ n] :
( ! [C: n] :
( ( root @ ( A @ C ) )
= C )
=> ( ( gram_L250615845e_path @ A @ B )
=> ( gram_L716654942_subtr @ ( set2 @ n @ B ) @ ( A @ ( last @ n @ B ) ) @ ( A @ ( hd @ n @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(36,axiom,
( gram_L646766332egular
= ( ^ [A: dtree] :
? [B: n > dtree] : ( gram_L1918716148le_reg @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_regular__def) ).
thf(317,plain,
( gram_L646766332egular
= ( ^ [A: dtree] :
? [B: n > dtree] : ( gram_L1918716148le_reg @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_shift__def) ).
thf(388,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(49,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_184_subset__Collect__iff) ).
thf(356,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)],[49]) ).
thf(40,axiom,
! [A: dtree,B: set @ n,C: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( gram_L716654942_subtr @ B @ C @ A )
=> ( gram_L864798063lle_wf @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_wf__subtr) ).
thf(328,plain,
! [A: dtree,B: set @ n,C: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( gram_L716654942_subtr @ B @ C @ A )
=> ( gram_L864798063lle_wf @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(192,axiom,
( gram_L1614515765ubtrOf
= ( ^ [A: dtree,B: n] :
@+[C: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
& ( ( root @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_subtrOf__def) ).
thf(884,plain,
( gram_L1614515765ubtrOf
= ( ^ [A: dtree,B: n] :
@+[C: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
& ( ( root @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(225,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_distinct__length__2__or__more) ).
thf(642,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct @ TA @ ( cons @ TA @ A @ C ) )
& ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_list_Oinject) ).
thf(526,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_list_Oset__intros_I2_J) ).
thf(706,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( '!' @ ( sum_sum @ TA @ TB ) )
= ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
( ! [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
& ! [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_split__sum__all) ).
thf(457,plain,
! [TA: $tType,TB: $tType] :
( ( '!' @ ( sum_sum @ TA @ TB ) )
= ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
( ! [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
& ! [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_distinct_Osimps_I2_J) ).
thf(503,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
& ( distinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(124,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_distinct__product__lists) ).
thf(622,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ! [B: list @ TA] :
( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
=> ( distinct @ TA @ B ) )
=> ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(176,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_subtr__rootL__in) ).
thf(837,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( set2 @ TA @ ( insert @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_List_Oset__insert) ).
thf(244,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( set2 @ TA @ ( insert @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_member__remove) ).
thf(792,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(209,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_in__set__insert) ).
thf(938,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(129,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subtr2__rootR__in) ).
thf(633,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert2 @ TA @ A @ ( insert2 @ TA @ B @ C ) )
= ( insert2 @ TA @ B @ ( insert2 @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_insert__commute) ).
thf(311,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert2 @ TA @ A @ ( insert2 @ TA @ B @ C ) )
= ( insert2 @ TA @ B @ ( insert2 @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(203,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_splice_Oinduct) ).
thf(921,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(138,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_remdups__adj_Ocases) ).
thf(662,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(21,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_135_Collect__mono) ).
thf(279,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)],[21]) ).
thf(107,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ? [D: dtree] :
( ( gram_L716654942_subtr @ A @ D @ B )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inFr__subtr) ).
thf(573,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ? [D: dtree] :
( ( gram_L716654942_subtr @ A @ D @ B )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(27,axiom,
gram_L716654942_subtr @ nsa @ tr2 @ tr1a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_tr2__tr1) ).
thf(296,plain,
gram_L716654942_subtr @ nsa @ tr2 @ tr1a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(117,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_128_subset__eq) ).
thf(601,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)],[117]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_sum_Oinject_I2_J) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(200,axiom,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ( gram_L1333338417e_inFr @ ( insert2 @ n @ ( root @ D ) @ A ) @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_inFr__Ind__minus) ).
thf(904,plain,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ( gram_L1333338417e_inFr @ ( insert2 @ n @ ( root @ D ) @ A ) @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(178,axiom,
! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_set__subset__Cons) ).
thf(843,plain,
! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(150,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_last__ConsR) ).
thf(711,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(25,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_subset__refl) ).
thf(291,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(100,axiom,
! [A: n > dtree,B: dtree,C: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ B ) )
=> ( gram_L1918716148le_reg @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_reg__Inr__cont) ).
thf(545,plain,
! [A: n > dtree,B: dtree,C: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ B ) )
=> ( gram_L1918716148le_reg @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(66,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_product__lists_Osimps_I1_J) ).
thf(413,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert2 @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_mk__disjoint__insert) ).
thf(391,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert2 @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(57,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_list_Oexhaust) ).
thf(382,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(213,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_insert__iff) ).
thf(947,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(140,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_remdups__adj_Oinduct) ).
thf(672,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1,conjecture,
( ? [A: n] :
( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ A @ ( nil @ n ) ) )
| ? [A: n,B: list @ n,C: n] :
( ( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
& ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ? [A: n] :
( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ A @ ( nil @ n ) ) )
| ? [A: n,B: list @ n,C: n] :
( ( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
& ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(219,plain,
~ ( ? [A: n] :
( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ A @ ( nil @ n ) ) )
| ? [A: n,B: list @ n,C: n] :
( ( ( cons @ n @ ( root @ tra ) @ nl )
= ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
& ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(155,axiom,
! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
( ( root @ ( node @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_root__Node) ).
thf(736,plain,
! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
( ( root @ ( node @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(122,axiom,
! [A: set @ n,B: dtree,C: n,D: set @ n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L830233218_inItr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inItr__mono) ).
thf(616,plain,
! [A: set @ n,B: dtree,C: n,D: set @ n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L830233218_inItr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_obj__sumE) ).
thf(863,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(160,axiom,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( member @ n @ ( root @ D ) @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ( gram_L805317441_inFr2 @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_inFr2__Ind) ).
thf(764,plain,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( member @ n @ ( root @ D ) @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
=> ( gram_L805317441_inFr2 @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(118,axiom,
( gram_L716654942_subtr
= ( ^ [A: set @ n,B: dtree,C: dtree] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
( ( A = E )
& ( B = F )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E )
& ( gram_L716654942_subtr @ E @ F @ G )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_subtr_Osimps) ).
thf(604,plain,
( gram_L716654942_subtr
= ( ^ [A: set @ n,B: dtree,C: dtree] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
( ( A = E )
& ( B = F )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E )
& ( gram_L716654942_subtr @ E @ F @ G )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(88,axiom,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
=> ( ( gram_L1283001940subtr2 @ B @ C @ D )
=> ( gram_L1283001940subtr2 @ B @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_subtr2_OStep) ).
thf(509,plain,
! [A: dtree,B: set @ n,C: dtree,D: dtree] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
=> ( ( gram_L1283001940subtr2 @ B @ C @ D )
=> ( gram_L1283001940subtr2 @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(134,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(649,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_list_Oset__cases) ).
thf(434,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ! [C: list @ TA] :
( B
!= ( cons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(128,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_distinct__singleton) ).
thf(631,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_set__ConsD) ).
thf(367,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
=> ( ( A = B )
| ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(120,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_the__elem__set) ).
thf(609,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(146,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_insertE) ).
thf(700,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(196,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_125_subsetD) ).
thf(895,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)],[196]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insertI2) ).
thf(462,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: ( sum_sum @ TA @ TB ) > $o,B: sum_sum @ TA @ TB] :
( ! [C: TA] : ( A @ ( sum_Inl @ TA @ TB @ C ) )
=> ( ! [C: TB] : ( A @ ( sum_Inr @ TB @ TA @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_old_Osum_Oinducts) ).
thf(959,plain,
! [TA: $tType,TB: $tType,A: ( sum_sum @ TA @ TB ) > $o,B: sum_sum @ TA @ TB] :
( ! [C: TA] : ( A @ ( sum_Inl @ TA @ TB @ C ) )
=> ( ! [C: TB] : ( A @ ( sum_Inr @ TB @ TA @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( remove @ TA @ A @ ( coset @ TA @ B ) )
= ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_remove__code_I2_J) ).
thf(299,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( remove @ TA @ A @ ( coset @ TA @ B ) )
= ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_distinct__insert) ).
thf(226,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
= ( distinct @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(69,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_sublists_Osimps_I1_J) ).
thf(431,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(9,axiom,
! [A: dtree,B: set @ n,C: dtree] :
( ( gram_L646766332egular @ A )
=> ( ( gram_L716654942_subtr @ B @ C @ A )
=> ( gram_L646766332egular @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_regular__subtr) ).
thf(241,plain,
! [A: dtree,B: set @ n,C: dtree] :
( ( gram_L646766332egular @ A )
=> ( ( gram_L716654942_subtr @ B @ C @ A )
=> ( gram_L646766332egular @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(137,axiom,
! [A: dtree,B: dtree,C: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( ( root @ B )
= ( root @ C ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_wf__inj) ).
thf(658,plain,
! [A: dtree,B: dtree,C: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( ( root @ B )
= ( root @ C ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(154,axiom,
! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n,G: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
=> ( D @ F @ E @ G ) ) )
=> ( ! [E: dtree,F: dtree,G: set @ n,H: t] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ F ) )
=> ( ( gram_L805317441_inFr2 @ G @ E @ H )
=> ( ( D @ G @ E @ H )
=> ( D @ ( insert2 @ n @ ( root @ F ) @ G ) @ F @ H ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_inFr2_Oinducts) ).
thf(722,plain,
! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n,G: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
=> ( D @ F @ E @ G ) ) )
=> ( ! [E: dtree,F: dtree,G: set @ n,H: t] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ F ) )
=> ( ( gram_L805317441_inFr2 @ G @ E @ H )
=> ( ( D @ G @ E @ H )
=> ( D @ ( insert2 @ n @ ( root @ F ) @ G ) @ F @ H ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(81,axiom,
( ( f @ ( last @ n @ nl ) )
= tr2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_last__nl) ).
thf(490,plain,
( ( f @ ( last @ n @ nl ) )
= tr2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(113,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_166_pred__subset__eq) ).
thf(589,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)],[113]) ).
thf(168,axiom,
! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n,G: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
=> ( D @ F @ E @ G ) ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
=> ( ( gram_L1333338417e_inFr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inFr_Oinducts) ).
thf(795,plain,
! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n,G: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
=> ( D @ F @ E @ G ) ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: t] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
=> ( ( gram_L1333338417e_inFr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( D @ F @ E @ H ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(101,axiom,
! [A: dtree,B: dtree] :
( ( ( root @ A )
= ( root @ B ) )
=> ( ( ( cont @ A )
= ( cont @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dtree__cong) ).
thf(548,plain,
! [A: dtree,B: dtree] :
( ( ( root @ A )
= ( root @ B ) )
=> ( ( ( cont @ A )
= ( cont @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(205,axiom,
( gram_L646766332egular
= ( ^ [A: dtree] :
? [B: n > dtree] :
( ( gram_L1918716148le_reg @ B @ A )
& ! [C: n] :
( ( root @ ( B @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_regular__def2) ).
thf(927,plain,
( gram_L646766332egular
= ( ^ [A: dtree] :
? [B: n > dtree] :
( ( gram_L1918716148le_reg @ B @ A )
& ! [C: n] :
( ( root @ ( B @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(133,axiom,
gram_L1918716148le_reg @ f @ tra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Step_Oprems) ).
thf(648,plain,
gram_L1918716148le_reg @ f @ tra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(169,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_126_subsetCE) ).
thf(812,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)],[169]) ).
thf(90,axiom,
! [A: dtree,B: set @ n,C: dtree,D: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L1333338417e_inFr @ B @ C @ D )
=> ( gram_L1333338417e_inFr @ B @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inFr_OInd) ).
thf(516,plain,
! [A: dtree,B: set @ n,C: dtree,D: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
=> ( ( gram_L1333338417e_inFr @ B @ C @ D )
=> ( gram_L1333338417e_inFr @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(45,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_146_rev__predicate1D) ).
thf(342,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)],[45]) ).
thf(103,axiom,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ E ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( gram_L716654942_subtr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ H ) @ ( cont @ E ) )
=> ( D @ F @ G @ E ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_subtr_Oinducts) ).
thf(553,plain,
! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ! [E: dtree,F: set @ n] :
( ( member @ n @ ( root @ E ) @ F )
=> ( D @ F @ E @ E ) )
=> ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
( ( member @ n @ ( root @ E ) @ F )
=> ( ( gram_L716654942_subtr @ F @ G @ H )
=> ( ( D @ F @ G @ H )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ H ) @ ( cont @ E ) )
=> ( D @ F @ G @ E ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(173,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_subtr__rootR__in) ).
thf(823,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(95,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inFr2__root__in) ).
thf(531,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(211,axiom,
ord_less_eq @ ( set @ n ) @ ( set2 @ n @ nl ) @ nsa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_set) ).
thf(944,plain,
ord_less_eq @ ( set @ n ) @ ( set2 @ n @ nl ) @ nsa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert2 @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__insert) ).
thf(690,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert2 @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(22,axiom,
! [A: set @ n,B: dtree,C: dtree,D: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( gram_L1283001940subtr2 @ A @ C @ D )
=> ( gram_L1283001940subtr2 @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subtr2__trans) ).
thf(282,plain,
! [A: set @ n,B: dtree,C: dtree,D: dtree] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( gram_L1283001940subtr2 @ A @ C @ D )
=> ( gram_L1283001940subtr2 @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(156,axiom,
( gram_L1918716148le_reg
= ( ^ [A: n > dtree,B: dtree] :
! [C: set @ n,D: dtree] :
( ( gram_L716654942_subtr @ C @ D @ B )
=> ( D
= ( A @ ( root @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_reg__def2) ).
thf(739,plain,
( gram_L1918716148le_reg
= ( ^ [A: n > dtree,B: dtree] :
! [C: set @ n,D: dtree] :
( ( gram_L716654942_subtr @ C @ D @ B )
=> ( D
= ( A @ ( root @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(16,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_147_predicate1D) ).
thf(263,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)],[16]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Osum_Oinject_I2_J) ).
thf(580,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(182,axiom,
! [A: n > dtree,B: list @ n,C: ( list @ n ) > $o] :
( ( gram_L250615845e_path @ A @ B )
=> ( ! [D: n] : ( C @ ( cons @ n @ D @ ( nil @ n ) ) )
=> ( ! [D: n,E: list @ n,F: n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ D @ E ) )
=> ( ( C @ ( cons @ n @ D @ E ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ D ) ) @ ( cont @ ( A @ F ) ) )
=> ( C @ ( cons @ n @ F @ ( cons @ n @ D @ E ) ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_path_Oinducts) ).
thf(855,plain,
! [A: n > dtree,B: list @ n,C: ( list @ n ) > $o] :
( ( gram_L250615845e_path @ A @ B )
=> ( ! [D: n] : ( C @ ( cons @ n @ D @ ( nil @ n ) ) )
=> ( ! [D: n,E: list @ n,F: n] :
( ( gram_L250615845e_path @ A @ ( cons @ n @ D @ E ) )
=> ( ( C @ ( cons @ n @ D @ E ) )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ D ) ) @ ( cont @ ( A @ F ) ) )
=> ( C @ ( cons @ n @ F @ ( cons @ n @ D @ E ) ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(41,axiom,
! [A: set @ n,B: dtree,C: n,D: dtree] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ B @ D )
=> ( gram_L830233218_inItr @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subtr__inItr) ).
thf(331,plain,
! [A: set @ n,B: dtree,C: n,D: dtree] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ B @ D )
=> ( gram_L830233218_inItr @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert2 @ TA @ A @ B )
= ( insert2 @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert2 @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert2 @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_insert__eq__iff) ).
thf(370,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert2 @ TA @ A @ B )
= ( insert2 @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert2 @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert2 @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(177,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_transpose_Ocases) ).
thf(840,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(44,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_130_equalityD2) ).
thf(338,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)],[44]) ).
thf(108,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_last__ConsL) ).
thf(576,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(50,axiom,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ( ! [C: n] :
( B
!= ( cons @ n @ C @ ( nil @ n ) ) )
=> ~ ! [C: n,D: list @ n,E: n] :
( ( B
= ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
=> ( ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_path_Ocases) ).
thf(359,plain,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ( ! [C: n] :
( B
!= ( cons @ n @ C @ ( nil @ n ) ) )
=> ~ ! [C: n,D: list @ n,E: n] :
( ( B
= ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
=> ( ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(201,axiom,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ( C
= ( root @ B ) )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
=> ~ ( gram_L830233218_inItr @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inItr_Ocases) ).
thf(907,plain,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ( C
= ( root @ B ) )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
=> ~ ( gram_L830233218_inItr @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(43,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ C @ A ) @ ( insert2 @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_insert__mono) ).
thf(336,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ C @ A ) @ ( insert2 @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(147,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert2 @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_insert__absorb) ).
thf(703,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert2 @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(35,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(314,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(106,axiom,
( gram_L830233218_inItr
= ( ^ [A: set @ n,B: dtree,C: n] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C
= ( root @ D ) )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: n] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
& ( gram_L830233218_inItr @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inItr_Osimps) ).
thf(571,plain,
( gram_L830233218_inItr
= ( ^ [A: set @ n,B: dtree,C: n] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C
= ( root @ D ) )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: n] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
& ( gram_L830233218_inItr @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(115,axiom,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inItr__root__in) ).
thf(595,plain,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(121,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_185_subset__CollectI) ).
thf(612,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)],[121]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__subset) ).
thf(497,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inl @ TB @ TA @ A )
!= ( sum_Inr @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_sum_Odistinct_I1_J) ).
thf(876,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inl @ TB @ TA @ A )
!= ( sum_Inr @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(179,axiom,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ( B
!= ( nil @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_path__NE) ).
thf(845,plain,
! [A: n > dtree,B: list @ n] :
( ( gram_L250615845e_path @ A @ B )
=> ( B
!= ( nil @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(12,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_129_equalityD1) ).
thf(250,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)],[12]) ).
thf(126,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_distinct_Osimps_I1_J) ).
thf(627,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list__induct2_H) ).
thf(539,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(83,axiom,
! [A: n > dtree,B: n] : ( gram_L250615845e_path @ A @ ( cons @ n @ B @ ( nil @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_path_OBase) ).
thf(495,plain,
! [A: n > dtree,B: n] : ( gram_L250615845e_path @ A @ ( cons @ n @ B @ ( nil @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ @+[D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_someI2__bex) ).
thf(891,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ @+[D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(163,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_not__in__set__insert) ).
thf(771,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
=> ( ( insert @ TA @ A @ B )
= ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(218,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_132_subset__iff) ).
thf(961,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)],[218]) ).
thf(37,axiom,
! [A: n > dtree,B: dtree,C: set @ n,D: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( gram_L716654942_subtr @ C @ D @ B )
=> ( gram_L1918716148le_reg @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_reg__subtr) ).
thf(319,plain,
! [A: n > dtree,B: dtree,C: set @ n,D: dtree] :
( ( gram_L1918716148le_reg @ A @ B )
=> ( ( gram_L716654942_subtr @ C @ D @ B )
=> ( gram_L1918716148le_reg @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(165,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(786,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(135,axiom,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1283001940subtr2 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_subtr2__mono) ).
thf(652,plain,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L1283001940subtr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1283001940subtr2 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(47,axiom,
! [A: dtree,B: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( gram_L864798063lle_wf @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_wf__cont) ).
thf(351,plain,
! [A: dtree,B: dtree] :
( ( gram_L864798063lle_wf @ A )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
=> ( gram_L864798063lle_wf @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_neq__Nil__conv) ).
thf(568,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7,axiom,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ B @ D )
=> ( gram_L1333338417e_inFr @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subtr__inFr) ).
thf(235,plain,
! [A: set @ n,B: dtree,C: t,D: dtree] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ A @ B @ D )
=> ( gram_L1333338417e_inFr @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(206,axiom,
member @ n @ ( root @ tra ) @ nsa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_rtr) ).
thf(929,plain,
member @ n @ ( root @ tra ) @ nsa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(18,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_145_predicate1I) ).
thf(272,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)],[18]) ).
thf(198,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_94_less__eq__set__def) ).
thf(899,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)],[198]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Inr__inject) ).
thf(536,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inr @ TA @ TB @ A )
= ( sum_Inr @ TA @ TB @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(152,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_hd__in__set) ).
thf(716,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(158,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ( C = B )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ C ) @ A )
=> ! [D: dtree] :
( ( gram_L716654942_subtr @ A @ B @ D )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_subtr_Ocases) ).
thf(752,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ( C = B )
=> ~ ( member @ n @ ( root @ B ) @ A ) )
=> ~ ( ( member @ n @ ( root @ C ) @ A )
=> ! [D: dtree] :
( ( gram_L716654942_subtr @ A @ B @ D )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(214,axiom,
( gram_L1333338417e_inFr
= ( ^ [A: set @ n,B: dtree,C: t] :
( ? [D: dtree,E: set @ n,F: t] :
( ( A = E )
& ( B = D )
& ( C = F )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
| ? [D: dtree,E: set @ n,F: dtree,G: t] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
& ( gram_L1333338417e_inFr @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_inFr_Osimps) ).
thf(950,plain,
( gram_L1333338417e_inFr
= ( ^ [A: set @ n,B: dtree,C: t] :
( ? [D: dtree,E: set @ n,F: t] :
( ( A = E )
& ( B = D )
& ( C = F )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
| ? [D: dtree,E: set @ n,F: dtree,G: t] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
& ( gram_L1333338417e_inFr @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(186,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( last @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_last__in__set) ).
thf(867,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( last @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(53,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_insert__Nil) ).
thf(373,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(31,axiom,
gram_L716654942_subtr = gram_L1283001940subtr2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_subtr__subtr2) ).
thf(305,plain,
gram_L716654942_subtr = gram_L1283001940subtr2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(202,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_87_subsetI) ).
thf(918,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)],[202]) ).
thf(87,axiom,
! [A: dtree,B: dtree,C: set @ n,D: t] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
=> ( ( gram_L805317441_inFr2 @ C @ A @ D )
=> ( gram_L805317441_inFr2 @ ( insert2 @ n @ ( root @ B ) @ C ) @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_inFr2_OInd) ).
thf(506,plain,
! [A: dtree,B: dtree,C: set @ n,D: t] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
=> ( ( gram_L805317441_inFr2 @ C @ A @ D )
=> ( gram_L805317441_inFr2 @ ( insert2 @ n @ ( root @ B ) @ C ) @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(63,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ( member @ n @ ( root @ B ) @ A )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
=> ~ ( gram_L1333338417e_inFr @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_inFr_Ocases) ).
thf(400,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ( member @ n @ ( root @ B ) @ A )
=> ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
=> ~ ( ( member @ n @ ( root @ B ) @ A )
=> ! [D: dtree] :
( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
=> ~ ( gram_L1333338417e_inFr @ A @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(130,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_list__nonempty__induct) ).
thf(635,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(144,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_123_set__mp) ).
thf(696,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)],[144]) ).
thf(216,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert2 @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Set_Oset__insert) ).
thf(955,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert2 @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(193,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list_Osel_I1_J) ).
thf(886,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(197,axiom,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L1283001940subtr2 @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subtr2_ORefl) ).
thf(897,plain,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L1283001940subtr2 @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_old_Osum_Oexhaust) ).
thf(767,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ! [B: TB] :
( A
!= ( sum_Inl @ TB @ TA @ B ) )
=> ~ ! [B: TA] :
( A
!= ( sum_Inr @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(61,axiom,
( gram_L1283001940subtr2
= ( ^ [A: set @ n,B: dtree,C: dtree] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ F ) )
& ( gram_L1283001940subtr2 @ E @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subtr2_Osimps) ).
thf(395,plain,
( gram_L1283001940subtr2
= ( ^ [A: set @ n,B: dtree,C: dtree] :
( ? [D: dtree,E: set @ n] :
( ( A = E )
& ( B = D )
& ( C = D )
& ( member @ n @ ( root @ D ) @ E ) )
| ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
( ( A = E )
& ( B = D )
& ( C = G )
& ( member @ n @ ( root @ D ) @ E )
& ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ F ) )
& ( gram_L1283001940subtr2 @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,axiom,
~ ! [A: list @ n] :
( ( gram_L250615845e_path @ f @ A )
=> ( ( ( f @ ( hd @ n @ A ) )
= tr1a )
=> ( ( ( f @ ( last @ n @ A ) )
= tr2 )
=> ~ ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062nl_O_A_092_060lbrakk_062path_Af_Anl_059_Af_A_Ihd_Anl_J_A_061_Atr1_059_Af_A_Ilast_Anl_J_A_061_Atr2_059_Aset_Anl_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(464,plain,
~ ! [A: list @ n] :
( ( gram_L250615845e_path @ f @ A )
=> ( ( ( f @ ( hd @ n @ A ) )
= tr1a )
=> ( ( ( f @ ( last @ n @ A ) )
= tr2 )
=> ~ ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,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(254,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)],[13]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_old_Osum_Oinject_I1_J) ).
thf(322,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( sum_Inl @ TA @ TB @ A )
= ( sum_Inl @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(48,axiom,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L716654942_subtr @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_subtr_ORefl) ).
thf(354,plain,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L716654942_subtr @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(208,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list_Oset__sel_I1_J) ).
thf(935,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(33,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_136_subset__trans) ).
thf(309,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)],[33]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inl @ TB @ TA @ A )
!= ( sum_Inr @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_old_Osum_Odistinct_I1_J) ).
thf(592,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( sum_Inl @ TB @ TA @ A )
!= ( sum_Inr @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(191,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_181_prop__restrict) ).
thf(882,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)],[191]) ).
thf(149,axiom,
! [A: dtree,B: set @ n,C: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
=> ( gram_L805317441_inFr2 @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inFr2_OBase) ).
thf(708,plain,
! [A: dtree,B: set @ n,C: t] :
( ( member @ n @ ( root @ A ) @ B )
=> ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
=> ( gram_L805317441_inFr2 @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert2 @ TA @ A @ ( insert2 @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_insert__absorb2) ).
thf(232,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert2 @ TA @ A @ ( insert2 @ TA @ A @ B ) )
= ( insert2 @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(969,plain,
$false,
inference(cvc4,[status(thm)],[645,629,941,408,276,741,873,247,379,861,523,762,440,655,385,500,472,814,698,945,930,829,288,565,257,719,344,587,619,542,460,870,606,770,416,325,817,902,492,789,376,238,475,924,293,866,453,774,411,428,397,687,265,849,307,380,529,534,714,512,439,334,825,952,302,260,598,820,297,693,275,625,879,852,665,583,889,551,285,229,484,519,317,388,356,328,884,225,642,526,706,457,503,622,837,244,792,938,633,311,921,662,279,573,296,601,584,904,843,711,291,545,413,391,382,947,672,219,736,616,863,764,604,509,649,434,631,367,609,700,895,462,959,299,226,431,241,658,722,490,589,795,548,927,648,812,516,342,553,823,531,944,690,282,739,263,580,855,331,370,840,338,576,359,907,336,703,314,571,595,612,497,876,845,250,627,539,495,891,771,961,319,786,652,351,568,235,929,272,899,536,716,752,950,867,373,305,918,506,400,635,696,955,886,897,767,395,464,254,322,354,935,309,592,882,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : COM191^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 10:20:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.15 % [INFO] Parsing done (291ms).
% 1.79/1.16 % [INFO] Running in sequential loop mode.
% 2.58/1.40 % [INFO] eprover registered as external prover.
% 2.58/1.41 % [INFO] cvc4 registered as external prover.
% 2.58/1.41 % [INFO] Scanning for conjecture ...
% 2.79/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 268 axioms. Running axiom selection ...
% 3.08/1.62 % [INFO] Axiom selection finished. Selected 216 axioms (removed 52 axioms).
% 3.79/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 3.79/1.80 % [INFO] Type checking passed.
% 3.99/1.81 % [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 ...
% 147.60/90.48 % External prover 'cvc4' found a proof!
% 147.60/90.49 % [INFO] Killing All external provers ...
% 147.60/90.49 % Time passed: 89977ms (effective reasoning time: 89324ms)
% 147.60/90.49 % 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)>
% 147.60/90.49 % Axioms used in derivation (216): fact_210_insert__ident, fact_40_list__induct2_H, fact_147_predicate1D, fact_144_inItr_Osimps, fact_230_obj__sumE, fact_34_map__tailrec__rev_Oinduct, fact_183_Collect__restrict, fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062nl_O_A_092_060lbrakk_062path_Af_Anl_059_Af_A_Ihd_Anl_J_A_061_Atr1_059_Af_A_Ilast_Anl_J_A_061_Atr2_059_Aset_Anl_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_1_tr, fact_54_Step_Ohyps_I3_J, fact_78_subtr_OStep, fact_238_inFr__root__in, fact_63_list_Oset__intros_I2_J, fact_219_subtr2__rootL__in, fact_195_insertCI, fact_17_sum_Oinject_I2_J, fact_191_inFr2_OInd, fact_92_the__elem__set, fact_251_inFr2_OBase, fact_66_list_Oset__cases, fact_242_old_Osum_Oexhaust, fact_4_f, fact_130_equalityD2, fact_24_list_Oexhaust, fact_68_subtr__rootL__in, fact_143_inItr_Oinducts, fact_222_subtr2__StepR, fact_98_distinct_Osimps_I2_J, fact_239_inFr__subtr, fact_129_equalityD1, fact_182_member__remove, fact_50_set, fact_19_list_Oinject, fact_61_inFr2__mono, fact_236_Inl__inject, fact_79_subtr_Ocases, fact_252_inFr_OInd, fact_85_subtrOf__root, fact_241_old_Osum_Oinducts, fact_228_old_Osum_Oinject_I1_J, fact_84_regular__def, fact_139_Collect__mono__iff, fact_244_split__sum__ex, fact_35_list__nonempty__induct, fact_140_distinct__union, fact_6_rtr, fact_237_not__root__inFr, fact_148_inItr_OBase, fact_131_set__rev__mp, fact_135_Collect__mono, fact_154_inItr_Ocases, fact_232_subtr__inFr, fact_82_subtr_Oinducts, fact_231_inFr__mono, fact_138_contra__subsetD, fact_73_hd__in__set, fact_65_set__ConsD, fact_199_insert__subsetI, fact_7_tr1, fact_5_f__nl, fact_10_path_OBase, fact_215_insert__compr, fact_59_subtr__trans, fact_220_subtr2__rootR__in, fact_74_last__in__set, fact_250_inFr__inFr2, fact_153_inItr_OInd, fact_77_wf__cont, fact_137_set__eq__subset, fact_234_inFr_Osimps, fact_2_tr1__tr, fact_253_inFr2_Oinducts, fact_180_conj__subset__def, fact_87_subsetI, fact_91_product__lists_Osimps_I1_J, fact_25_list_Oinducts, fact_62_wf__subtr, fact_235_inFr_Ocases, fact_141_subtrOf__def, fact_184_subset__Collect__iff, fact_162_someI2__bex, fact_240_inFr_OBase, help_If_1_1_T, fact_190_univ__def, fact_81_subtr__StepL, fact_26_neq__Nil__conv, fact_133_rev__subsetD, fact_37_remdups__adj_Ocases, fact_21_hsubst__c__def, fact_216_insert__Collect, fact_127_equalityE, fact_134_subset__refl, fact_245_Inr__not__Inl, fact_33_Inr__inject, fact_145_predicate1I, fact_13_path_Osimps, fact_93_distinct__product__lists, fact_20_dtree__cong, fact_36_remdups__adj_Oinduct, fact_41_n, fact_52_wf__inj, fact_3_nl, fact_15_last__nl, fact_53_inFr2__Ind, fact_189_shift__def, fact_196_insert__subset, fact_56_subset__code_I1_J, fact_60_subtr__mono, fact_225_inFr__Ind__minus, fact_71_inFr2__root__in, fact_192_subtr2_OStep, fact_14_path_Oinducts, fact_9_path_OInd, fact_69_subtr__rootR__in, fact_207_insert__commute, fact_86_subset__antisym, fact_226_inFr2_Ocases, fact_227_sum_Oinject_I1_J, fact_202_subset__insert, fact_29_last__ConsL, fact_181_prop__restrict, fact_168_subset__code_I3_J, fact_90_path__distinct, fact_213_insertI1, fact_132_subset__iff, fact_152_inItr__subtr, fact_169_subset__code_I2_J, fact_198_List_Oset__insert, fact_76_reg__def2, fact_171_Itr__def, fact_12_path_Ocases, fact_193_insert__absorb2, fact_218_subtr2_ORefl, fact_51_Step_Oprems, fact_197_list_Osimps_I15_J, help_If_3_1_T, fact_8_path__NE, fact_211_Set_Oset__insert, fact_246_sumE, fact_177_List_Oinsert__def, fact_30_last_Osimps, fact_188_not__arg__cong__Inr, fact_64_list_Oset__intros_I1_J, fact_173_in__set__insert, help_If_2_1_T, fact_149_inItr__root__in, fact_150_subtr__inItr, fact_89_sublists_Osimps_I1_J, fact_94_less__eq__set__def, fact_203_subset__insertI, fact_18_old_Osum_Oinject_I2_J, fact_11_path__post, fact_212_insertI2, fact_125_subsetD, fact_80_subtr_Osimps, fact_83_subtr__inductL, fact_45_Collect__mem__eq, fact_247_old_Osum_Odistinct_I1_J, fact_151_inItr__mono, fact_39_splice_Oinduct, fact_166_pred__subset__eq, fact_179_remove__code_I2_J, fact_58_regular__subtr, fact_224_subtr2_Ocases, fact_233_inFr_Oinducts, fact_57_set__subset__Cons, fact_221_subtr2_Oinducts, fact_175_insert__Nil, fact_49_regular__def2, fact_206_mk__disjoint__insert, fact_128_subset__eq, fact_95_distinct__length__2__or__more, fact_146_rev__predicate1D, fact_174_distinct__insert, fact_126_subsetCE, fact_229_old_Osum_Osimps_I7_J, fact_0_reg__root, fact_214_insertE, fact_27_tr2__tr1, fact_205_subtr2__trans, fact_70_reg__subtr, fact_96_distinct_Osimps_I1_J, fact_97_distinct__singleton, fact_194_insert__iff, fact_72_list_Oset__sel_I1_J, fact_67_subtr_ORefl, fact_28_last__ConsR, fact_204_subset__insertI2, fact_208_insert__eq__iff, fact_75_path__subtr, fact_55_root__Node, fact_254_inFr2_Osimps, fact_32_not__Cons__self2, fact_23_list_OdiscI, fact_43_old_Osum_Osimps_I8_J, fact_48_Node__root__cont, fact_223_subtr2_Osimps, fact_136_subset__trans, fact_249_sum_Odistinct_I1_J, fact_200_subtr2__mono, fact_22_list_Odistinct_I1_J, fact_201_insert__mono, fact_16_reg__Inr__cont, fact_209_insert__absorb, fact_44_mem__Collect__eq, fact_248_old_Osum_Odistinct_I2_J, fact_31_list_Osel_I1_J, fact_142_hsubst__r__def, fact_243_split__sum__all, fact_185_subset__CollectI, fact_217_subtr__subtr2, fact_124_in__mono, fact_172_not__in__set__insert, fact_46_Collect__cong, fact_123_set__mp, fact_38_transpose_Ocases
% 147.60/90.49 % No. of inferences in proof: 436
% 147.60/90.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 89977 ms resp. 89324 ms w/o parsing
% 148.48/90.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 148.48/90.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------