TSTP Solution File: LCL776_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL776_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:37 EDT 2023
% Result : Theorem 8.30s 2.97s
% Output : Refutation 8.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 141
% Syntax : Number of formulae : 250 ( 87 unt; 34 typ; 0 def)
% Number of atoms : 699 ( 392 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 4418 ( 86 ~; 25 |; 126 &;3984 @)
% ( 31 <=>; 166 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 12 con; 0-5 aty)
% Number of variables : 759 ( 0 ^; 694 !; 44 ?; 759 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_type,type,
it: fun @ dB @ bool ).
thf(beta_type,type,
beta: fun @ dB @ ( fun @ dB @ bool ) ).
thf(abs_type,type,
abs: dB > dB ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(step1_type,type,
step1:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ bool ) ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(listsp_type,type,
listsp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(sublist_type,type,
sublist:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ nat @ bool ) > ( list @ TA ) ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(i_type,type,
i: nat ).
thf(r_type,type,
r: dB ).
thf(s_type,type,
s: dB ).
thf(ss_type,type,
ss: list @ dB ).
thf(9,axiom,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_sublist__nil) ).
thf(142,plain,
! [TA: $tType,A: fun @ nat @ bool] :
( ( sublist @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(61,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_beta__cases_I2_J) ).
thf(376,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ A ) )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_append__Nil2) ).
thf(569,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_list_Oinject) ).
thf(365,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(57,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_append__eq__Cons__conv) ).
thf(347,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) ) )
& ( ( ( ( D
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ B @ A ) ) )
| ? [E: list @ TA] :
( ( D
= ( cons @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) ) )
=> ( ( append @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(70,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Var__apps__eq__Var__apps__conv) ).
thf(408,plain,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_appR) ).
thf(217,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(47,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Beta) ).
thf(308,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) ) )
=> ( ( pp @ ( aa @ dB @ bool @ it @ B ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= B )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_append__self__conv) ).
thf(417,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= B )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( append @ TA @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(92,axiom,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_head__Var__reduction) ).
thf(565,plain,
! [A: dB,B: list @ dB,C: nat] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) ) @ A ) )
=> ? [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
& ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_not__step1__Nil) ).
thf(184,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(110,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(87,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(542,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(106,axiom,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( step1 @ dB @ beta @ C @ B )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_apps__preserves__betas) ).
thf(638,plain,
! [A: dB,B: list @ dB,C: list @ dB] :
( ( step1 @ dB @ beta @ C @ B )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ A @ C ) ) @ ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(52,axiom,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ s ) @ ( var @ i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(325,plain,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ s ) @ ( var @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_foldl__fun__comm) ).
thf(152,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ! [E: TA,F: TA,G: TB] :
( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ E ) ) @ F )
= ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ G ) @ F ) ) @ E ) )
=> ( ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ ( foldl @ TB @ TA @ D @ C @ B ) ) @ A )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sublist__singleton) ).
thf(147,plain,
! [TA: $tType,A: TA,B: fun @ nat @ bool] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ B )
=> ( ( sublist @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= ( nil @ TA ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_append__is__Nil__conv) ).
thf(453,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= ( nil @ TA ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( append @ TA @ B @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list_Oexhaust) ).
thf(248,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)],[35]) ).
thf(62,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_subst__App) ).
thf(380,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(23,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list_Osimps_I3_J) ).
thf(201,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ E @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
=> ( ( ( step1 @ TA @ E @ D @ B )
& ( C = A ) )
| ( ( D = B )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Snoc__step1__SnocD) ).
thf(534,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ E @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
=> ( ( ( step1 @ TA @ E @ D @ B )
& ( C = A ) )
| ( ( D = B )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(99,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_subst__eq) ).
thf(598,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(91,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_dB_Osimps_I7_J) ).
thf(561,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(74,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dB_Osimps_I2_J) ).
thf(429,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(31,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_dB_Osimps_I3_J) ).
thf(229,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
pp @ ( aa @ dB @ bool @ it @ s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(329,plain,
pp @ ( aa @ dB @ bool @ it @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(79,axiom,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_IT_OVar) ).
thf(461,plain,
! [A: nat,B: list @ dB] :
( ( listsp @ dB @ it @ B )
=> ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( var @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_not__Nil__step1) ).
thf(317,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ ( fun @ TA @ bool )] :
~ ( step1 @ TA @ B @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( ( step1 @ TA @ E @ D @ C )
& ( B = A ) )
| ( ( D = C )
& ( step1 @ TA @ E @ B @ A ) ) )
=> ( step1 @ TA @ E @ ( append @ TA @ D @ B ) @ ( append @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_append__step1I) ).
thf(388,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( ( step1 @ TA @ E @ D @ C )
& ( B = A ) )
| ( ( D = C )
& ( step1 @ TA @ E @ B @ A ) ) )
=> ( step1 @ TA @ E @ ( append @ TA @ D @ B ) @ ( append @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_splice_Osimps_I3_J) ).
thf(169,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(103,axiom,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rev__induct) ).
thf(610,plain,
! [TA: $tType,A: list @ TA,B: fun @ ( list @ TA ) @ bool] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1,conjecture,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ s ) @ ( append @ dB @ ss @ ( cons @ dB @ ( var @ i ) @ ( nil @ dB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ s ) @ ( append @ dB @ ss @ ( cons @ dB @ ( var @ i ) @ ( nil @ dB ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ r ) ) @ s ) @ ( append @ dB @ ss @ ( cons @ dB @ ( var @ i ) @ ( nil @ dB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_abs) ).
thf(193,plain,
! [A: dB,B: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ A ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( abs @ B ) ) @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(67,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dB_Osimps_I4_J) ).
thf(398,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT) ).
thf(128,plain,
! [A: nat] : ( pp @ ( aa @ dB @ bool @ it @ ( var @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_subst__Var__IT) ).
thf(237,plain,
! [A: nat,B: nat,C: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ C ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( subst @ C @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(73,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dB_Osimps_I5_J) ).
thf(425,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(100,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__Nil) ).
thf(601,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(72,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_apps__preserves__beta) ).
thf(423,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ A ) ) @ ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(68,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Var__apps__neq__Abs__apps) ).
thf(402,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(43,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ D @ E ) @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ B @ E ) )
=> ~ ( step1 @ TA @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Cons__step1E) ).
thf(286,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ A ) )
=> ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ D @ E ) @ B ) ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ B @ E ) )
=> ~ ( step1 @ TA @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(96,axiom,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_beta) ).
thf(579,plain,
! [A: dB,B: dB] : ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Abs__App__neq__Var__apps) ).
thf(118,plain,
! [A: list @ dB,B: nat,C: dB,D: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ D ) ) @ C )
!= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_dB_Osimps_I6_J) ).
thf(204,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_append__Nil) ).
thf(572,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( append @ TB @ ( aa @ TA @ ( list @ TB ) @ C @ B ) @ ( maps @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_maps__simps_I1_J) ).
thf(181,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( list @ TB )] :
( ( maps @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( append @ TB @ ( aa @ TA @ ( list @ TB ) @ C @ B ) @ ( maps @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(101,axiom,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_beta__cases_I1_J) ).
thf(604,plain,
! [A: dB,B: nat] :
~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( var @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(69,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_subst__preserves__beta) ).
thf(406,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ D ) @ C ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(15,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ B @ A )
= A )
<=> ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_append__self__conv2) ).
thf(172,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( append @ TA @ B @ A )
= A )
=> ( B
= ( nil @ TA ) ) )
& ( ( B
= ( nil @ TA ) )
=> ( ( append @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( cons @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( cons @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Cons__eq__appendI) ).
thf(219,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: TA] :
( ( ( cons @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( cons @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_foldl__Nil) ).
thf(274,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ TA )] :
( ( foldl @ TA @ TB @ B @ A @ ( nil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_foldl__Cons) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( aa @ TA @ TB @ ( aa @ TB @ ( fun @ TA @ TB ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(25,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_appL) ).
thf(208,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ B ) )
=> ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89,axiom,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ r @ s @ ( zero_zero @ nat ) ) @ ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(552,plain,
pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ r @ s @ ( zero_zero @ nat ) ) @ ss ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ bool] :
( ( listsp @ TA @ C @ ( append @ TA @ B @ A ) )
<=> ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_append__in__listsp__conv) ).
thf(213,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ TA @ bool] :
( ( ( listsp @ TA @ C @ ( append @ TA @ B @ A ) )
=> ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) ) )
& ( ( ( listsp @ TA @ C @ B )
& ( listsp @ TA @ C @ A ) )
=> ( listsp @ TA @ C @ ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_list_Osimps_I5_J) ).
thf(251,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
<=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Cons__step1__Cons) ).
thf(155,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: fun @ TA @ ( fun @ TA @ bool )] :
( ( ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) ) )
& ( ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ E @ D ) @ B ) )
& ( A = C ) )
| ( ( B = D )
& ( step1 @ TA @ E @ C @ A ) ) )
=> ( step1 @ TA @ E @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_append__Cons) ).
thf(198,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( append @ TA @ ( cons @ TA @ C @ B ) @ A )
= ( cons @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(55,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
<=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Nil__is__append__conv) ).
thf(330,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( nil @ TA )
= ( append @ TA @ B @ A ) )
=> ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) ) )
& ( ( ( B
= ( nil @ TA ) )
& ( A
= ( nil @ TA ) ) )
=> ( ( nil @ TA )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8,axiom,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_beta__cases_I3_J) ).
thf(130,plain,
! [A: dB,B: dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_append__same__eq) ).
thf(223,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(46,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_listsp_ONil) ).
thf(306,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( listsp @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(438,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_not__Cons__self2) ).
thf(531,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_list_Osimps_I4_J) ).
thf(255,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dB_Osimps_I1_J) ).
thf(487,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(90,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_append1__eq__conv) ).
thf(553,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(10,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Lambda) ).
thf(145,plain,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( pp @ ( aa @ dB @ bool @ it @ ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(105,axiom,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_App__eq__foldl__conv) ).
thf(617,plain,
! [A: list @ dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) ) )
& ( ( ( ( A
= ( nil @ dB ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= B ) )
& ( ( A
!= ( nil @ dB ) )
=> ? [E: list @ dB] :
( ( A
= ( append @ dB @ E @ ( cons @ dB @ C @ ( nil @ dB ) ) ) )
& ( D
= ( foldl @ dB @ dB @ app @ B @ E ) ) ) ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(84,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
<=> ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Cons__eq__append__conv) ).
thf(516,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
=> ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) )
& ( ( ( ( B
= ( nil @ TA ) )
& ( ( cons @ TA @ D @ C )
= A ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) )
=> ( ( cons @ TA @ D @ C )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(107,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list_Osimps_I2_J) ).
thf(640,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(48,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_dB_Osimps_I9_J) ).
thf(310,plain,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(76,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Abs__apps__eq__Abs__apps__conv) ).
thf(441,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( listsp @ TA @ B @ A )
<=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_listsp_Osimps) ).
thf(585,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( listsp @ TA @ B @ A )
=> ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) ) )
& ( ( ( A
= ( nil @ TA ) )
| ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ( listsp @ TA @ B @ D ) ) )
=> ( listsp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
<=> ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_append__eq__append__conv2) ).
thf(463,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) )
=> ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) ) )
& ( ? [E: list @ TA] :
( ( ( D
= ( append @ TA @ B @ E ) )
& ( ( append @ TA @ E @ C )
= A ) )
| ( ( ( append @ TA @ D @ E )
= B )
& ( C
= ( append @ TA @ E @ A ) ) ) )
=> ( ( append @ TA @ D @ C )
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(56,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Abs__eq__apps__conv) ).
thf(338,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( abs @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( abs @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(108,axiom,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_dB_Osize_I4_J) ).
thf(643,plain,
! [A: nat] :
( ( size_size @ dB @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(104,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( append @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_append__eq__appendI) ).
thf(613,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ E @ D )
= C )
=> ( ( B
= ( append @ TA @ D @ A ) )
=> ( ( append @ TA @ E @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(64,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(386,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(49,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dB_Osize_I1_J) ).
thf(314,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(77,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rev__cases) ).
thf(450,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(97,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_dB_Osimps_I8_J) ).
thf(581,plain,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
! [A: dB] :
( ( pp @ ( aa @ dB @ bool @ it @ A ) )
<=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_IT_Osimps) ).
thf(495,plain,
! [A: dB] :
( ( ( pp @ ( aa @ dB @ bool @ it @ A ) )
=> ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) ) )
& ( ( ? [B: list @ dB,C: nat] :
( ( A
= ( foldl @ dB @ dB @ app @ ( var @ C ) @ B ) )
& ( listsp @ dB @ it @ B ) )
| ? [B: dB] :
( ( A
= ( abs @ B ) )
& ( pp @ ( aa @ dB @ bool @ it @ B ) ) )
| ? [B: dB,C: dB,D: list @ dB] :
( ( A
= ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ C ) @ D ) )
& ( pp @ ( aa @ dB @ bool @ it @ ( foldl @ dB @ dB @ app @ ( subst @ B @ C @ ( zero_zero @ nat ) ) @ D ) ) )
& ( pp @ ( aa @ dB @ bool @ it @ C ) ) ) )
=> ( pp @ ( aa @ dB @ bool @ it @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rotate1__is__Nil__conv) ).
thf(319,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( rotate1 @ TA @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(39,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( subst @ D @ E @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_apps__betasE) ).
thf(258,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A ) )
=> ( ! [D: dB] :
( ( pp @ ( aa @ dB @ bool @ ( aa @ dB @ ( fun @ dB @ bool ) @ beta @ C ) @ D ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ D @ B ) ) )
=> ( ! [D: list @ dB] :
( ( step1 @ dB @ beta @ B @ D )
=> ( A
!= ( foldl @ dB @ dB @ app @ C @ D ) ) )
=> ~ ! [D: dB] :
( ( C
= ( abs @ D ) )
=> ! [E: dB,F: list @ dB] :
( ( B
= ( cons @ dB @ E @ F ) )
=> ( A
!= ( foldl @ dB @ dB @ app @ ( subst @ D @ E @ ( zero_zero @ nat ) ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_apps__eq__tail__conv) ).
thf(186,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(81,axiom,
! [A: list @ dB,B: dB,C: nat] :
( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
<=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Var__eq__apps__conv) ).
thf(478,plain,
! [A: list @ dB,B: dB,C: nat] :
( ( ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) )
=> ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) ) )
& ( ( ( ( var @ C )
= B )
& ( A
= ( nil @ dB ) ) )
=> ( ( var @ C )
= ( foldl @ dB @ dB @ app @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_not__Cons__self) ).
thf(383,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_rotate__simps) ).
thf(300,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA] :
( ( ( rotate1 @ TB @ ( nil @ TB ) )
= ( nil @ TB ) )
& ( ( rotate1 @ TA @ ( cons @ TA @ B @ A ) )
= ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(60,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_splice__Nil2) ).
thf(373,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(26,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( append @ dB @ B @ ( cons @ dB @ A @ ( nil @ dB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_app__last) ).
thf(210,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ C @ B ) ) @ A )
= ( foldl @ dB @ dB @ app @ C @ ( append @ dB @ B @ ( cons @ dB @ A @ ( nil @ dB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_maps__simps_I2_J) ).
thf(326,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(44,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( append @ TA @ A @ B ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_self__append__conv2) ).
thf(294,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( append @ TA @ A @ B ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(21,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(195,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_splice_Osimps_I1_J) ).
thf(283,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_rev__exhaust2) ).
thf(239,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(34,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B
= ( append @ TA @ B @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_self__append__conv) ).
thf(242,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( B
= ( append @ TA @ B @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( B
= ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( append @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( foldl @ TB @ TA @ D @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_foldl__append) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TA,C: TB,D: fun @ TB @ ( fun @ TA @ TB )] :
( ( foldl @ TB @ TA @ D @ C @ ( append @ TA @ B @ A ) )
= ( foldl @ TB @ TA @ D @ ( foldl @ TB @ TA @ D @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(95,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( append @ TA @ ( nil @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_eq__Nil__appendI) ).
thf(575,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( B = A )
=> ( B
= ( append @ TA @ ( nil @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_splice_Osimps_I2_J) ).
thf(178,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_same__append__eq) ).
thf(277,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( append @ TA @ C @ B )
= ( append @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_append__assoc) ).
thf(607,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ C @ B ) @ A )
= ( append @ TA @ C @ ( append @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(4,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__reorient) ).
thf(111,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,axiom,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ ( subst @ r @ s @ ( zero_zero @ nat ) ) @ ss ) ) @ ( var @ i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(254,plain,
pp @ ( aa @ dB @ bool @ it @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( foldl @ dB @ dB @ app @ ( subst @ r @ s @ ( zero_zero @ nat ) ) @ ss ) ) @ ( var @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_neq__Nil__conv) ).
thf(122,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
<=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_apps__eq__Abs__conv) ).
thf(543,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) )
=> ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) ) )
& ( ( ( C
= ( abs @ A ) )
& ( B
= ( nil @ dB ) ) )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(646,plain,
$false,
inference(e,[status(thm)],[142,376,569,365,347,408,217,308,417,565,184,110,542,638,325,152,147,453,248,380,201,534,598,561,429,229,329,461,317,388,169,610,109,193,398,128,237,425,601,423,402,286,579,118,204,572,181,604,406,172,219,274,362,208,552,213,251,155,198,330,130,223,306,438,531,255,487,553,145,617,516,640,310,441,585,463,338,643,613,386,314,450,581,495,319,258,186,478,383,300,373,210,326,294,195,283,239,242,395,575,178,277,607,111,254,122,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL776_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n018.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 16:19:58 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.93/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.08 % [INFO] Parsing done (208ms).
% 1.73/1.09 % [INFO] Running in sequential loop mode.
% 2.25/1.29 % [INFO] eprover registered as external prover.
% 2.25/1.29 % [INFO] cvc4 registered as external prover.
% 2.25/1.30 % [INFO] Scanning for conjecture ...
% 2.58/1.40 % [INFO] Found a conjecture and 106 axioms. Running axiom selection ...
% 2.80/1.48 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 3.26/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.26/1.64 % [INFO] Type checking passed.
% 3.26/1.65 % [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 ...
% 8.30/2.97 % External prover 'e' found a proof!
% 8.30/2.97 % [INFO] Killing All external provers ...
% 8.30/2.97 % Time passed: 2448ms (effective reasoning time: 1872ms)
% 8.30/2.97 % 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)>
% 8.30/2.97 % Axioms used in derivation (106): fact_56_dB_Osize_I1_J, fact_96_splice__Nil2, fact_86_Cons__step1E, conj_2, fact_64_listsp_Osimps, fact_57_IT_OVar, fact_33_list_Osimps_I3_J, fact_73_apps__preserves__beta, fact_92_foldl__fun__comm, fact_52_rev__cases, fact_68_appR, fact_38_append__Nil, fact_19_dB_Osimps_I1_J, fact_9_App__eq__foldl__conv, fact_98_list_Osimps_I5_J, fact_91_maps__simps_I2_J, conj_3, fact_62_sublist__nil, fact_78_apps__betasE, fact_7_Var__apps__eq__Var__apps__conv, fact_28_foldl__append, fact_51_Abs__App__neq__Var__apps, fact_5_Var__eq__apps__conv, fact_75_mem__def, fact_95_splice_Osimps_I1_J, fact_20_dB_Osimps_I3_J, fact_35_Cons__eq__appendI, fact_0_Var__IT, fact_37_append__Nil2, fact_87_rev__exhaust2, fact_32_append__eq__append__conv2, fact_15_append__same__eq, fact_41_dB_Osimps_I5_J, fact_84_append__step1I, fact_39_foldl__Cons, fact_36_eq__Nil__appendI, fact_14_list_Oinject, fact_43_dB_Osimps_I8_J, fact_44_dB_Osimps_I9_J, fact_97_list_Osimps_I4_J, fact_3_Abs__eq__apps__conv, fact_74_ext, fact_25_self__append__conv2, fact_22_append__self__conv2, fact_59_sublist__singleton, fact_50_Var__apps__neq__Abs__apps, fact_54_list_Oexhaust, fact_40_foldl__Nil, fact_49_append__eq__Cons__conv, fact_30_not__Cons__self, fact_93_splice_Osimps_I2_J, fact_10_app__last, fact_6_Abs__apps__eq__Abs__apps__conv, fact_66_beta, fact_34_list_Osimps_I2_J, fact_8_append1__eq__conv, fact_12_subst__App, fact_53_rev__induct, fact_90_rotate1__is__Nil__conv, fact_4_apps__eq__Abs__conv, fact_85_Snoc__step1__SnocD, fact_17_append__assoc, fact_31_append__eq__appendI, fact_13_apps__eq__tail__conv, fact_89_maps__simps_I1_J, fact_24_append__is__Nil__conv, fact_55_neq__Nil__conv, fact_47_subst__eq, fact_21_append__Cons, arity_Nat_Onat___Groups_Ozero, fact_69_beta__cases_I1_J, fact_82_not__step1__Nil, fact_58_insert__Nil, fact_29_not__Cons__self2, fact_42_dB_Osimps_I4_J, fact_2_Beta, fact_1_subst__Var__IT, fact_80_head__Var__reduction, fact_71_subst__preserves__beta, fact_27_Nil__is__append__conv, fact_67_appL, fact_94_splice_Osimps_I3_J, fact_18_dB_Osimps_I2_J, fact_45_dB_Osimps_I6_J, conj_1, fact_11_Lambda, fact_63_zero__reorient, fact_70_abs, fact_81_Cons__step1__Cons, fact_26_self__append__conv, fact_88_rotate__simps, fact_61_append__in__listsp__conv, fact_65_IT_Osimps, fact_48_Cons__eq__append__conv, help_pp_1_1_U, fact_77_dB_Osize_I4_J, fact_16_same__append__eq, fact_79_apps__preserves__betas, fact_83_not__Nil__step1, conj_0, fact_23_append__self__conv, help_pp_2_1_U, fact_60_listsp_ONil, fact_76_beta__cases_I3_J, fact_46_dB_Osimps_I7_J, fact_72_beta__cases_I2_J
% 8.30/2.97 % No. of inferences in proof: 216
% 8.30/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2448 ms resp. 1872 ms w/o parsing
% 8.64/3.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.64/3.07 % [INFO] Killing All external provers ...
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