%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL774_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:52:50 AM UTC 2026
% Result : Theorem 8.72s 2.65s
% Output : Refutation 9.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 110
% Syntax : Number of formulae : 222 ( 118 unt; 0 typ; 0 def)
% Number of atoms : 637 ( 304 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 3784 ( 50 ~; 12 |; 66 &;3507 @)
% ( 21 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 9 con; 0-5 aty)
% Number of variables : 546 ( 0 ^; 526 !; 20 ?; 546 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(beta_decl,type,
beta: dB > dB > $o ).
thf(abs_decl,type,
abs: dB > dB ).
thf(app_decl,type,
app: dB @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_rec_decl,type,
dB_rec:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( TA @ fun ) @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB > nat > dB ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB > dB > nat > dB ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(i_decl,type,
i: nat ).
thf(r_decl,type,
r: dB ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(4,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Zero__not__Suc) ).
thf(115,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add__Suc__right) ).
thf(379,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(6,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Suc__not__Zero) ).
thf(120,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zero__induct) ).
thf(247,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(72,axiom,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Var__apps__eq__Var__apps__conv) ).
thf(385,plain,
! [A: dB @ list,B: nat,C: dB @ list,D: nat] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(89,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_dB_Osimps_I8_J) ).
thf(472,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(61,axiom,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__IT) ).
thf(340,plain,
! [A: nat] : ( A @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat_Oexhaust) ).
thf(185,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_apps__preserves__beta) ).
thf(288,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(53,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_dB_Orecs_I1_J) ).
thf(301,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Zero__neq__Suc) ).
thf(189,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(37,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_dB_Osimps_I5_J) ).
thf(228,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__zero__sym) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(33,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_substn__subst__n) ).
thf(216,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(82,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(443,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
<=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_one__is__add) ).
thf(253,plain,
! [A: nat,B: nat] :
( ( ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) )
=> ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ) )
& ( ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__0__left) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_substn__subst__0) ).
thf(147,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ subst ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_appL) ).
thf(293,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( A @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dB_Osimps_I7_J) ).
thf(512,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(81,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_dB_Osimps_I4_J) ).
thf(439,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_dB_Osize_I2_J) ).
thf(270,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(103,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
<=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_IT_Osimps) ).
thf(529,plain,
! [A: dB] :
( ( ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) )
=> ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
& ( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( D @ ( C @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
| ? [B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( A
= ( B @ abs ) ) )
| ? [B: dB @ list,C: nat] :
( ( B @ ( it @ ( dB @ listsp ) ) )
& ( A
= ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(59,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__App) ).
thf(334,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_dB_Osimps_I1_J) ).
thf(429,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zero__reorient) ).
thf(137,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(87,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_subst__eq) ).
thf(467,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(93,axiom,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Abs__App__neq__Var__apps) ).
thf(484,plain,
! [A: dB @ list,B: nat,C: dB,D: dB] :
( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_double__eq__0__iff) ).
thf(522,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__0) ).
thf(551,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(56,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dB_Osimps_I6_J) ).
thf(324,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__left__imp__eq) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__0__right) ).
thf(519,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(74,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_dB_Osimps_I2_J) ).
thf(403,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(57,axiom,
! [A: dB] :
( ( A @ abs @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dB_Osize_I3_J) ).
thf(328,plain,
! [A: dB] :
( ( A @ abs @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ semigroup_add )
=> ! [A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_foldl__assoc) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ semigroup_add )
=> ! [A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(105,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_substn_Osimps_I2_J) ).
thf(554,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(28,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_beta__cases_I2_J) ).
thf(193,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__eq__self__zero) ).
thf(476,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(7,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lift__preserves__beta) ).
thf(124,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( TA @ fun ) @ ( dB @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Orecs_I2_J) ).
thf(225,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( TA @ fun ) @ ( dB @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_foldl__Nil) ).
thf(173,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Suc__inject) ).
thf(129,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_subst__preserves__beta) ).
thf(134,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Nat_Oadd__0__right) ).
thf(343,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(40,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Abs__eq__apps__conv) ).
thf(237,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) )
=> ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ abs )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(176,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__right__imp__eq) ).
thf(579,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(46,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dB_Osimps_I9_J) ).
thf(281,plain,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(75,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_subst__Var__IT) ).
thf(413,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_foldl__absorb0) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(71,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_plus__nat_Oadd__0) ).
thf(382,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nat__add__left__cancel) ).
thf(498,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(24,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(181,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero @ suc ) )
<=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__is__1) ).
thf(350,plain,
! [A: nat,B: nat] :
( ( ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero @ suc ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero @ suc ) )
=> ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero ) ) )
| ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(3,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_listsp_ONil) ).
thf(113,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Suc__n__not__n) ).
thf(219,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Suc__shift) ).
thf(419,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(98,axiom,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dB_Osimps_I12_J) ).
thf(509,plain,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_nat__add__commute) ).
thf(367,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_liftn__0) ).
thf(213,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(92,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(483,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(42,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_lift__IT) ).
thf(251,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ lift ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subst__lift) ).
thf(155,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(198,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(85,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
<=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_apps__eq__Abs__conv) ).
thf(455,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ abs ) )
=> ( ( B
= ( dB @ nil ) )
& ( C
= ( A @ abs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(35,axiom,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_IT_OVar) ).
thf(223,plain,
! [A: nat,B: dB @ list] :
( ( B @ ( it @ ( dB @ listsp ) ) )
=> ( B @ ( A @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(108,axiom,
! [A: dB @ list,B: dB,C: nat] :
( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Var__eq__apps__conv) ).
thf(563,plain,
! [A: dB @ list,B: dB,C: nat] :
( ( ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) )
=> ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( A
= ( dB @ nil ) )
& ( ( C @ var )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(52,axiom,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_beta) ).
thf(299,plain,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ subst ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(19,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(162,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
i @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( i @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(112,plain,
~ ( i @ var @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__imp__eq) ).
thf(516,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
i @ var @ ( r @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(342,plain,
i @ var @ ( r @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(13,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_abs) ).
thf(145,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(106,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_lift_Osimps_I2_J) ).
thf(557,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(51,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__induct) ).
thf(295,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(15,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_n__not__Suc__n) ).
thf(150,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_nat_Osimps_I3_J) ).
thf(199,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(58,axiom,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dB_Orecs_I3_J) ).
thf(331,plain,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(67,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_beta__cases_I1_J) ).
thf(370,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(23,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Suc__neq__Zero) ).
thf(177,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ lift ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_liftn__lift) ).
thf(182,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ lift ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_appR) ).
thf(470,plain,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( B @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(110,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_dB_Osimps_I10_J) ).
thf(576,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(16,axiom,
nat @ semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Osemigroup__add) ).
thf(154,plain,
nat @ semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(55,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Abs__apps__eq__Abs__apps__conv) ).
thf(314,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( C @ ( D @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(86,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Beta) ).
thf(465,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ subst ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(31,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osimps_I3_J) ).
thf(203,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_add__is__0) ).
thf(304,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(18,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat_Osimps_I2_J) ).
thf(158,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(77,axiom,
r @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(418,plain,
r @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(39,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Lambda) ).
thf(235,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(64,axiom,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Var__apps__neq__Abs__apps) ).
thf(346,plain,
! [A: dB @ list,B: dB,C: dB @ list,D: nat] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(49,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_dB_Osimps_I11_J) ).
thf(290,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( C @ ( D @ ( E @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(119,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_add__left__cancel) ).
thf(422,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(45,axiom,
! [A: dB,B: dB @ list,C: dB] :
( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_apps__eq__tail__conv) ).
thf(273,plain,
! [A: dB,B: dB @ list,C: dB] :
( ( ( C = A )
=> ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( B @ ( A @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat__add__left__commute) ).
thf(373,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__Suc) ).
thf(506,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add_Ocomm__neutral) ).
thf(415,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(8,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_not0__implies__Suc) ).
thf(126,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(136,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nat__add__right__cancel) ).
thf(395,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_nat_Oinject) ).
thf(163,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_nat__add__assoc) ).
thf(337,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(107,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_liftn_Osimps_I2_J) ).
thf(560,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_add__right__cancel) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(38,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_dB_Osize_I1_J) ).
thf(232,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(588,plain,
$false,
inference(e,[status(thm)],[573,115,379,120,247,385,472,340,185,288,301,189,228,448,216,443,376,253,480,147,293,512,439,270,529,334,429,137,467,484,522,551,324,285,519,403,328,488,554,193,476,124,225,173,129,134,343,237,176,579,281,413,445,382,498,181,350,113,219,419,509,367,213,483,251,155,198,455,223,563,299,162,112,516,342,145,557,295,150,199,331,370,177,182,470,576,154,314,465,203,304,158,418,235,346,290,119,422,273,373,506,415,126,136,395,163,337,560,491,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL774_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n006.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 23:32:26 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.95/0.88 % [INFO] Parsing done (176ms).
% 0.95/0.89 % [INFO] Running in sequential loop mode.
% 1.89/1.09 % [INFO] eprover registered as external prover.
% 1.89/1.09 % [INFO] Scanning for conjecture ...
% 2.16/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 2.30/1.25 % [INFO] Axiom selection finished. Selected 109 axioms (removed 0 axioms).
% 2.74/1.39 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.17/1.41 % [INFO] Type checking passed.
% 3.17/1.41 % [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 ...
% 8.72/2.64 % External prover 'e' found a proof!
% 8.72/2.65 % [INFO] Killing All external provers ...
% 8.72/2.65 % Time passed: 2146ms (effective reasoning time: 1752ms)
% 8.72/2.65 % 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)>
% 8.72/2.65 % Axioms used in derivation (109): fact_34_dB_Osimps_I8_J, fact_74_foldl__assoc, fact_19_Var__eq__apps__conv, fact_51_Zero__neq__Suc, fact_56_zero__induct, fact_71_beta__cases_I1_J, fact_58_dB_Osize_I3_J, fact_53_foldl__Nil, fact_32_dB_Orecs_I3_J, fact_88_add_Ocomm__neutral, fact_62_add__left__cancel, fact_82_nat__add__left__commute, fact_59_dB_Osize_I2_J, fact_96_double__eq__0__iff, fact_85_add__0, fact_61_add__right__cancel, fact_9_dB_Osimps_I11_J, fact_94_add__is__1, fact_78_add__imp__eq, fact_27_dB_Osimps_I3_J, fact_25_dB_Orecs_I1_J, fact_37_liftn__0, fact_47_Zero__not__Suc, fact_38_dB_Osimps_I12_J, fact_69_appL, fact_40_IT_Osimps, fact_68_add__Suc, fact_5_subst__Var__IT, fact_0_Var__IT, fact_24_substn__subst__0, fact_1_dB_Osimps_I1_J, fact_79_add__left__imp__eq, fact_18_substn__subst__n, fact_92_foldl__absorb0, arity_Nat_Onat___Groups_Ocomm__monoid__add, arity_Nat_Onat___Groups_Osemigroup__add, fact_3_dB_Osimps_I4_J, fact_90_add__Suc__shift, fact_2_dB_Osimps_I2_J, fact_50_nat_Osimps_I3_J, fact_17_subst__eq, fact_93_one__is__add, fact_89_Nat_Oadd__0__right, fact_26_dB_Orecs_I2_J, fact_7_dB_Osimps_I10_J, fact_39_listsp_ONil, fact_67_add__Suc__right, fact_73_ext, fact_6_lift__IT, fact_75_subst__preserves__beta, fact_77_add__right__imp__eq, fact_49_Suc__not__Zero, fact_72_abs, fact_41_nat_Oinject, fact_8_Var__apps__eq__Var__apps__conv, fact_16_subst__lift, fact_22_liftn__lift, fact_70_appR, fact_84_add__0__left, fact_54_not0__implies__Suc, fact_4_dB_Osimps_I5_J, fact_13_apps__eq__tail__conv, fact_76_lift__preserves__beta, fact_60_beta, fact_35_dB_Osimps_I7_J, fact_45_Suc__n__not__n, fact_63_nat__add__right__cancel, arity_Nat_Onat___Groups_Ozero, fact_10_substn_Osimps_I2_J, fact_23_Abs__apps__eq__Abs__apps__conv, fact_86_plus__nat_Oadd__0, fact_48_nat_Osimps_I2_J, fact_81_ab__semigroup__add__class_Oadd__ac_I1_J, fact_31_Beta, fact_57_nat_Oexhaust, fact_30_Abs__eq__apps__conv, fact_80_nat__add__assoc, conj_1, fact_55_nat__induct, fact_87_add__0__right, fact_43_zero__reorient, fact_11_IT_OVar, fact_28_Lambda, fact_46_Suc__inject, fact_36_dB_Osimps_I6_J, fact_33_dB_Osimps_I9_J, fact_21_Abs__App__neq__Var__apps, fact_44_n__not__Suc__n, fact_66_add__is__0, fact_64_nat__add__left__cancel, help_pp_1_1_U, fact_20_Var__apps__neq__Abs__apps, fact_83_nat__add__commute, arity_Nat_Onat___Groups_Omonoid__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_95_beta__cases_I2_J, fact_65_double__zero__sym, fact_14_subst__App, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_42_dB_Osize_I1_J, conj_0, help_pp_2_1_U, fact_15_lift_Osimps_I2_J, fact_29_apps__eq__Abs__conv, fact_52_Suc__neq__Zero, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_12_liftn_Osimps_I2_J, fact_97_apps__preserves__beta, fact_91_add__eq__self__zero
% 8.72/2.65 % No. of inferences in proof: 222
% 8.72/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2146 ms resp. 1752 ms w/o parsing
% 9.72/2.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.72/2.81 % [INFO] Killing All external provers ...
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