%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL800_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 : n019.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 07:52:59 AM UTC 2026
% Result : Theorem 8.74s 8.64s
% Output : Refutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 104
% Syntax : Number of formulae : 210 ( 136 unt; 0 typ; 0 def)
% Number of atoms : 416 ( 267 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2013 ( 53 ~; 9 |; 43 &;1790 @)
% ( 20 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 11 con; 0-5 aty)
% Number of variables : 508 ( 0 ^; 500 !; 8 ?; 508 :)
% 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(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 > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(it_decl,type,
it: dB > $o ).
thf(app_decl,type,
app: dB > dB > dB ).
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(listMem_decl,type,
listMem:
!>[TA: $tType] : ( TA > ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(member1_decl,type,
member1:
!>[TA: $tType] : ( ( TA @ list ) > TA > $o ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: dB ).
thf(as_decl,type,
as: dB @ list ).
thf(i_decl,type,
i: nat ).
thf(n_decl,type,
n: nat ).
thf(rs_decl,type,
rs: dB @ list ).
thf(t_decl,type,
t: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_list_Osimps_I5_J) ).
thf(365,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(65,axiom,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_elem) ).
thf(389,plain,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(105,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_subst__lift) ).
thf(519,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(90,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ app ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_liftn_Osimps_I2_J) ).
thf(471,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( A @ ( B @ ( C @ app ) @ ( D @ liftn ) ) )
= ( A @ ( B @ ( D @ liftn ) ) @ ( A @ ( C @ ( D @ liftn ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(87,axiom,
( rs
= ( as @ ( a @ ( dB @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Cons) ).
thf(464,plain,
( rs
= ( as @ ( a @ ( dB @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(20,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Suc__not__Zero) ).
thf(170,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,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_65_nat__induct) ).
thf(217,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)],[29]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_double__zero__sym) ).
thf(379,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__Suc) ).
thf(269,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_splice_Osimps_I1_J) ).
thf(142,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ app ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dB_Osize_I2_J) ).
thf(500,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ app ) @ dB_size )
= ( nat @ zero_zero @ suc @ ( A @ dB_size @ ( B @ dB_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(77,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(436,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_null__rec_I1_J) ).
thf(257,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat__add__left__commute) ).
thf(174,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(69,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_neq__Nil__conv) ).
thf(404,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_list_Osimps_I3_J) ).
thf(421,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Ocomm__neutral) ).
thf(289,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(81,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_21_substn__subst__0) ).
thf(448,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)],[81]) ).
thf(18,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(164,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_nat_Oinject) ).
thf(321,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)],[51]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__right__imp__eq) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1,conjecture,
i @ ( u @ ( a @ subst ) ) @ ( u @ app ) @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( i @ ( u @ ( a @ subst ) ) @ ( u @ app ) @ it ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(106,plain,
~ ( i @ ( u @ ( a @ subst ) ) @ ( u @ app ) @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(93,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_dB_Osimps_I2_J) ).
thf(480,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) ) )
& ( ( ( C @ ( D @ app ) )
= ( A @ ( B @ app ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nat__add__commute) ).
thf(211,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_n__not__Suc__n) ).
thf(253,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) )
<=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_member__rec_I1_J) ).
thf(221,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 ) ) )
=> ( ( A @ ( B @ ( TA @ member1 ) ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_splice_Osimps_I2_J) ).
thf(132,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(70,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_list_Oexhaust) ).
thf(411,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zero__reorient) ).
thf(428,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)],[76]) ).
thf(40,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Suc__n__not__n) ).
thf(265,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_nat__add__assoc) ).
thf(307,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(44,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_66_zero__induct) ).
thf(292,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)],[44]) ).
thf(5,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_null__rec_I2_J) ).
thf(117,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(101,axiom,
ua @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(512,plain,
ua @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(53,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_list_Oinject) ).
thf(334,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_sublist__singleton) ).
thf(349,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(75,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_nat_Oexhaust) ).
thf(424,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Suc__inject) ).
thf(165,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Osimps_I1_J) ).
thf(229,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)],[31]) ).
thf(85,axiom,
t @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(461,plain,
t @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__right__cancel) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_sublist__nil) ).
thf(129,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(98,axiom,
n = i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_True) ).
thf(503,plain,
n = i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(100,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_dB_Osimps_I4_J) ).
thf(508,plain,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(102,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ app ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_lift_Osimps_I2_J) ).
thf(513,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ app ) @ lift ) )
= ( A @ ( B @ lift ) @ ( A @ ( C @ lift ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(17,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_34_dB_Orecs_I1_J) ).
thf(161,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)],[17]) ).
thf(13,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_member__rec_I2_J) ).
thf(149,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__is__0) ).
thf(180,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dB_Osize_I1_J) ).
thf(296,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_list_Osimps_I2_J) ).
thf(191,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(38,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dB_Osize_I4_J) ).
thf(259,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_insert) ).
thf(391,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(80,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_splice_Osimps_I3_J) ).
thf(445,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(96,axiom,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_subst__Var__IT) ).
thf(498,plain,
! [A: nat,B: nat,C: dB] :
( ( C @ it )
=> ( A @ ( B @ var @ ( C @ subst ) ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_substn_Osimps_I2_J) ).
thf(466,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ substn ) ) )
= ( A @ ( B @ ( C @ substn ) ) @ ( A @ ( B @ ( D @ substn ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Nat_Oadd__0__right) ).
thf(318,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(59,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_not__Cons__self2) ).
thf(362,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(82,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__eq) ).
thf(451,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(92,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 ) @ ( 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_36_dB_Orecs_I2_J) ).
thf(477,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 ) @ ( 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)],[92]) ).
thf(94,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ app ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_subst__App) ).
thf(494,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ app ) @ subst ) ) )
= ( A @ ( B @ ( C @ subst ) ) @ ( A @ ( B @ ( D @ subst ) ) @ app ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_list_Orecs_I1_J) ).
thf(155,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(86,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_lift__IT) ).
thf(462,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_List_Onull__def) ).
thf(135,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) )
& ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(299,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(99,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_28_substn__subst__n) ).
thf(505,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)],[99]) ).
thf(103,axiom,
nat @ zero_zero @ ( i @ ( u @ ( a @ subst ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ app ) @ subst ) ) @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
thf(516,plain,
nat @ zero_zero @ ( i @ ( u @ ( a @ subst ) ) @ ( nat @ zero_zero @ var @ ( nat @ zero_zero @ ( u @ lift ) @ app ) @ subst ) ) @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(57,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Zero__not__Suc) ).
thf(355,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(84,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ app ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_dB_Osize_I5_J) ).
thf(458,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ app ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_size ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( nat @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus ) ) ) )
<=> ( ( ( 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_83_one__is__add) ).
thf(194,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 @ zero_zero @ suc )
= ( A @ ( B @ ( nat @ plus_plus ) ) ) )
=> ( ( ( 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)],[26]) ).
thf(12,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_equal__Nil__null) ).
thf(145,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal ) ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(414,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_nat__add__left__cancel) ).
thf(310,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list_Orecs_I2_J) ).
thf(177,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(52,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_37_liftn__lift) ).
thf(331,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)],[52]) ).
thf(79,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Suc__neq__Zero) ).
thf(441,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__left__imp__eq) ).
thf(359,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(64,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_insert__Nil) ).
thf(386,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(95,axiom,
u @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(497,plain,
u @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(35,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_plus__nat_Oadd__0) ).
thf(250,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat__add__right__cancel) ).
thf(368,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(104,axiom,
! [A: nat] : ( A @ var @ it ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Var__IT) ).
thf(517,plain,
! [A: nat] : ( A @ var @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(16,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not0__implies__Suc) ).
thf(158,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_splice__Nil2) ).
thf(114,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(73,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_liftn__0) ).
thf(418,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_eq__Nil__null) ).
thf(119,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__eq__self__zero) ).
thf(246,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( 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_84_add__is__1) ).
thf(272,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 @ zero_zero @ suc ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( 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)],[42]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__Suc__shift) ).
thf(346,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_not__Cons__self) ).
thf(214,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(151,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__left__cancel) ).
thf(300,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__Suc__right) ).
thf(262,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(190,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_equal__list__def) ).
thf(107,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal ) ) ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_list_Osimps_I4_J) ).
thf(126,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(78,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat_Osimps_I3_J) ).
thf(437,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(91,axiom,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( 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_23_dB_Osimps_I11_J) ).
thf(474,plain,
! [TA: $tType,A: dB,B: dB,C: TA @ ( dB @ fun ),D: TA @ ( dB @ fun ) @ ( dB @ fun ),E: TA @ ( nat @ fun )] :
( ( A @ ( B @ app ) @ ( 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)],[91]) ).
thf(68,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat_Osimps_I2_J) ).
thf(400,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(72,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_22_dB_Osimps_I10_J) ).
thf(415,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)],[72]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__imp__eq) ).
thf(239,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(33,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Zero__neq__Suc) ).
thf(242,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(89,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ app ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_app__Var__IT) ).
thf(469,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ var @ ( B @ app ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ app ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dB_Osimps_I5_J) ).
thf(454,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ app ) )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(539,plain,
$false,
inference(e,[status(thm)],[365,389,519,471,464,170,217,379,269,142,500,436,257,174,404,421,289,448,164,321,376,106,480,211,253,221,132,411,428,265,307,292,117,512,334,349,424,165,229,461,393,129,503,343,508,513,161,149,180,296,191,259,391,445,498,466,318,362,451,477,494,155,462,135,299,505,516,355,458,194,145,414,310,177,331,441,359,386,497,250,368,517,158,114,418,119,246,272,346,214,151,300,262,190,107,126,437,474,400,415,239,242,469,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.13/5.40 % Computer : n019.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Fri Sep 25 23:36:24 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/5.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/6.29 % [INFO] Parsing done (301ms).
% 1.93/6.31 % [INFO] Running in sequential loop mode.
% 2.89/6.70 % [INFO] eprover registered as external prover.
% 2.89/6.71 % [INFO] Scanning for conjecture ...
% 3.07/6.85 % [INFO] Found a conjecture (or negated_conjecture) and 105 axioms. Running axiom selection ...
% 3.26/6.95 % [INFO] Axiom selection finished. Selected 103 axioms (removed 2 axioms).
% 3.83/7.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.83/7.16 % [INFO] Type checking passed.
% 3.83/7.16 % [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 ...
% 8.74/8.63 % External prover 'e' found a proof!
% 8.74/8.63 % [INFO] Killing All external provers ...
% 8.74/8.63 % Time passed: 3086ms (effective reasoning time: 2314ms)
% 8.74/8.63 % 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)>
% 8.74/8.64 % Axioms used in derivation (103): fact_93_ab__semigroup__add__class_Oadd__ac_I1_J, fact_37_liftn__lift, fact_75_add__right__cancel, fact_22_dB_Osimps_I10_J, fact_74_add__left__cancel, fact_33_null__rec_I1_J, fact_43_list_Osimps_I2_J, fact_54_neq__Nil__conv, fact_84_add__is__1, fact_11_lift_Osimps_I2_J, fact_71_dB_Osize_I2_J, fact_20_dB_Osize_I4_J, fact_24_substn_Osimps_I2_J, fact_67_nat_Oexhaust, fact_28_substn__subst__n, fact_8_app__Var__IT, fact_85_add__Suc__shift, fact_2_uIT, fact_62_nat_Osimps_I3_J, fact_48_splice_Osimps_I1_J, fact_92_equal__list__def, fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096, fact_73_mem__def, fact_56_n__not__Suc__n, fact_31_list_Orecs_I2_J, fact_36_dB_Orecs_I2_J, fact_14_subst__eq, fact_0__096IT_At_096, fact_44_list_Osimps_I3_J, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_89_nat__add__commute, fact_83_one__is__add, fact_78_double__zero__sym, fact_90_nat__add__left__commute, fact_9_dB_Osimps_I2_J, fact_3_True, fact_96_add__right__imp__eq, fact_50_eq__Nil__null, fact_94_add__left__imp__eq, fact_13_subst__lift, fact_61_Suc__not__Zero, fact_81_add__Suc__right, fact_87_Nat_Oadd__0__right, fact_30_splice_Osimps_I3_J, fact_77_nat__add__right__cancel, fact_60_nat_Osimps_I2_J, fact_88_add__eq__self__zero, fact_65_nat__induct, fact_63_Zero__neq__Suc, fact_82_dB_Osize_I5_J, fact_68_insert__Nil, fact_18_list_Oinject, fact_1_Var_I3_J, fact_52_nat_Oinject, fact_55_Suc__neq__Zero, fact_58_Suc__inject, fact_15_dB_Osimps_I4_J, fact_72_equal__Nil__null, fact_25_zero__reorient, fact_53_list_Oexhaust, fact_35_liftn__0, fact_7_subst__Var__IT, fact_19_dB_Osize_I1_J, fact_38_elem, arity_Nat_Onat___Groups_Ozero, fact_16_dB_Osimps_I5_J, fact_46_null__rec_I2_J, fact_86_plus__nat_Oadd__0, fact_12_Cons, fact_27_not__Cons__self, fact_49_splice__Nil2, fact_6_subst__App, fact_51_list_Orecs_I1_J, fact_23_dB_Osimps_I11_J, fact_80_add__Suc, fact_42_member__rec_I2_J, fact_32_liftn_Osimps_I2_J, fact_26_not__Cons__self2, fact_40_insert, fact_69_sublist__singleton, fact_21_substn__subst__0, fact_34_dB_Orecs_I1_J, fact_5_lift__IT, fact_79_add__is__0, fact_10_Var__IT, fact_29_list_Osimps_I5_J, fact_59_Zero__not__Suc, fact_76_nat__add__left__cancel, fact_95_add__imp__eq, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_39_member__rec_I1_J, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_91_nat__add__assoc, fact_64_not0__implies__Suc, fact_41_splice_Osimps_I2_J, fact_97_add_Ocomm__neutral, fact_66_zero__induct, fact_57_Suc__n__not__n, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_47_List_Onull__def, fact_45_list_Osimps_I4_J, fact_17_dB_Osimps_I1_J, fact_70_sublist__nil
% 8.74/8.64 % No. of inferences in proof: 210
% 8.74/8.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3086 ms resp. 2314 ms w/o parsing
% 9.36/8.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.36/8.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------