%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL759_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 07:52:45 AM UTC 2026
% Result : Theorem 247.49s 99.72s
% Output : Refutation 248.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 128
% Syntax : Number of formulae : 556 ( 297 unt; 0 typ; 9 def)
% Number of atoms : 2278 ( 770 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 13993 ( 440 ~; 225 |; 74 &;13087 @)
% ( 19 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 16 con; 0-5 aty)
% Number of variables : 1142 ( 11 ^;1073 !; 49 ?;1142 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
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(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
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_size_decl,type,
dB_size: dB > nat ).
thf(lift_decl,type,
lift: dB @ ( nat @ fun ) @ ( dB @ fun ) ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ).
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(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( 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(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(ia_decl,type,
ia: nat ).
thf(ja_decl,type,
ja: nat ).
thf(ra_decl,type,
ra: dB ).
thf(s_decl,type,
s: dB ).
thf(ss_decl,type,
ss: dB @ list ).
thf(sk1_decl,type,
sk1: nat > nat ).
thf(sk2_decl,type,
sk2: dB > dB > dB > $o ).
thf(sk3_decl,type,
sk3: dB > dB > dB > dB ).
thf(sk4_decl,type,
sk4: dB > dB > dB > dB ).
thf(sk5_decl,type,
sk5: dB > dB > dB > dB ).
thf(sk6_decl,type,
sk6: dB > dB ).
thf(sk9_decl,type,
sk9: nat > nat ).
thf(sk11_decl,type,
sk11: nat > nat ).
thf(sk20_decl,type,
sk20: dB > nat ).
thf(sk22_decl,type,
sk22: nat > nat ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: nat] :
@+[B: nat] :
( A
= ( B @ suc ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: dB,B: dB,C: dB] :
@+[D: dB] :
~ ( ( C
= ( nat @ zero_zero @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
=> ( A
!= ( D @ abs ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: dB,B: dB,C: dB] :
@+[D: dB] :
~ ( ( C
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( A @ beta ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: dB,B: dB,C: dB] :
@+[D: dB] :
~ ( ( C
= ( D @ ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: dB > dB] :
! [B: dB] :
( ( B @ abs @ A )
= B ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: nat > nat] :
! [B: nat] :
( ( B @ suc @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: nat > nat] :
! [B: nat] :
( ( B @ suc @ A )
= B ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: dB > nat] :
! [B: nat] :
( ( B @ var @ A )
= B ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: nat] :
@+[B: nat] :
( A
= ( B @ suc ) ) ) ) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_3_Var__apps__eq__Var__apps__conv) ).
thf(139,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)],[7]) ).
thf(140,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 ) ) ) ) ) ) )
& ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[139]) ).
thf(141,plain,
! [H: nat,G: dB @ list,F: nat,E: dB @ list,D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( ( ( G @ ( H @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
= ( E @ ( F @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) )
| ( G != E )
| ( H != F ) )
& ( ( C = A )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) )
& ( ( D = B )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( D = B )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[141]) ).
thf(145,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( D = B )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(34,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nat_Osimps_I2_J) ).
thf(273,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(274,plain,
~ ? [A: nat] :
( ( nat @ zero_zero )
= ( A @ suc ) ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(728,plain,
! [E: nat,D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( B
!= ( E @ suc ) )
| ( D
!= ( nat @ zero_zero ) )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[145,276]) ).
thf(729,plain,
! [D: nat,C: nat,B: dB @ list,A: dB @ list] :
( ( C
!= ( nat @ zero_zero ) )
| ( ( B @ ( C @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( D @ suc @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( A )),bind(B,$thf( F @ suc )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(1036,plain,
! [C: nat,B: dB @ list,A: dB @ list] :
( ( B @ ( nat @ zero_zero @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( C @ suc @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(simp,[status(thm)],[729]) ).
thf(49,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(320,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(321,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(cnf,[status(esa)],[320]) ).
thf(322,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(lifteq,[status(thm)],[321]) ).
thf(89,axiom,
! [A: dB,B: dB,C: nat] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_dB_Osimps_I4_J) ).
thf(456,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)],[89]) ).
thf(457,plain,
~ ? [A: dB,B: dB,C: nat] :
( ( C @ var )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(miniscope,[status(thm)],[456]) ).
thf(458,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[457]) ).
thf(459,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(lifteq,[status(thm)],[458]) ).
thf(3000,plain,
! [D: nat,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( D @ var ) ) ),
inference(paramod_ordered,[status(thm)],[322,459]) ).
thf(3003,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3000]) ).
thf(3006,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3003]) ).
thf(4174,plain,
! [D: nat,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( D @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,3006]) ).
thf(4183,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4174]) ).
thf(4201,plain,
! [C: nat,B: dB,A: dB] :
( ( C @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4183]) ).
thf(9,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_not0__implies__Suc) ).
thf(150,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(151,plain,
! [A: nat] :
( ( A
= ( A @ sk1 @ suc ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(152,plain,
! [A: nat] :
( ( ( A @ sk1 @ suc )
= A )
| ( A
= ( nat @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nat_Oinject) ).
thf(479,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)],[94]) ).
thf(480,plain,
( ! [A: nat,B: nat] :
( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[479]) ).
thf(481,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( ( D @ suc )
= ( C @ suc ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ suc )
!= ( A @ suc ) ) ) ),
inference(cnf,[status(esa)],[480]) ).
thf(482,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ suc )
!= ( A @ suc ) ) ),
inference(cnfConj,[status(thm)],[481]) ).
thf(484,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ suc )
!= ( A @ suc ) ) ),
inference(lifteq,[status(thm)],[482]) ).
thf(485,plain,
? [A: nat > nat] :
! [B: nat] :
( ( B @ suc @ A )
= B ),
inference(detectInverse,[status(thm)],[484]) ).
thf(486,plain,
! [A: nat] :
( ( A @ suc @ sk11 )
= A ),
inference(cnf,[status(esa)],[485]) ).
thf(1704,plain,
! [A: nat] :
( ( A @ suc @ sk11 )
= A ),
inference(lifteq,[status(thm)],[486]) ).
thf(1713,plain,
! [B: nat,A: nat] :
( ( ( A @ sk1 @ suc )
!= ( B @ suc ) )
| ( ( A @ sk11 )
= B )
| ( A
= ( nat @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[152,1704]) ).
thf(1714,plain,
! [A: nat] :
( ( ( A @ sk11 )
= ( A @ sk1 ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[1713:[bind(A,$thf( C )),bind(B,$thf( C @ sk1 ))]]) ).
thf(1718,plain,
! [A: nat] :
( ( ( A @ sk11 )
= ( A @ sk1 ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(simp,[status(thm)],[1714]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_45_dB_Osize_I3_J) ).
thf(326,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)],[51]) ).
thf(327,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(cnf,[status(esa)],[326]) ).
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(lifteq,[status(thm)],[327]) ).
thf(66,axiom,
( ( nat @ one_one )
= ( nat @ zero_zero @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_One__nat__def) ).
thf(375,plain,
( ( nat @ one_one )
= ( nat @ zero_zero @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(376,plain,
( ( nat @ zero_zero @ suc )
= ( nat @ one_one ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(3008,plain,
! [A: dB] :
( ( A @ abs @ dB_size )
= ( nat @ one_one @ ( A @ dB_size @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(rewrite,[status(thm)],[328,376]) ).
thf(58,axiom,
! [A: nat,B: dB,C: dB @ list,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_subst__map) ).
thf(352,plain,
! [A: nat,B: dB,C: dB @ list,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( C @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(62,axiom,
! [A: nat,B: nat] : ( ss @ ( B @ ( A @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( B @ suc @ ( A @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(365,plain,
! [A: nat,B: nat] : ( ss @ ( B @ ( A @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( B @ suc @ ( A @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6,axiom,
! [A: nat,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_lift__map) ).
thf(136,plain,
! [A: nat,B: dB @ list,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(137,plain,
! [C: dB,B: dB @ list,A: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(138,plain,
! [C: dB,B: dB @ list,A: nat] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(1,conjecture,
ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(121,plain,
~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ 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)],[2]) ).
thf(626,plain,
( ( ( ia @ suc )
!= ( nat @ zero_zero @ suc ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(paramod_ordered,[status(thm)],[376,121]) ).
thf(628,plain,
( ( ia
!= ( nat @ zero_zero ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[626]) ).
thf(31,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_subst__eq) ).
thf(249,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_54_double__zero__sym) ).
thf(518,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)],[99]) ).
thf(67,axiom,
s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(377,plain,
s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4,axiom,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lift__IT) ).
thf(130,plain,
! [A: nat,B: dB] :
( ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(131,plain,
! [B: dB,A: nat] :
( ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
| ~ ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(cnf,[status(esa)],[130]) ).
thf(649,plain,
! [B: dB,A: nat] :
( ( ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
| ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[377,131]) ).
thf(650,plain,
! [B: dB,A: nat] :
( ( ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( B @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
| ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
! [A: nat] : ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(pattern_uni,[status(thm)],[650:[bind(A,$thf( A )),bind(B,$thf( s ))]]) ).
thf(84,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(444,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(445,plain,
~ ( fFalse @ pp ),
inference(polarity_switch,[status(thm)],[444]) ).
thf(1748,plain,
! [A: nat] :
( ( ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[651,445]) ).
thf(1749,plain,
! [A: nat] :
( ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[1748]) ).
thf(1765,plain,
! [A: nat] :
( ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[1749]) ).
thf(1772,plain,
! [B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A != fFalse ) ),
inference(paramod_ordered,[status(thm)],[322,1765]) ).
thf(1776,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1772]) ).
thf(1777,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1776]) ).
thf(2179,plain,
! [B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1777]) ).
thf(2183,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2179]) ).
thf(2186,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2493,plain,
! [B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2186]) ).
thf(2497,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2499,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2497]) ).
thf(45,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_liftn__lift) ).
thf(308,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(119,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_subst__App) ).
thf(597,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( A @ ( B @ ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(23,axiom,
! [A: dB,B: dB,C: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dB_Osimps_I9_J) ).
thf(214,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)],[23]) ).
thf(215,plain,
~ ? [A: dB,B: dB,C: dB] :
( ( C @ abs )
= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(216,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(217,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(83,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Zero__neq__Suc) ).
thf(440,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',fact_78_nat__add__assoc) ).
thf(511,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)],[96]) ).
thf(16,axiom,
! [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dB_Osimps_I8_J) ).
thf(181,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)],[16]) ).
thf(182,plain,
~ ? [A: dB,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ abs ) ),
inference(miniscope,[status(thm)],[181]) ).
thf(183,plain,
! [C: dB,B: dB,A: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [C: dB,B: dB,A: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ abs ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(2641,plain,
! [D: dB,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( B @ abs ) ) ),
inference(paramod_ordered,[status(thm)],[322,184]) ).
thf(2643,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2641]) ).
thf(2646,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2643]) ).
thf(3765,plain,
! [D: dB,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( B @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2646]) ).
thf(3775,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3765]) ).
thf(3794,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3775]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(384,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(109,axiom,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_beta__cases_I1_J) ).
thf(550,plain,
! [A: dB,B: nat] :
~ ( A @ ( B @ var @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
<=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_listsp__conj__eq) ).
thf(472,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list] :
( ( ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) )
=> ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) ) )
& ( ( C @ ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ listsp ) ) )
=> ( ( C @ ( A @ ( TA @ listsp ) ) )
& ( C @ ( B @ ( TA @ listsp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_23_IT_OVar) ).
thf(340,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)],[54]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__commute) ).
thf(153,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)],[10]) ).
thf(13,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_substn__subst__n) ).
thf(172,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(173,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ ( B @ ( C @ substn ) ) )
= ( A @ ( nat @ zero_zero @ ( B @ ( A @ liftn ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',fact_69_add__eq__self__zero) ).
thf(185,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)],[17]) ).
thf(29,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_dB_Osimps_I3_J) ).
thf(236,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)],[29]) ).
thf(237,plain,
( ! [A: dB,B: dB] :
( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[236]) ).
thf(238,plain,
! [D: dB,C: dB,B: dB,A: dB] :
( ( ( ( D @ abs )
= ( C @ abs ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ abs )
!= ( A @ abs ) ) ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [B: dB,A: dB] :
( ( B = A )
| ( ( B @ abs )
!= ( A @ abs ) ) ),
inference(cnfConj,[status(thm)],[238]) ).
thf(241,plain,
! [B: dB,A: dB] :
( ( B = A )
| ( ( B @ abs )
!= ( A @ abs ) ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(242,plain,
? [A: dB > dB] :
! [B: dB] :
( ( B @ abs @ A )
= B ),
inference(detectInverse,[status(thm)],[241]) ).
thf(243,plain,
! [A: dB] :
( ( A @ abs @ sk6 )
= A ),
inference(cnf,[status(esa)],[242]) ).
thf(1441,plain,
! [A: dB] :
( ( A @ abs @ sk6 )
= A ),
inference(lifteq,[status(thm)],[243]) ).
thf(82,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Zero__not__Suc) ).
thf(436,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1756,plain,
! [C: dB,B: nat,A: nat] :
( ( ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
| ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[651,131]) ).
thf(1757,plain,
! [C: dB,B: nat,A: nat] :
( ( ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
| ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1756]) ).
thf(1758,plain,
! [B: nat,A: nat] : ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(pattern_uni,[status(thm)],[1757:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ))]]) ).
thf(1770,plain,
! [B: nat,A: nat] : ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(simp,[status(thm)],[1758]) ).
thf(4222,plain,
! [B: nat,A: nat] :
( ( ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1770,445]) ).
thf(4223,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[4222]) ).
thf(4249,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[4223]) ).
thf(2979,plain,
! [D: dB,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( D @ abs ) ) ),
inference(paramod_ordered,[status(thm)],[322,217]) ).
thf(2981,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2979]) ).
thf(2985,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2981]) ).
thf(37,axiom,
! [A: dB] :
( ( A @ abs @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_dB_Osize_I6_J) ).
thf(281,plain,
! [A: dB] :
( ( A @ abs @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(282,plain,
! [A: dB] :
( ( A @ abs @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [A: dB] :
( ( A @ abs @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(2227,plain,
! [A: dB] :
( ( A @ abs @ ( dB @ size_size ) )
= ( nat @ one_one @ ( A @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(rewrite,[status(thm)],[283,376]) ).
thf(71,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Nat_Oadd__0__right) ).
thf(387,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)],[71]) ).
thf(388,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(lifteq,[status(thm)],[388]) ).
thf(116,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Suc__not__Zero) ).
thf(587,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(643,plain,
( ( ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[377,445]) ).
thf(644,plain,
( ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[643]) ).
thf(652,plain,
( ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[644]) ).
thf(1158,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A != fFalse ) ),
inference(paramod_ordered,[status(thm)],[322,652]) ).
thf(1172,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1158]) ).
thf(1433,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1172]) ).
thf(1434,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1433]) ).
thf(1439,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1434]) ).
thf(1440,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1463,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1440]) ).
thf(1464,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1463]) ).
thf(1473,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1464]) ).
thf(1474,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1473]) ).
thf(1789,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1474]) ).
thf(1790,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[1789]) ).
thf(2486,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,1790]) ).
thf(2487,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2486]) ).
thf(3484,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2487]) ).
thf(3485,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3484]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_51_add__right__cancel) ).
thf(344,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)],[56]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_55_add__is__0) ).
thf(460,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)],[90]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_6_apps__eq__tail__conv) ).
thf(284,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)],[38]) ).
thf(726,plain,
! [E: nat,D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( D
!= ( E @ suc ) )
| ( B
!= ( nat @ zero_zero ) )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[145,276]) ).
thf(727,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( B
!= ( nat @ zero_zero ) )
| ( ( C @ ( D @ suc @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[726:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ suc )),bind(E,$thf( F ))]]) ).
thf(1035,plain,
! [C: nat,B: dB @ list,A: dB @ list] :
( ( B @ ( C @ suc @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( nat @ zero_zero @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(simp,[status(thm)],[727]) ).
thf(4488,plain,
! [C: nat,B: dB @ list,A: dB @ list] :
( ( B != A )
| ( ( C @ suc @ var )
!= ( nat @ zero_zero @ var ) )
| ( app != app ) ),
inference(simp,[status(thm)],[1035]) ).
thf(4507,plain,
! [A: nat] :
( ( A @ suc @ var )
!= ( nat @ zero_zero @ var ) ),
inference(simp,[status(thm)],[4488]) ).
thf(4301,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,3485]) ).
thf(4302,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( s @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4301]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__ident) ).
thf(201,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(202,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(cnf,[status(esa)],[201]) ).
thf(203,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(lifteq,[status(thm)],[202]) ).
thf(97,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(514,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(618,plain,
( ( ( fTrue @ pp )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[514,121]) ).
thf(619,plain,
( ( fTrue @ pp )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[618]) ).
thf(622,plain,
( fTrue
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(629,plain,
( ( ( ja @ suc )
!= ( nat @ zero_zero @ suc ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[376,622]) ).
thf(631,plain,
( ( ja
!= ( nat @ zero_zero ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[629]) ).
thf(1078,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[203,631]) ).
thf(1081,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1078]) ).
thf(1087,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1081]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_52_nat__add__left__cancel) ).
thf(189,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)],[18]) ).
thf(63,axiom,
ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(367,plain,
ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1800,plain,
( ( ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,445]) ).
thf(1801,plain,
( ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1822,plain,
( ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[1801]) ).
thf(2199,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A != fFalse ) ),
inference(paramod_ordered,[status(thm)],[322,1822]) ).
thf(2200,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2199]) ).
thf(2220,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2200]) ).
thf(2222,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2220]) ).
thf(11,axiom,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_beta__cases_I3_J) ).
thf(156,plain,
! [A: dB,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
=> ( ! [D: dB] :
( ( A
= ( nat @ zero_zero @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
=> ( C
!= ( D @ abs ) ) )
=> ( ! [D: dB] :
( ( A
= ( B @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( C @ beta ) ) )
=> ~ ! [D: dB] :
( ( A
= ( D @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
=> ~ ( D @ ( B @ beta ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(157,plain,
! [C: dB,B: dB,A: dB] :
( ( ( A @ ( B @ ( C @ sk5 ) ) @ ( B @ beta ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) )
& ( ( A
= ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) )
& ( ( A @ ( B @ ( C @ sk5 ) ) @ ( B @ beta ) )
| ( A
= ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) )
& ( ( A
= ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
= ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) )
& ( ( C @ ( B @ ( A @ sk2 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk3 ) ) @ abs ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) )
& ( ( C @ ( B @ ( A @ sk2 ) ) )
| ( A
= ( nat @ zero_zero @ ( B @ ( A @ ( B @ ( C @ sk3 ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(160,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ ( B @ ( A @ sk2 ) ) )
| ( C
= ( A @ ( B @ ( C @ sk3 ) ) @ abs ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(164,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
| ( ( A @ ( B @ ( C @ sk3 ) ) @ abs )
= C ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_73_ext) ).
thf(591,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)],[117]) ).
thf(65,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_dB_Osimps_I5_J) ).
thf(371,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)],[65]) ).
thf(372,plain,
~ ? [A: nat,B: dB,C: dB] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= ( A @ var ) ),
inference(miniscope,[status(thm)],[371]) ).
thf(373,plain,
! [C: dB,B: dB,A: nat] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(cnf,[status(esa)],[372]) ).
thf(374,plain,
! [C: dB,B: dB,A: nat] :
( ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ var ) ),
inference(lifteq,[status(thm)],[373]) ).
thf(2990,plain,
! [D: dB,C: dB,B: nat,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( B @ var ) ) ),
inference(paramod_ordered,[status(thm)],[322,374]) ).
thf(2993,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2990]) ).
thf(2996,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2993]) ).
thf(2644,plain,
! [C: dB,B: dB,A: dB] :
( ( ( A @ abs )
!= B )
| ( ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) )
!= ( dB @ combi ) ) ),
inference(simp,[status(thm)],[2641]) ).
thf(2647,plain,
! [A: dB] :
( ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) )
!= ( dB @ combi ) ),
inference(simp,[status(thm)],[2644]) ).
thf(2648,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi ) ) ),
inference(paramod_ordered,[status(thm)],[322,2647]) ).
thf(2649,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2648]) ).
thf(2650,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2649]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_81_add__right__imp__eq) ).
thf(574,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)],[114]) ).
thf(36,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(280,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(24,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dB_Osimps_I6_J) ).
thf(218,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(219,plain,
~ ? [A: dB,B: nat] :
( ( B @ var )
= ( A @ abs ) ),
inference(miniscope,[status(thm)],[218]) ).
thf(220,plain,
! [B: nat,A: dB] :
( ( B @ var )
!= ( A @ abs ) ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
! [B: nat,A: dB] :
( ( B @ var )
!= ( A @ abs ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_8_Var__apps__neq__Abs__apps) ).
thf(132,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)],[5]) ).
thf(74,axiom,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_dB_Osize_I1_J) ).
thf(396,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(39,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_subst__preserves__beta) ).
thf(292,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( C @ ( D @ beta ) )
=> ( A @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( D @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(452,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(3496,plain,
! [B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2499]) ).
thf(3501,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3496]) ).
thf(3507,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3501]) ).
thf(4317,plain,
! [B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,3507]) ).
thf(4320,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4317]) ).
thf(4323,plain,
! [A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4320]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_59_appR) ).
thf(529,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)],[102]) ).
thf(107,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dB_Osimps_I7_J) ).
thf(543,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(544,plain,
~ ? [A: nat,B: dB] :
( ( B @ abs )
= ( A @ var ) ),
inference(miniscope,[status(thm)],[543]) ).
thf(545,plain,
! [B: dB,A: nat] :
( ( B @ abs )
!= ( A @ var ) ),
inference(cnf,[status(esa)],[544]) ).
thf(546,plain,
! [B: dB,A: nat] :
( ( B @ abs )
!= ( A @ var ) ),
inference(lifteq,[status(thm)],[545]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_dB_Osimps_I1_J) ).
thf(577,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)],[115]) ).
thf(578,plain,
( ! [A: nat,B: nat] :
( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[577]) ).
thf(579,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( ( D @ var )
= ( C @ var ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ var )
!= ( A @ var ) ) ) ),
inference(cnf,[status(esa)],[578]) ).
thf(580,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ var )
!= ( A @ var ) ) ),
inference(cnfConj,[status(thm)],[579]) ).
thf(582,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ var )
!= ( A @ var ) ) ),
inference(lifteq,[status(thm)],[580]) ).
thf(583,plain,
? [A: dB > nat] :
! [B: nat] :
( ( B @ var @ A )
= B ),
inference(detectInverse,[status(thm)],[582]) ).
thf(584,plain,
! [A: nat] :
( ( A @ var @ sk20 )
= A ),
inference(cnf,[status(esa)],[583]) ).
thf(1736,plain,
! [A: nat] :
( ( A @ var @ sk20 )
= A ),
inference(lifteq,[status(thm)],[584]) ).
thf(1076,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(paramod_ordered,[status(thm)],[203,628]) ).
thf(1085,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1091,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1085]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_57_add__Suc) ).
thf(302,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)],[43]) ).
thf(111,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_liftn__0) ).
thf(561,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(41,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(297,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(4270,plain,
! [C: nat,B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( C @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A != fFalse ) ),
inference(paramod_ordered,[status(thm)],[322,4249]) ).
thf(4279,plain,
! [B: nat,A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4270]) ).
thf(4284,plain,
! [B: nat,A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( A @ ( B @ ( s @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4279]) ).
thf(161,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ ( B @ ( A @ sk2 ) ) )
| ( A
= ( nat @ zero_zero @ ( B @ ( A @ ( B @ ( C @ sk3 ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(165,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
| ( ( nat @ zero_zero @ ( B @ ( A @ ( B @ ( C @ sk3 ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',fact_50_add__left__cancel) ).
thf(229,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)],[28]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_38_zero__induct) ).
thf(252,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)],[32]) ).
thf(19,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(197,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(61,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_n__not__Suc__n) ).
thf(361,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(52,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(329,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_58_appL) ).
thf(224,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)],[26]) ).
thf(1075,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[203,622]) ).
thf(1083,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1075]) ).
thf(1089,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1083]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_80_add__imp__eq) ).
thf(317,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)],[48]) ).
thf(2653,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2650]) ).
thf(2654,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2653]) ).
thf(2656,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2661,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2656]) ).
thf(2662,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2661]) ).
thf(2665,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2662]) ).
thf(2672,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2665]) ).
thf(2673,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2672]) ).
thf(2674,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2673]) ).
thf(2686,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2674]) ).
thf(2687,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2686]) ).
thf(2692,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[2687]) ).
thf(3853,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2692]) ).
thf(3854,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3853]) ).
thf(3860,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3854]) ).
thf(4537,plain,
! [B: dB,A: dB @ ( dB @ fun )] :
( ( ( A @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) )
| ( A
!= ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,3860]) ).
thf(4538,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4537]) ).
thf(4544,plain,
! [A: dB] :
( ( dB @ combi @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) @ ( dB @ ( dB @ fun ) @ combi @ ( dB @ ( dB @ fun ) @ ( dB @ ( dB @ fun ) @ aa ) ) ) )
!= ( A @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4538]) ).
thf(12,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_plus__nat_Oadd__0) ).
thf(169,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)],[12]) ).
thf(91,axiom,
! [A: nat,B: nat] : ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(470,plain,
! [A: nat,B: nat] : ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(471,plain,
! [B: nat,A: nat] : ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ),
inference(cnf,[status(esa)],[470]) ).
thf(3704,plain,
! [B: nat,A: nat] :
( ( ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,445]) ).
thf(3705,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[3704]) ).
thf(3723,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[3705]) ).
thf(3740,plain,
! [C: nat,B: nat,A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( C @ ( B @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A != fFalse ) ),
inference(paramod_ordered,[status(thm)],[322,3723]) ).
thf(3743,plain,
! [B: nat,A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3740]) ).
thf(3746,plain,
! [B: nat,A: nat] :
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( B @ ( A @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3743]) ).
thf(101,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lift_Osimps_I2_J) ).
thf(526,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(95,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 @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_35_IT_Osimps) ).
thf(489,plain,
! [A: dB] :
( ( ( ? [B: dB,C: dB,D: dB @ list] :
( ( C @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
& ( D @ ( nat @ zero_zero @ ( C @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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 @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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)],[95]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_47_dB_Osize_I2_J) ).
thf(547,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)],[108]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_86_one__is__add) ).
thf(256,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)],[33]) ).
thf(73,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_subst__Abs) ).
thf(393,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_74_foldl__assoc) ).
thf(515,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)],[98]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(311,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(40,axiom,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_dB_Osize_I4_J) ).
thf(294,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(295,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(cnf,[status(esa)],[294]) ).
thf(296,plain,
! [A: nat] :
( ( A @ var @ ( dB @ size_size ) )
= ( nat @ zero_zero ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(2250,plain,
! [B: dB,A: nat] :
( ( ( A @ var @ ( dB @ size_size ) )
!= ( B @ ( dB @ size_size ) ) )
| ( ( nat @ one_one @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ abs @ ( dB @ size_size ) ) ) ),
inference(paramod_ordered,[status(thm)],[296,2227]) ).
thf(2251,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ ( dB @ size_size ) ) ),
inference(pattern_uni,[status(thm)],[2250:[bind(A,$thf( C )),bind(B,$thf( C @ var ))]]) ).
thf(2281,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ ( dB @ size_size ) ) ),
inference(simp,[status(thm)],[2251]) ).
thf(170,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(lifteq,[status(thm)],[170]) ).
thf(2318,plain,
! [A: nat] :
( ( A @ var @ abs @ ( dB @ size_size ) )
= ( nat @ one_one ) ),
inference(rewrite,[status(thm)],[2281,171]) ).
thf(2319,plain,
! [B: dB,A: nat] :
( ( ( A @ var @ abs @ ( dB @ size_size ) )
!= ( B @ abs @ ( dB @ size_size ) ) )
| ( ( nat @ one_one @ ( B @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[2318,2227]) ).
thf(2320,plain,
! [A: nat] :
( ( nat @ one_one @ ( A @ var @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ one_one ) ),
inference(pattern_uni,[status(thm)],[2319:[bind(A,$thf( C )),bind(B,$thf( C @ var ))]]) ).
thf(2333,plain,
! [A: nat] :
( ( nat @ one_one @ ( A @ var @ ( dB @ size_size ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ one_one ) ),
inference(simp,[status(thm)],[2320]) ).
thf(2338,plain,
( ( nat @ one_one @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ one_one ) ),
inference(rewrite,[status(thm)],[2333,296]) ).
thf(397,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [A: nat] :
( ( A @ var @ dB_size )
= ( nat @ zero_zero ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Suc__inject) ).
thf(425,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_92_substn_Osimps_I2_J) ).
thf(430,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)],[80]) ).
thf(426,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ suc )
!= ( A @ suc ) ) ),
inference(cnf,[status(esa)],[425]) ).
thf(427,plain,
! [B: nat,A: nat] :
( ( B = A )
| ( ( B @ suc )
!= ( A @ suc ) ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(428,plain,
? [A: nat > nat] :
! [B: nat] :
( ( B @ suc @ A )
= B ),
inference(detectInverse,[status(thm)],[427]) ).
thf(429,plain,
! [A: nat] :
( ( A @ suc @ sk9 )
= A ),
inference(cnf,[status(esa)],[428]) ).
thf(1442,plain,
! [A: nat] :
( ( A @ suc @ sk9 )
= A ),
inference(lifteq,[status(thm)],[429]) ).
thf(1675,plain,
! [B: nat,A: nat] :
( ( ( A @ sk1 @ suc )
!= ( B @ suc ) )
| ( ( A @ sk9 )
= B )
| ( A
= ( nat @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[152,1442]) ).
thf(1676,plain,
! [A: nat] :
( ( ( A @ sk9 )
= ( A @ sk1 ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[1675:[bind(A,$thf( C )),bind(B,$thf( C @ sk1 ))]]) ).
thf(1698,plain,
! [A: nat] :
( ( ( A @ sk9 )
= ( A @ sk1 ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(simp,[status(thm)],[1676]) ).
thf(3039,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2222]) ).
thf(3042,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3039]) ).
thf(159,plain,
! [C: dB,B: dB,A: dB] :
( ( A
= ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
= ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(166,plain,
! [C: dB,B: dB,A: dB] :
( ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= A )
| ( ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[159]) ).
thf(8,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(149,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_79_add__left__imp__eq) ).
thf(178,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)],[15]) ).
thf(179,plain,
! [TA: $tType,C: TA,B: TA,A: 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 ) ) ) ) )
| ~ ( TA @ cancel_semigroup_add ) ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ cancel_semigroup_add )
| ( 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 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_12_dB_Osimps_I2_J) ).
thf(204,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)],[22]) ).
thf(1077,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(paramod_ordered,[status(thm)],[203,121]) ).
thf(1086,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1077]) ).
thf(1092,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1086]) ).
thf(630,plain,
( ( ( ia @ suc )
!= ( nat @ zero_zero @ suc ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[376,622]) ).
thf(632,plain,
( ( ia
!= ( nat @ zero_zero ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[630]) ).
thf(1080,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[203,632]) ).
thf(1084,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ( ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1080]) ).
thf(1090,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ia
!= ( nat @ zero_zero ) )
| ( ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( ja @ suc @ ( nat @ one_one @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1084]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_89_double__eq__0__iff) ).
thf(567,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)],[113]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_90_apps__preserves__beta) ).
thf(477,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)],[93]) ).
thf(104,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(535,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_72_add__Suc__shift) ).
thf(323,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)],[50]) ).
thf(118,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(594,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(250,plain,
! [B: nat,A: dB] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [B: nat,A: dB] :
( ( B @ ( A @ ( B @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= A ),
inference(lifteq,[status(thm)],[250]) ).
thf(623,plain,
! [A: nat] :
( ( ( nat @ zero_zero @ suc )
!= ( A @ suc ) )
| ( ( nat @ one_one )
!= ( nat @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[376,276]) ).
thf(624,plain,
( ( nat @ one_one )
!= ( nat @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[623:[bind(A,$thf( nat @ zero_zero ))]]) ).
thf(938,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( D
!= ( nat @ one_one ) )
| ( B
!= ( nat @ zero_zero ) )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[145,624]) ).
thf(939,plain,
! [C: dB @ list,B: nat,A: dB @ list] :
( ( B
!= ( nat @ zero_zero ) )
| ( ( C @ ( nat @ one_one @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[938:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( nat @ one_one ))]]) ).
thf(1022,plain,
! [B: dB @ list,A: dB @ list] :
( ( B @ ( nat @ one_one @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( nat @ zero_zero @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(simp,[status(thm)],[939]) ).
thf(154,plain,
! [C: nat,B: nat,A: 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(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [C: nat,B: nat,A: 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(lifteq,[status(thm)],[154]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_75_nat__add__commute) ).
thf(198,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)],[20]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_2_Abs__apps__eq__Abs__apps__conv) ).
thf(330,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)],[53]) ).
thf(551,plain,
~ ? [A: dB,B: nat] : ( A @ ( B @ var @ beta ) ),
inference(miniscope,[status(thm)],[550]) ).
thf(552,plain,
! [B: nat,A: dB] :
~ ( A @ ( B @ var @ beta ) ),
inference(cnf,[status(esa)],[551]) ).
thf(75,axiom,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_lift__preserves__beta) ).
thf(399,plain,
! [A: nat,B: dB,C: dB] :
( ( B @ ( C @ beta ) )
=> ( A @ ( B @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(299,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',fact_85_foldl__absorb0) ).
thf(226,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)],[27]) ).
thf(162,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ ( B @ ( C @ sk5 ) ) @ ( B @ beta ) )
| ( A
= ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(167,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ ( B @ ( C @ sk5 ) ) @ ( B @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
| ( ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(133,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(miniscope,[status(thm)],[132]) ).
thf(134,plain,
! [D: nat,C: dB @ list,B: dB,A: dB @ list] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [D: nat,C: dB @ list,B: dB,A: dB @ list] :
( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(562,plain,
! [B: dB,A: nat] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(cnf,[status(esa)],[561]) ).
thf(563,plain,
! [B: dB,A: nat] :
( ( A @ ( B @ ( nat @ zero_zero @ liftn ) ) )
= B ),
inference(lifteq,[status(thm)],[562]) ).
thf(55,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_abs) ).
thf(342,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ beta ) )
=> ( A @ abs @ ( B @ abs @ beta ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(59,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Suc__neq__Zero) ).
thf(355,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_53_nat__add__right__cancel) ).
thf(553,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)],[110]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_7_Abs__App__neq__Var__apps) ).
thf(531,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)],[103]) ).
thf(100,axiom,
nat @ semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Osemigroup__add) ).
thf(525,plain,
nat @ semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(3048,plain,
! [B: dB @ list,A: dB @ list] :
( ( B != A )
| ( ( nat @ one_one @ var )
!= ( nat @ zero_zero @ var ) )
| ( app != app ) ),
inference(simp,[status(thm)],[1022]) ).
thf(3058,plain,
( ( nat @ one_one @ var )
!= ( nat @ zero_zero @ var ) ),
inference(simp,[status(thm)],[3048]) ).
thf(1451,plain,
! [A: nat] :
( ( ( nat @ zero_zero @ suc )
!= ( A @ suc ) )
| ( ( nat @ one_one @ sk9 )
= A ) ),
inference(paramod_ordered,[status(thm)],[376,1442]) ).
thf(1452,plain,
( ( nat @ one_one @ sk9 )
= ( nat @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[1451:[bind(A,$thf( nat @ zero_zero ))]]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_77_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(175,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)],[14]) ).
thf(176,plain,
! [TA: $tType,C: TA,B: TA,A: 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 ) ) ) ) )
| ~ ( TA @ ab_semigroup_add ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ ab_semigroup_add )
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(60,axiom,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_beta) ).
thf(359,plain,
! [A: dB,B: dB] : ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( A @ ( B @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1715,plain,
! [A: nat] :
( ( ( nat @ zero_zero @ suc )
!= ( A @ suc ) )
| ( ( nat @ one_one @ sk11 )
= A ) ),
inference(paramod_ordered,[status(thm)],[376,1704]) ).
thf(1716,plain,
( ( nat @ one_one @ sk11 )
= ( nat @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[1715:[bind(A,$thf( nat @ zero_zero ))]]) ).
thf(3813,plain,
! [D: dB,C: dB,B: dB,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( D @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2985]) ).
thf(3815,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3813]) ).
thf(3828,plain,
! [C: dB,B: dB,A: dB] :
( ( C @ abs @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3815]) ).
thf(940,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( D
!= ( nat @ zero_zero ) )
| ( B
!= ( nat @ one_one ) )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[145,624]) ).
thf(941,plain,
! [C: dB @ list,B: nat,A: dB @ list] :
( ( B
!= ( nat @ one_one ) )
| ( ( C @ ( nat @ zero_zero @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[940:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( nat @ zero_zero ))]]) ).
thf(1023,plain,
! [B: dB @ list,A: dB @ list] :
( ( B @ ( nat @ zero_zero @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( nat @ one_one @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ),
inference(simp,[status(thm)],[941]) ).
thf(120,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nat_Oexhaust) ).
thf(600,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(4121,plain,
! [D: dB,C: dB,B: nat,A: dB] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( C @ ( D @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A
!= ( B @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,2996]) ).
thf(4134,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4121]) ).
thf(4143,plain,
! [C: dB,B: dB,A: nat] :
( ( A @ var @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ combi @ ( dB @ ( dB @ aa ) ) ) )
!= ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[4134]) ).
thf(47,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_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/sandbox/benchmark/theBenchmark.p',fact_63_dB_Osize_I5_J) ).
thf(314,plain,
! [A: dB,B: dB] :
( ( A @ ( B @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( dB @ size_size ) )
= ( nat @ zero_zero @ suc @ ( A @ ( dB @ size_size ) @ ( B @ ( dB @ size_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)],[47]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_37_nat__induct) ).
thf(446,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)],[85]) ).
thf(625,plain,
( ( ( ja @ suc )
!= ( nat @ zero_zero @ suc ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(paramod_ordered,[status(thm)],[376,121]) ).
thf(627,plain,
( ( ja
!= ( nat @ zero_zero ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[625]) ).
thf(86,axiom,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Lambda) ).
thf(450,plain,
! [A: dB] :
( ( A @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp )
=> ( A @ abs @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(106,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_nat_Osimps_I3_J) ).
thf(539,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_67_add__0__right) ).
thf(368,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)],[64]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TC,D: TC @ ( TB @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) @ ( C @ ( D @ ( TB @ ( TC @ foldl ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( TA @ ( TC @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_foldl__map) ).
thf(390,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TC,D: TC @ ( TB @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) @ ( C @ ( D @ ( TB @ ( TC @ foldl ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ fun ) @ ( TC @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ combc ) ) ) ) @ ( TA @ ( TC @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_87_add__is__1) ).
thf(401,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)],[76]) ).
thf(77,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Suc__n__not__n) ).
thf(418,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(57,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(351,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(68,axiom,
! [A: dB,B: dB] :
( ( A @ ( B @ abs @ beta ) )
=> ~ ! [C: dB] :
( ( A
= ( C @ abs ) )
=> ~ ( C @ ( B @ beta ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_beta__cases_I2_J) ).
thf(378,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)],[68]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_66_add__0) ).
thf(246,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)],[30]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_65_add__0__left) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(2321,plain,
! [B: dB,A: nat] :
( ( ( A @ var @ abs @ ( dB @ size_size ) )
!= ( B @ ( dB @ size_size ) ) )
| ( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ abs @ ( dB @ size_size ) ) ) ),
inference(paramod_ordered,[status(thm)],[2318,2227]) ).
thf(2322,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ abs @ ( dB @ size_size ) ) ),
inference(pattern_uni,[status(thm)],[2321:[bind(A,$thf( D )),bind(B,$thf( D @ var @ abs ))]]) ).
thf(2334,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ abs @ ( dB @ size_size ) ) ),
inference(simp,[status(thm)],[2322]) ).
thf(2395,plain,
! [B: dB,A: nat] :
( ( ( A @ var @ abs @ abs @ ( dB @ size_size ) )
!= ( B @ ( dB @ size_size ) ) )
| ( ( nat @ one_one @ ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ abs @ ( dB @ size_size ) ) ) ),
inference(paramod_ordered,[status(thm)],[2334,2227]) ).
thf(2396,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ abs @ abs @ ( dB @ size_size ) ) ),
inference(pattern_uni,[status(thm)],[2395:[bind(A,$thf( E )),bind(B,$thf( E @ var @ abs @ abs ))]]) ).
thf(2462,plain,
! [A: nat] :
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ var @ abs @ abs @ abs @ ( dB @ size_size ) ) ),
inference(simp,[status(thm)],[2396]) ).
thf(69,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(383,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_56_add__Suc__right) ).
thf(536,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)],[105]) ).
thf(614,plain,
( ( ( fTrue @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[514,445]) ).
thf(615,plain,
( ( fTrue @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[614]) ).
thf(620,plain,
fTrue != fFalse,
inference(simp,[status(thm)],[615]) ).
thf(158,plain,
! [C: dB,B: dB,A: dB] :
( ( A
= ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(168,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(143,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( C = A )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[141]) ).
thf(146,plain,
! [D: nat,C: dB @ list,B: nat,A: dB @ list] :
( ( C = A )
| ( ( C @ ( D @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) )
!= ( A @ ( B @ var @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(3512,plain,
! [A: nat] :
( ( ( A @ sk9 )
!= ( nat @ one_one @ sk9 ) )
| ( ( A @ sk1 )
= ( nat @ zero_zero ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[1698,1452]) ).
thf(3513,plain,
( ( ( nat @ one_one @ sk1 )
= ( nat @ zero_zero ) )
| ( ( nat @ one_one )
= ( nat @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[3512:[bind(A,$thf( nat @ one_one ))]]) ).
thf(3892,plain,
( ( nat @ one_one @ sk1 )
= ( nat @ zero_zero ) ),
inference(simplifyReflect,[status(thm)],[3513,624]) ).
thf(78,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_subst__lift) ).
thf(422,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ ( lift @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(601,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ~ ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(miniscope,[status(thm)],[600]) ).
thf(602,plain,
! [A: nat] :
( ( A
= ( A @ sk22 @ suc ) )
| ( A
= ( nat @ zero_zero ) ) ),
inference(cnf,[status(esa)],[601]) ).
thf(603,plain,
! [A: nat] :
( ( ( A @ sk22 @ suc )
= A )
| ( A
= ( nat @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[602]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_62_liftn_Osimps_I2_J) ).
thf(564,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)],[112]) ).
thf(44,axiom,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_substn__subst__0) ).
thf(305,plain,
! [A: dB,B: dB] :
( ( nat @ zero_zero @ ( A @ ( B @ substn ) ) )
= ( nat @ zero_zero @ ( A @ ( B @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3883,plain,
! [A: bool] :
( ( ( A @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) )
| ( A
!= ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[322,3042]) ).
thf(3886,plain,
( ( fFalse @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) @ ( bool @ combi @ ( bool @ ( bool @ aa ) ) ) )
!= ( ss @ ( nat @ zero_zero @ ( s @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) ) ),
inference(simp,[status(thm)],[3883]) ).
thf(163,plain,
! [C: dB,B: dB,A: dB] :
( ( A @ ( B @ ( C @ sk5 ) ) @ ( B @ beta ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ beta ) )
| ~ ( C @ ( B @ ( A @ sk2 ) ) )
| ~ ( A @ ( B @ ( C @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ beta ) ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_68_add_Ocomm__neutral) ).
thf(277,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)],[35]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zero__reorient) ).
thf(122,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)],[3]) ).
thf(1079,plain,
! [A: dB @ list] :
( ( ( A @ ( dB @ combi @ ( dB @ ( dB @ map ) ) ) )
!= ( ss @ ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(paramod_ordered,[status(thm)],[203,627]) ).
thf(1082,plain,
! [A: dB @ list] :
( ( A != ss )
| ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ~ ( A @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1079]) ).
thf(1088,plain,
( ( ( dB @ combi )
!= ( ja @ ( ia @ var @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) ) )
| ( ja
!= ( nat @ zero_zero ) )
| ~ ( ss @ ( ja @ ( ia @ var @ ( s @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( nat @ one_one @ ( ia @ suc @ var @ ( ra @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ abs @ ( app @ ( dB @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( dB @ aa ) ) ) @ ( app @ ( dB @ ( dB @ foldl ) ) ) ) @ ( it @ ( bool @ ( dB @ aa ) ) ) @ pp ) ),
inference(simp,[status(thm)],[1082]) ).
thf(25,axiom,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_0_Beta) ).
thf(222,plain,
! [A: dB @ list,B: dB,C: dB] :
( ( A @ ( nat @ zero_zero @ ( B @ ( C @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ fun ) @ ( dB @ aa ) ) ) @ ( dB @ ( nat @ aa ) ) ) @ ( 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)],[25]) ).
thf(88,axiom,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_lifts__IT) ).
thf(454,plain,
! [A: dB @ list] :
( ( A @ ( it @ ( dB @ listsp ) ) )
=> ( A @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(362,plain,
~ ? [A: nat] :
( A
= ( A @ suc ) ),
inference(miniscope,[status(thm)],[361]) ).
thf(363,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(cnf,[status(esa)],[362]) ).
thf(364,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(lifteq,[status(thm)],[363]) ).
thf(15315,plain,
$false,
inference(e,[status(thm)],[1036,4201,1718,3008,479,352,365,138,628,249,518,2499,308,597,217,276,440,511,3794,384,550,472,340,153,174,185,1441,320,436,4249,651,2985,2227,389,184,587,3485,344,460,1704,284,152,4507,4302,1087,189,2222,164,591,2996,376,2650,574,121,514,280,221,132,396,292,452,4323,529,546,2646,201,1736,1091,302,561,297,4284,165,229,252,197,361,329,2200,456,224,1089,317,156,4544,2692,169,3746,526,489,3723,547,471,256,622,393,515,2487,371,1434,311,2338,398,1035,425,430,1698,3042,166,444,149,375,180,296,2674,577,281,204,445,1092,181,1464,236,1765,1090,172,377,567,477,387,631,535,323,594,251,3006,2647,1022,155,198,330,367,552,130,399,1474,299,226,167,135,563,2318,374,342,355,553,145,531,2665,525,1770,3507,150,3058,2656,1452,177,359,1790,1716,3828,470,1023,600,4143,175,314,446,627,450,539,203,218,368,390,632,401,171,418,652,351,139,1822,378,246,433,1777,2462,1440,383,1442,536,214,620,3860,168,146,3892,422,273,603,564,305,326,2334,2186,1172,294,136,624,459,131,3886,163,178,277,322,122,543,1088,222,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL759_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.48 % Computer : n018.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Fri Sep 25 23:32:52 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.27 % [INFO] Parsing done (300ms).
% 1.80/1.28 % [INFO] Running in sequential loop mode.
% 3.16/1.61 % [INFO] eprover registered as external prover.
% 3.16/1.62 % [INFO] Scanning for conjecture ...
% 3.41/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 118 axioms. Running axiom selection ...
% 4.16/1.93 % [INFO] Axiom selection finished. Selected 118 axioms (removed 0 axioms).
% 5.42/2.15 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.42/2.19 % [INFO] Type checking passed.
% 5.42/2.19 % [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 ...
% 247.49/99.72 % External prover 'e' found a proof!
% 247.49/99.72 % [INFO] Killing All external provers ...
% 247.49/99.72 % Time passed: 99089ms (effective reasoning time: 98430ms)
% 247.49/99.72 % 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)>
% 247.49/99.72 % Axioms used in derivation (118): fact_43_lift__map, fact_82_subst__preserves__beta, fact_17_dB_Osimps_I6_J, fact_87_add__is__1, help_COMBS_1_1_U, fact_96_One__nat__def, fact_93_substn__subst__0, fact_12_dB_Osimps_I2_J, fact_42_lift__IT, fact_53_nat__add__right__cancel, help_fconj_3_1_U, fact_69_add__eq__self__zero, fact_31_Suc__n__not__n, fact_51_add__right__cancel, fact_71_plus__nat_Oadd__0, fact_63_dB_Osize_I5_J, help_COMBI_1_1_U, conj_3, fact_64_dB_Osize_I6_J, fact_4_Lambda, fact_78_nat__add__assoc, fact_90_apps__preserves__beta, fact_47_dB_Osize_I2_J, fact_91_substn__subst__n, fact_7_Abs__App__neq__Var__apps, fact_66_add__0, fact_24_Suc__neq__Zero, fact_84_liftn__0, fact_37_nat__induct, fact_79_add__left__imp__eq, fact_62_liftn_Osimps_I2_J, fact_48_beta, arity_Nat_Onat___Groups_Ocomm__monoid__add, arity_Nat_Onat___Groups_Osemigroup__add, fact_80_add__imp__eq, fact_6_apps__eq__tail__conv, fact_38_zero__induct, fact_72_add__Suc__shift, fact_95_subst__Abs, fact_92_substn_Osimps_I2_J, fact_74_foldl__assoc, fact_44_subst__lift, help_COMBB_1_1_U, fact_89_double__eq__0__iff, conj_2, fact_61_beta__cases_I1_J, fact_33_Zero__not__Suc, fact_65_add__0__left, fact_73_ext, fact_52_nat__add__left__cancel, fact_56_add__Suc__right, help_fconj_2_1_U, fact_3_Var__apps__eq__Var__apps__conv, fact_46_liftn__lift, fact_76_nat__add__left__commute, fact_2_Abs__apps__eq__Abs__apps__conv, fact_10_dB_Osimps_I3_J, fact_23_IT_OVar, fact_45_dB_Osize_I3_J, fact_54_double__zero__sym, fact_25_Zero__neq__Suc, fact_15_dB_Osimps_I4_J, fact_94_beta__cases_I3_J, fact_1_subst__map, fact_32_Suc__inject, arity_Nat_Onat___Groups_Ozero, fact_40_lifts__IT, fact_49_dB_Osize_I4_J, fact_68_add_Ocomm__neutral, fact_19_subst__eq, fact_41_lift_Osimps_I2_J, fact_55_add__is__0, help_COMBC_1_1_U, fact_20_foldl__map, fact_88_beta__cases_I2_J, fact_67_add__0__right, fact_13_dB_Osimps_I5_J, conj_1, fact_9_map__ident, fact_21_nat_Oinject, fact_36_not0__implies__Suc, fact_30_n__not__Suc__n, fact_22_dB_Osize_I1_J, help_fconj_1_1_U, fact_57_add__Suc, fact_83_lift__preserves__beta, arity_Nat_Onat___Groups_Oone, fact_29_zero__reorient, fact_14_dB_Osimps_I8_J, fact_58_appL, fact_77_ab__semigroup__add__class_Oadd__ac_I1_J, help_pp_1_1_U, fact_85_foldl__absorb0, fact_81_add__right__imp__eq, arity_Nat_Onat___Groups_Omonoid__add, fact_60_abs, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_75_nat__add__commute, fact_11_dB_Osimps_I1_J, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, conj_0, help_pp_2_1_U, fact_39_nat_Oexhaust, fact_34_nat_Osimps_I2_J, fact_59_appR, fact_8_Var__apps__neq__Abs__apps, fact_18_dB_Osimps_I7_J, fact_50_add__left__cancel, fact_0_Beta, fact_70_Nat_Oadd__0__right, fact_26_nat_Osimps_I3_J, fact_35_IT_Osimps, fact_86_one__is__add, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_5_subst__App, fact_27_Suc__not__Zero, fact_28_listsp__conj__eq, fact_16_dB_Osimps_I9_J
% 247.49/99.72 % No. of inferences in proof: 547
% 247.49/99.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 99089 ms resp. 98430 ms w/o parsing
% 248.38/99.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 248.38/99.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------