%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT157^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n014.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 : Wed Sep 30 07:48:03 AM UTC 2026
% Result : Theorem 11.53s 4.14s
% Output : Refutation 12.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 175
% Syntax : Number of formulae : 352 ( 116 unt; 0 typ; 0 def)
% Number of atoms : 1192 ( 240 equ; 2 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 3652 ( 150 ~; 36 |; 56 &;3038 @)
% ( 0 <=>; 372 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 10 con; 0-6 aty)
% Number of variables : 894 ( 22 ^; 864 !; 8 ?; 894 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coindu351974385stinct_decl,type,
coindu351974385stinct:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lfinite_decl,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_LCons_decl,type,
coinductive_LCons:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(coinductive_lset_decl,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_lsorted_decl,type,
coinductive_lsorted:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(condit2040224947_above_decl,type,
condit2040224947_above:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(condit1201339847_below_decl,type,
condit1201339847_below:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(finite_folding_decl,type,
finite_folding:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > $o ) ).
thf(semigroup_decl,type,
semigroup:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(hammin1328233080lmerge_decl,type,
hammin1328233080lmerge:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(semilattice_decl,type,
semilattice:
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf(lattic1693879045er_set_decl,type,
lattic1693879045er_set:
!>[TA: $tType] : ( ( TA > TA > TA ) > ( TA > TA > $o ) > ( TA > TA > $o ) > $o ) ).
thf(insort_key_decl,type,
insort_key:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TA > TB ) > TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(least_decl,type,
least:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > TA ) ).
thf(min_decl,type,
min:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(ordering_decl,type,
ordering:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > $o ) ).
thf(transp_decl,type,
transp:
!>[TA: $tType] : ( ( TA > TA > $o ) > $o ) ).
thf(set_atLeast_decl,type,
set_atLeast:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_atLeastAtMost_decl,type,
set_atLeastAtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atLeastLessThan_decl,type,
set_atLeastLessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atMost_decl,type,
set_atMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_greaterThan_decl,type,
set_greaterThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_gr323396891AtMost_decl,type,
set_gr323396891AtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_gr1161524159ssThan_decl,type,
set_gr1161524159ssThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_lessThan_decl,type,
set_lessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(less_decl,type,
less: a > a > $o ).
thf(less_eq_decl,type,
less_eq: a > a > $o ).
thf(thesis_decl,type,
thesis: $o ).
thf(x_decl,type,
x: a ).
thf(x2_decl,type,
x2: a ).
thf(xsa_decl,type,
xsa: coinductive_llist @ a ).
thf(ysa_decl,type,
ysa: coinductive_llist @ a ).
thf(54,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ ( min @ a @ less_eq @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_local_Omin_Ostrict__boundedE) ).
thf(320,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ ( min @ a @ less_eq @ B @ C ) )
=> ~ ( ( less @ A @ B )
=> ~ ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(106,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ B @ D ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) )
=> ( C @ D ) ) )
=> ( C @ ( least @ a @ less_eq @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_local_OLeastI2__order) ).
thf(479,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ B @ D ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ D @ E ) )
=> ( C @ D ) ) )
=> ( C @ ( least @ a @ less_eq @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
& ( coindu351974385stinct @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ldistinct__LCons) ).
thf(628,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
& ( coindu351974385stinct @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(101,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( min @ a @ less_eq @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_local_Omin_Oabsorb__iff1) ).
thf(468,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( min @ a @ less_eq @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(157,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_local_OatLeast__iff) ).
thf(666,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(12,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ord_Olfinite__lmergeI) ).
thf(202,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_local_Obdd__above__Ioc) ).
thf(217,plain,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( min @ a @ less_eq @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_local_Omin_Ostrict__coboundedI2) ).
thf(276,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( min @ a @ less_eq @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(77,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_local_OleI) ).
thf(384,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(117,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( min @ a @ less_eq @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_local_Omin_Oabsorb__iff2) ).
thf(533,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( min @ a @ less_eq @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(62,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_local_Oless__linear) ).
thf(340,plain,
! [A: a,B: a] :
( ( less @ A @ B )
| ( A = B )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(5,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_local_OlessThan__iff) ).
thf(184,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(140,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_local_Oord__eq__le__trans) ).
thf(619,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(10,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_local_Ole__neq__trans) ).
thf(196,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( A != B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Odual__order_Ostrict__trans) ).
thf(189,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) )
=> ( ( coinductive_lfinite @ a @ A )
| ( coinductive_lfinite @ a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_local_Olfinite__lmergeD) ).
thf(284,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) )
=> ( ( coinductive_lfinite @ a @ A )
| ( coinductive_lfinite @ a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(90,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_local_Odual__order_Ostrict__trans2) ).
thf(416,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(42,axiom,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_local_Obdd__above__Ico) ).
thf(289,plain,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_local_Oless__trans) ).
thf(261,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(150,axiom,
! [A: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_local_Obdd__below__def) ).
thf(646,plain,
! [A: set @ a] :
( ( condit1201339847_below @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(65,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Oantisym__conv3) ).
thf(348,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( ~ ( less @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_local_Ole__imp__less__or__eq) ).
thf(353,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(83,axiom,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Onot__less__iff__gr__or__eq) ).
thf(397,plain,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( ( less @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(20,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_local_Odual__order_Ostrict__implies__order) ).
thf(221,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(82,axiom,
lattic1693879045er_set @ a @ ( min @ a @ less_eq ) @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_local_OMin_Osemilattice__order__set__axioms) ).
thf(396,plain,
lattic1693879045er_set @ a @ ( min @ a @ less_eq ) @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(154,axiom,
member @ a @ x @ ( coinductive_lset @ a @ xsa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_step_Ohyps_I1_J) ).
thf(660,plain,
member @ a @ x @ ( coinductive_lset @ a @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(25,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_Ole__less__linear) ).
thf(243,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_lset__intros_I1_J) ).
thf(507,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(44,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_local_Ole__less) ).
thf(292,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(27,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_local_Oless__imp__not__less) ).
thf(248,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(111,axiom,
! [A: a,B: a] :
( ( min @ a @ less_eq @ ( min @ a @ less_eq @ A @ B ) @ B )
= ( min @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_local_Omin_Oright__idem) ).
thf(512,plain,
! [A: a,B: a] :
( ( min @ a @ less_eq @ ( min @ a @ less_eq @ A @ B ) @ B )
= ( min @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(161,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_local_Omin_OboundedE) ).
thf(678,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_lset__intros_I2_J) ).
thf(661,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(76,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_local_Odual__order_Ostrict__trans1) ).
thf(381,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ C @ A )
=> ( less @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(71,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_local_Oorder_Ostrict__trans2) ).
thf(366,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(169,axiom,
! [A: a,B: a] :
( ~ ( less_eq @ A @ B )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_local_Ole__cases) ).
thf(714,plain,
! [A: a,B: a] :
( ~ ( less_eq @ A @ B )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(59,axiom,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_lessThan @ a @ less @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_local_Obdd__above__Iio) ).
thf(334,plain,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_lessThan @ a @ less @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(47,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_local_Oorder_Ostrict__implies__order) ).
thf(302,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(173,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_local_OatMost__iff) ).
thf(729,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(8,axiom,
ordering @ a @ less_eq @ less,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_local_Oorder_Oordering__axioms) ).
thf(192,plain,
ordering @ a @ less_eq @ less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(87,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B )
= ( set_gr323396891AtMost @ a @ less_eq @ less @ C @ D ) )
= ( ( ( less_eq @ B @ A )
& ( less_eq @ D @ C ) )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_local_OIoc__inj) ).
thf(407,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B )
= ( set_gr323396891AtMost @ a @ less_eq @ less @ C @ D ) )
= ( ( ( less_eq @ B @ A )
& ( less_eq @ D @ C ) )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_local_Obdd__below__Icc) ).
thf(252,plain,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(69,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Oorder_Oirrefl) ).
thf(361,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(162,axiom,
x != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_step_Ohyps_I2_J) ).
thf(682,plain,
x != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(122,axiom,
! [A: a,B: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ B ) )
= ( ( coinductive_lsorted @ a @ less_eq @ B )
& ! [C: a] :
( ( member @ a @ C @ ( coinductive_lset @ a @ B ) )
=> ( less_eq @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_local_Olsorted__LCons) ).
thf(551,plain,
! [A: a,B: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ B ) )
= ( ( coinductive_lsorted @ a @ less_eq @ B )
& ! [C: a] :
( ( member @ a @ C @ ( coinductive_lset @ a @ B ) )
=> ( less_eq @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(168,axiom,
? [A: a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ysa ) )
& ( less_eq @ x @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_step_Oprems_I3_J) ).
thf(710,plain,
? [A: a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ysa ) )
& ( less_eq @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(55,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_local_Oless__le) ).
thf(324,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(23,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( coinductive_lfinite @ a @ A )
=> ( ~ ( coinductive_lfinite @ a @ B )
=> ~ ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_local_Olinfinite__lmerge) ).
thf(229,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( coinductive_lfinite @ a @ A )
=> ( ~ ( coinductive_lfinite @ a @ B )
=> ~ ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(126,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Oantisym__conv) ).
thf(566,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_lset__induct_H) ).
thf(578,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(53,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_local_Odual__order_Ostrict__iff__order) ).
thf(317,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_local_Omin_Obounded__iff) ).
thf(615,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(79,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_local_Oorder_Ostrict__trans1) ).
thf(388,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(68,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Oord__less__eq__trans) ).
thf(356,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_local_Omin_Oabsorb2) ).
thf(554,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(9,axiom,
! [A: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ xsa )
=> ( ~ ( coinductive_lfinite @ a @ A )
=> ( ? [B: a] :
( ( member @ a @ B @ ( coinductive_lset @ a @ A ) )
& ( less_eq @ x @ B ) )
=> ( member @ a @ x @ ( coinductive_lset @ a @ ( hammin1328233080lmerge @ a @ less @ xsa @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_step_OIH) ).
thf(193,plain,
! [A: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ xsa )
=> ( ~ ( coinductive_lfinite @ a @ A )
=> ( ? [B: a] :
( ( member @ a @ B @ ( coinductive_lset @ a @ A ) )
& ( less_eq @ x @ B ) )
=> ( member @ a @ x @ ( coinductive_lset @ a @ ( hammin1328233080lmerge @ a @ less @ xsa @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(158,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( min @ a @ less_eq @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Omin_OorderE) ).
thf(669,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( min @ a @ less_eq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(104,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_local_Oeq__iff) ).
thf(476,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(147,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_local_Oantisym) ).
thf(637,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(166,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_local_Oorder__refl) ).
thf(706,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(57,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Oorder_Oorder__iff__strict) ).
thf(328,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(102,axiom,
! [A: a,B: coinductive_llist @ a,C: coinductive_llist @ a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ( hammin1328233080lmerge @ a @ less @ B @ C ) ) )
=> ( ( member @ a @ A @ ( coinductive_lset @ a @ B ) )
| ( member @ a @ A @ ( coinductive_lset @ a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_local_Oin__lset__lmergeD) ).
thf(471,plain,
! [A: a,B: coinductive_llist @ a,C: coinductive_llist @ a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ( hammin1328233080lmerge @ a @ less @ B @ C ) ) )
=> ( ( member @ a @ A @ ( coinductive_lset @ a @ B ) )
| ( member @ a @ A @ ( coinductive_lset @ a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(81,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ord_Olsorted__LCons__LCons) ).
thf(393,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1328233080lmerge @ TA @ B @ C @ D ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ord_Oin__lset__lmergeD) ).
thf(515,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1328233080lmerge @ TA @ B @ C @ D ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(171,axiom,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_local_Obdd__belowI) ).
thf(721,plain,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ B @ C ) )
=> ( condit1201339847_below @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(127,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_local_Oeq__refl) ).
thf(569,plain,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_lfinite__LCons) ).
thf(371,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(63,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Oorder_Oasym) ).
thf(343,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(51,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Oless__le__trans) ).
thf(311,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(153,axiom,
! [A: a,B: a] :
( ( A
= ( min @ a @ less_eq @ A @ B ) )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_local_Omin_OorderI) ).
thf(657,plain,
! [A: a,B: a] :
( ( A
= ( min @ a @ less_eq @ A @ B ) )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(46,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_local_Oless__imp__not__eq) ).
thf(298,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(139,axiom,
( finite_folding @ a @ ( list @ a )
@ ( insort_key @ a @ a @ less_eq
@ ^ [A: a] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_local_Osorted__list__of__set_Ofolding__axioms) ).
thf(618,plain,
( finite_folding @ a @ ( list @ a )
@ ( insort_key @ a @ a @ less_eq
@ ^ [A: a] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(33,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Oless__imp__neq) ).
thf(264,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_OneqE) ).
thf(279,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( less @ A @ B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(128,axiom,
! [A: a] :
( ( min @ a @ less_eq @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_local_Omin_Oidem) ).
thf(573,plain,
! [A: a] :
( ( min @ a @ less_eq @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(97,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_local_Oorder_Onot__eq__order__implies__strict) ).
thf(444,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ A @ B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(175,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_local_Oorder__trans) ).
thf(733,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(134,axiom,
! [A: a,B: a,C: a] :
( ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( min @ a @ less_eq @ B @ ( min @ a @ less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_local_Omin_Oleft__commute) ).
thf(601,plain,
! [A: a,B: a,C: a] :
( ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( min @ a @ less_eq @ B @ ( min @ a @ less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(92,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( ( A @ B @ C )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ B @ ( hammin1328233080lmerge @ TA @ A @ D @ ( coinductive_LCons @ TA @ C @ E ) ) ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ C @ ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ E ) ) ) )
& ( ~ ( A @ C @ B )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ C @ ( hammin1328233080lmerge @ TA @ A @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ord_Olmerge__simps) ).
thf(423,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA,E: coinductive_llist @ TA] :
( ( ( A @ B @ C )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ B @ ( hammin1328233080lmerge @ TA @ A @ D @ ( coinductive_LCons @ TA @ C @ E ) ) ) ) )
& ( ~ ( A @ B @ C )
=> ( ( ( A @ C @ B )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ C @ ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ E ) ) ) )
& ( ~ ( A @ C @ B )
=> ( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LCons @ TA @ B @ D ) @ ( coinductive_LCons @ TA @ C @ E ) )
= ( coinductive_LCons @ TA @ C @ ( hammin1328233080lmerge @ TA @ A @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(85,axiom,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_local_Onot__less) ).
thf(402,plain,
! [A: a,B: a] :
( ( ~ ( less @ A @ B ) )
= ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(174,axiom,
semilattice @ a @ ( min @ a @ less_eq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_local_Omin_Osemilattice__axioms) ).
thf(732,plain,
semilattice @ a @ ( min @ a @ less_eq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(41,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( min @ a @ less_eq @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_local_Omin_Ostrict__coboundedI1) ).
thf(286,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( less @ ( min @ a @ less_eq @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(43,axiom,
( ordering @ a
@ ^ [A: a,B: a] : ( less_eq @ B @ A )
@ ^ [A: a,B: a] : ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_local_Odual__order_Oordering__axioms) ).
thf(291,plain,
( ordering @ a
@ ^ [A: a,B: a] : ( less_eq @ B @ A )
@ ^ [A: a,B: a] : ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(13,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Ole__less__trans) ).
thf(204,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(120,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_local_Oorder_Otrans) ).
thf(545,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(31,axiom,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_local_Obdd__below__Ioc) ).
thf(259,plain,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(89,axiom,
! [A: a,B: a,C: a] :
( ( less @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( ( less @ A @ C )
| ( less @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_local_Omin__less__iff__disj) ).
thf(413,plain,
! [A: a,B: a,C: a] :
( ( less @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( ( less @ A @ C )
| ( less @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(80,axiom,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_local_Obdd__above__Iic) ).
thf(391,plain,
! [A: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atMost @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
=> ( ( least @ a @ less_eq @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_local_OLeast__equality) ).
thf(498,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ B @ C ) )
=> ( ( least @ a @ less_eq @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(4,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_local_OgreaterThan__iff) ).
thf(181,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(119,axiom,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_local_Obdd__aboveI) ).
thf(540,plain,
! [A: set @ a,B: a] :
( ! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) )
=> ( condit2040224947_above @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(159,axiom,
! [A: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_local_Obdd__above__def) ).
thf(672,plain,
! [A: set @ a] :
( ( condit2040224947_above @ a @ less_eq @ A )
= ( ? [B: a] :
! [C: a] :
( ( member @ a @ C @ A )
=> ( less_eq @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(135,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( min @ a @ less_eq @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_local_Omin_OcoboundedI1) ).
thf(604,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( min @ a @ less_eq @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(6,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_local_Oless__imp__le) ).
thf(187,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_local_Oless__asym) ).
thf(219,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(91,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Odual__order_Ostrict__implies__not__eq) ).
thf(419,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(176,axiom,
! [A: a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ysa ) )
=> ( ( less_eq @ x @ A )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(736,plain,
! [A: a] :
( ( member @ a @ A @ ( coinductive_lset @ a @ ysa ) )
=> ( ( less_eq @ x @ A )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(26,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_local_Odual__order_Onot__eq__order__implies__strict) ).
thf(245,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ( less_eq @ B @ A )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [A: a,B: a] :
( ~ ( less_eq @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_local_Onot__le__imp__less) ).
thf(271,plain,
! [A: a,B: a] :
( ~ ( less_eq @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(133,axiom,
~ ( coinductive_lfinite @ a @ ysa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_step_Oprems_I2_J) ).
thf(599,plain,
~ ( coinductive_lfinite @ a @ ysa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(110,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
| ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_local_Omin__le__iff__disj) ).
thf(509,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
| ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(151,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_local_Omin_Oabsorb1) ).
thf(649,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(94,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( min @ a @ less_eq @ A @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_local_Omin_Ostrict__order__iff) ).
thf(434,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( A
= ( min @ a @ less_eq @ A @ B ) )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(144,axiom,
semigroup @ a @ ( min @ a @ less_eq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_local_Omin_Osemigroup__axioms) ).
thf(631,plain,
semigroup @ a @ ( min @ a @ less_eq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(64,axiom,
! [A: a,B: a,C: coinductive_llist @ a] :
( ( less_eq @ A @ B )
=> ( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ B @ C ) )
=> ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ ( coinductive_LCons @ a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_local_Olsorted_OLCons__LCons) ).
thf(345,plain,
! [A: a,B: a,C: coinductive_llist @ a] :
( ( less_eq @ A @ B )
=> ( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ B @ C ) )
=> ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ ( coinductive_LCons @ a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(114,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_local_Omin__def) ).
thf(520,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ldistinct_OLCons) ).
thf(626,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(16,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Odual__order_Oasym) ).
thf(213,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(172,axiom,
! [A: a,B: a] :
( ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ A @ B ) )
= ( min @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_local_Omin_Oleft__idem) ).
thf(726,plain,
! [A: a,B: a] :
( ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ A @ B ) )
= ( min @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(163,axiom,
! [TA: $tType,A: TA > a,B: TA,C: TA,D: list @ TA] :
( ( ( A @ B )
!= ( A @ C ) )
=> ( ( insort_key @ a @ TA @ less_eq @ A @ C @ ( insort_key @ a @ TA @ less_eq @ A @ B @ D ) )
= ( insort_key @ a @ TA @ less_eq @ A @ B @ ( insort_key @ a @ TA @ less_eq @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_local_Oinsort__key__left__comm) ).
thf(685,plain,
! [TA: $tType,A: TA > a,B: TA,C: TA,D: list @ TA] :
( ( ( A @ B )
!= ( A @ C ) )
=> ( ( insort_key @ a @ TA @ less_eq @ A @ C @ ( insort_key @ a @ TA @ less_eq @ A @ B @ D ) )
= ( insort_key @ a @ TA @ less_eq @ A @ B @ ( insort_key @ a @ TA @ less_eq @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(21,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_local_Odual__order_Oorder__iff__strict) ).
thf(223,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( less @ A @ B )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(49,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( less_eq @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_local_Oantisym__conv1) ).
thf(306,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( less_eq @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(125,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( min @ a @ less_eq @ A @ C ) @ ( min @ a @ less_eq @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_local_Omin_Omono) ).
thf(563,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( min @ a @ less_eq @ A @ C ) @ ( min @ a @ less_eq @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(22,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( ~ ( less @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_local_Oantisym__conv2) ).
thf(226,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( ~ ( less @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_local_Oorder_Ostrict__trans) ).
thf(431,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(103,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( min @ a @ less_eq @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Omin_Oorder__iff) ).
thf(473,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( min @ a @ less_eq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(160,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_local_OatLeastAtMost__iff) ).
thf(675,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(131,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( min @ a @ less_eq @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_local_Omin_OcoboundedI2) ).
thf(589,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( min @ a @ less_eq @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(116,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
| ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_local_Olinear) ).
thf(531,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
| ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(74,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Oorder_Ostrict__implies__not__eq) ).
thf(374,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(156,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_local_Odual__order_Otrans) ).
thf(663,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ A )
=> ( less_eq @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(121,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_local_Oorder_Oantisym) ).
thf(548,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_lset__cases) ).
thf(557,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(148,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_local_Omin_OboundedI) ).
thf(640,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( min @ a @ less_eq @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(45,axiom,
! [A: a,B: a,C: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ ( coinductive_LCons @ a @ B @ C ) ) )
= ( ( less_eq @ A @ B )
& ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_local_Olsorted__LCons__LCons) ).
thf(295,plain,
! [A: a,B: a,C: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ A @ ( coinductive_LCons @ a @ B @ C ) ) )
= ( ( less_eq @ A @ B )
& ( coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(39,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ord_Olinfinite__lmerge) ).
thf(282,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(56,axiom,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ x2 @ xsa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_step_Oprems_I1_J) ).
thf(327,plain,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LCons @ a @ x2 @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( ( less @ A @ B )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_local_Omin__less__iff__conj) ).
thf(199,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ ( min @ a @ less_eq @ B @ C ) )
= ( ( less @ A @ B )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(177,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,axiom,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Oneq__iff) ).
thf(331,plain,
! [A: a,B: a] :
( ( A != B )
= ( ( less @ A @ B )
| ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(96,axiom,
! [A: a] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_local_Oless__irrefl) ).
thf(441,plain,
! [A: a] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(61,axiom,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_gr1161524159ssThan @ a @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_local_Obdd__below__Ioo) ).
thf(338,plain,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_gr1161524159ssThan @ a @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(129,axiom,
! [A: a,B: a] : ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_local_Omin_Ocobounded1) ).
thf(576,plain,
! [A: a,B: a] : ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(149,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_local_Odual__order_Oantisym) ).
thf(643,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(60,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_local_OleD) ).
thf(336,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(165,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_local_OIcc__eq__Icc) ).
thf(703,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( set_atLeastAtMost @ a @ less_eq @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(137,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_llist_Oset__intros_I2_J) ).
thf(613,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(78,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_local_Oless__not__sym) ).
thf(386,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_llist_Oinject) ).
thf(314,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA,D: coinductive_llist @ TA] :
( ( ( coinductive_LCons @ TA @ A @ B )
= ( coinductive_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(99,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_lset__induct) ).
thf(450,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: coinductive_llist @ TA] : ( C @ ( coinductive_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coinductive_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(164,axiom,
! [A: a,B: a,C: a] :
( ( ( less_eq @ A @ B )
=> ~ ( less_eq @ B @ C ) )
=> ( ( ( less_eq @ B @ A )
=> ~ ( less_eq @ A @ C ) )
=> ( ( ( less_eq @ A @ C )
=> ~ ( less_eq @ C @ B ) )
=> ( ( ( less_eq @ C @ B )
=> ~ ( less_eq @ B @ A ) )
=> ( ( ( less_eq @ B @ C )
=> ~ ( less_eq @ C @ A ) )
=> ~ ( ( less_eq @ C @ A )
=> ~ ( less_eq @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_local_Ole__cases3) ).
thf(688,plain,
! [A: a,B: a,C: a] :
( ( ( less_eq @ A @ B )
=> ~ ( less_eq @ B @ C ) )
=> ( ( ( less_eq @ B @ A )
=> ~ ( less_eq @ A @ C ) )
=> ( ( ( less_eq @ A @ C )
=> ~ ( less_eq @ C @ B ) )
=> ( ( ( less_eq @ C @ B )
=> ~ ( less_eq @ B @ A ) )
=> ( ( ( less_eq @ B @ C )
=> ~ ( less_eq @ C @ A ) )
=> ~ ( ( less_eq @ C @ A )
=> ~ ( less_eq @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(107,axiom,
! [A: a,B: a,C: a] :
( ( min @ a @ less_eq @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_local_Omin_Oassoc) ).
thf(495,plain,
! [A: a,B: a,C: a] :
( ( min @ a @ less_eq @ ( min @ a @ less_eq @ A @ B ) @ C )
= ( min @ a @ less_eq @ A @ ( min @ a @ less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(28,axiom,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_greaterThan @ a @ less @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_local_Obdd__below__Ioi) ).
thf(250,plain,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_greaterThan @ a @ less @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(100,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastLessThan @ a @ less_eq @ less @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_local_OatLeastLessThan__iff) ).
thf(465,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastLessThan @ a @ less_eq @ less @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(113,axiom,
! [A: a,B: a] :
( ( min @ a @ less_eq @ A @ B )
= ( min @ a @ less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_local_Omin_Ocommute) ).
thf(517,plain,
! [A: a,B: a] :
( ( min @ a @ less_eq @ A @ B )
= ( min @ a @ less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(48,axiom,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_local_Obdd__above__Icc) ).
thf(304,plain,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_atLeastAtMost @ a @ less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(145,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr323396891AtMost @ a @ less_eq @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_local_OgreaterThanAtMost__iff) ).
thf(632,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr323396891AtMost @ a @ less_eq @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(152,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_local_Oord__le__eq__trans) ).
thf(652,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(66,axiom,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_gr1161524159ssThan @ a @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_local_Obdd__above__Ioo) ).
thf(351,plain,
! [A: a,B: a] : ( condit2040224947_above @ a @ less_eq @ ( set_gr1161524159ssThan @ a @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(75,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_local_Oorder_Ostrict__iff__order) ).
thf(378,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [A: a,B: a] :
( ( ~ ( less_eq @ A @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_local_Onot__le) ).
thf(207,plain,
! [A: a,B: a] :
( ( ~ ( less_eq @ A @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(105,axiom,
transp @ a @ less_eq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_local_Otransp__le) ).
thf(478,plain,
transp @ a @ less_eq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(118,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ A )
=> ( ( coindu351974385stinct @ a @ A )
=> ( ( coinductive_lsorted @ a @ less_eq @ B )
=> ( ( coindu351974385stinct @ a @ B )
=> ( ( ( coinductive_lset @ a @ A )
= ( coinductive_lset @ a @ B ) )
=> ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_local_Olsorted__ldistinct__lset__unique) ).
thf(536,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lsorted @ a @ less_eq @ A )
=> ( ( coindu351974385stinct @ a @ A )
=> ( ( coinductive_lsorted @ a @ less_eq @ B )
=> ( ( coindu351974385stinct @ a @ B )
=> ( ( ( coinductive_lset @ a @ A )
= ( coinductive_lset @ a @ B ) )
=> ( A = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_llist_Oset__induct) ).
thf(716,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA,C: TA > ( coinductive_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [D: TA,E: coinductive_llist @ TA] : ( C @ D @ ( coinductive_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coinductive_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coinductive_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coinductive_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(98,axiom,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_local_Oless__imp__triv) ).
thf(447,plain,
! [A: a,B: a,C: $o] :
( ( less @ A @ B )
=> ( ( less @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(88,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lfinite @ a @ A )
=> ( ( coinductive_lfinite @ a @ B )
=> ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_local_Olfinite__lmergeI) ).
thf(410,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lfinite @ a @ A )
=> ( ( coinductive_lfinite @ a @ B )
=> ( coinductive_lfinite @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(86,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) )
=> ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ord_OLCons__LCons) ).
thf(405,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coinductive_llist @ TA] :
( ( A @ B @ C )
=> ( ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ C @ D ) )
=> ( coinductive_lsorted @ TA @ A @ ( coinductive_LCons @ TA @ B @ ( coinductive_LCons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(36,axiom,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Olinorder__cases) ).
thf(273,plain,
! [A: a,B: a] :
( ~ ( less @ A @ B )
=> ( ( A != B )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_local_Oless__le__not__le) ).
thf(210,plain,
! [A: a,B: a] :
( ( less @ A @ B )
= ( ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_lfinite__code_I2_J) ).
thf(268,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ A @ B ) )
= ( coinductive_lfinite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(95,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_local_Oless__imp__not__eq2) ).
thf(437,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(84,axiom,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_local_Obdd__below__Ici) ).
thf(400,plain,
! [A: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeast @ a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(146,axiom,
! [A: a,B: a] : ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_local_Omin_Ocobounded2) ).
thf(635,plain,
! [A: a,B: a] : ( less_eq @ ( min @ a @ less_eq @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(141,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_local_Oorder_Orefl) ).
thf(624,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(115,axiom,
! [A: a,B: a,C: list @ a] :
( ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ A
@ ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ B
@ C ) )
= ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ B
@ ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ A
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_local_Oinsort__left__comm) ).
thf(528,plain,
! [A: a,B: a,C: list @ a] :
( ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ A
@ ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ B
@ C ) )
= ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ B
@ ( insort_key @ a @ a @ less_eq
@ ^ [D: a] : D
@ A
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr1161524159ssThan @ a @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_local_OgreaterThanLessThan__iff) ).
thf(178,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr1161524159ssThan @ a @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,axiom,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_local_Obdd__below__Ico) ).
thf(369,plain,
! [A: a,B: a] : ( condit1201339847_below @ a @ less_eq @ ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_llist_Oset__cases) ).
thf(607,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ! [C: coinductive_llist @ TA] :
( B
!= ( coinductive_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coinductive_llist @ TA] :
( ( B
= ( coinductive_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(30,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Oord__eq__less__trans) ).
thf(254,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_lfinite__LConsI) ).
thf(309,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( coinductive_lfinite @ TA @ ( coinductive_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(17,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
=> ( ( coinductive_lfinite @ TA @ B )
| ( coinductive_lfinite @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ord_Olfinite__lmergeD) ).
thf(215,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
=> ( ( coinductive_lfinite @ TA @ B )
| ( coinductive_lfinite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(132,axiom,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( less_eq @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_local_Olinorder__wlog) ).
thf(592,plain,
! [A: a > a > $o,B: a,C: a] :
( ! [D: a,E: a] :
( ( less_eq @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: a,E: a] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(70,axiom,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_local_Oless__asym_H) ).
thf(364,plain,
! [A: a,B: a] :
( ( less @ A @ B )
=> ~ ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_llist_Oset__intros_I1_J) ).
thf(708,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] : ( member @ TA @ A @ ( coinductive_lset @ TA @ ( coinductive_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(24,axiom,
! [A: a,B: a,C: coinductive_llist @ a,D: coinductive_llist @ a] :
( ( ( less @ A @ B )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ A @ ( hammin1328233080lmerge @ a @ less @ C @ ( coinductive_LCons @ a @ B @ D ) ) ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ B @ ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ D ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ B @ ( hammin1328233080lmerge @ a @ less @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_local_Olmerge__simps) ).
thf(232,plain,
! [A: a,B: a,C: coinductive_llist @ a,D: coinductive_llist @ a] :
( ( ( less @ A @ B )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ A @ ( hammin1328233080lmerge @ a @ less @ C @ ( coinductive_LCons @ a @ B @ D ) ) ) ) )
& ( ~ ( less @ A @ B )
=> ( ( ( less @ B @ A )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ B @ ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ D ) ) ) )
& ( ~ ( less @ B @ A )
=> ( ( hammin1328233080lmerge @ a @ less @ ( coinductive_LCons @ a @ A @ C ) @ ( coinductive_LCons @ a @ B @ D ) )
= ( coinductive_LCons @ a @ B @ ( hammin1328233080lmerge @ a @ less @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(738,plain,
$false,
inference(e,[status(thm)],[320,479,628,468,666,202,217,276,384,533,340,184,619,196,189,284,416,289,261,646,348,353,397,221,396,660,243,507,292,248,512,678,661,381,366,714,334,302,729,192,407,252,361,682,551,710,324,229,566,578,317,615,388,356,554,193,669,476,637,706,328,471,393,515,721,569,371,343,311,657,298,618,264,279,573,444,733,601,423,402,732,286,291,204,545,259,413,391,498,181,540,672,604,187,219,419,736,245,271,599,509,649,434,631,345,520,626,213,726,685,223,306,563,226,431,473,675,589,531,374,663,548,557,640,295,282,327,199,177,331,441,338,576,643,336,703,613,386,314,450,688,495,250,465,517,304,632,652,351,378,207,478,536,716,447,410,405,273,210,268,437,400,635,624,528,178,369,607,254,309,215,592,364,708,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT157^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n014.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 18:02:30 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.01/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.23/1.22 % [INFO] Parsing done (412ms).
% 2.23/1.24 % [INFO] Running in sequential loop mode.
% 3.57/1.63 % [INFO] eprover registered as external prover.
% 3.57/1.64 % [INFO] Scanning for conjecture ...
% 3.77/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 261 axioms. Running axiom selection ...
% 4.31/1.91 % [INFO] Axiom selection finished. Selected 174 axioms (removed 87 axioms).
% 4.95/2.17 % [INFO] Problem is higher-order (TPTP THF).
% 4.95/2.19 % [INFO] Type checking passed.
% 5.14/2.20 % [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 ...
% 11.53/4.13 % External prover 'e' found a proof!
% 11.53/4.13 % [INFO] Killing All external provers ...
% 11.53/4.13 % Time passed: 3777ms (effective reasoning time: 2890ms)
% 11.53/4.13 % 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)>
% 11.53/4.14 % Axioms used in derivation (174): fact_68_local_Onot__le__imp__less, fact_156_local_Osorted__list__of__set_Ofolding__axioms, fact_1_local_Odual__order_Oasym, fact_14_local_Oless__trans, fact_145_llist_Oset__intros_I2_J, fact_57_local_OleI, fact_108_local_Omin_Oassoc, fact_204_local_Obdd__below__Ioo, fact_112_local_Olfinite__lmergeD, fact_129_ord_Olmerge__simps, fact_101_local_Omin_Ocommute, fact_85_local_Oinsort__key__left__comm, fact_37_local_Olinorder__wlog, fact_56_local_OleD, fact_153_ord_Olsorted__LCons__LCons, fact_8_local_Oless__imp__not__eq2, fact_164_local_Obdd__below__Ici, fact_167_local_Omin_Osemigroup__axioms, fact_66_local_Oless__le__trans, fact_197_local_OatLeastLessThan__iff, fact_200_local_Obdd__below__Ico, fact_134_lfinite__code_I2_J, fact_104_local_Omin_Ocobounded2, fact_139_local_OgreaterThanAtMost__iff, fact_141_local_Obdd__below__Ioc, fact_203_local_OgreaterThanLessThan__iff, fact_18_local_Onot__less__iff__gr__or__eq, fact_82_local_Oin__lset__lmergeD, fact_40_local_Oorder_Oantisym, fact_19_local_Oord__eq__less__trans, fact_132_local_OIoc__inj, fact_149_lset__induct_H, fact_80_local_Olsorted_OLCons__LCons, fact_136_step_Oprems_I1_J, fact_135_local_Oinsort__left__comm, fact_198_local_Obdd__above__Iio, fact_133_step_OIH, fact_27_step_Ohyps_I1_J, fact_62_local_Ole__neq__trans, fact_74_local_Oorder_Ostrict__trans1, fact_17_local_Oneq__iff, fact_163_local_Obdd__above__Iic, fact_83_local_Obdd__above__def, fact_92_local_Omin_Oabsorb__iff1, fact_2_local_Odual__order_Ostrict__implies__not__eq, fact_22_local_Oorder_Oirrefl, fact_72_local_Oorder_Ostrict__iff__order, fact_64_local_Oless__le, fact_95_local_Omin__def, fact_107_local_Omin_OboundedE, fact_99_local_Omin_Omono, fact_12_local_Oless__linear, fact_13_local_Oless__not__sym, fact_50_local_Odual__order_Onot__eq__order__implies__strict, fact_91_local_Omin_Oabsorb2, fact_109_local_Olmerge__simps, fact_151_llist_Oset__induct, fact_70_local_Oorder_Onot__eq__order__implies__strict, fact_29_local_Oantisym__conv, fact_143_lset__intros_I2_J, fact_63_local_Oless__imp__le, fact_102_local_Omin_OcoboundedI2, fact_168_local_OgreaterThan__iff, fact_69_local_Onot__less, fact_52_local_Odual__order_Ostrict__iff__order, fact_215_local_Obdd__above__Icc, fact_76_local_Oorder_Orefl, fact_105_local_Omin_Ocobounded1, fact_65_local_Oless__le__not__le, fact_98_local_Omin_OorderE, fact_36_local_Olinear, fact_96_local_Omin_Oorder__iff, fact_67_local_Onot__le, fact_77_local_Oorder__refl, fact_162_local_OatLeast__iff, fact_131_ldistinct__LCons, fact_120_local_Omin_Oidem, fact_126_ord_Olinfinite__lmerge, fact_9_local_Oless__imp__not__less, fact_154_ord_OLCons__LCons, fact_89_local_Olsorted__LCons__LCons, fact_93_local_Omin_Oabsorb__iff2, fact_161_local_OatMost__iff, fact_5_local_Oless__asym_H, fact_51_local_Odual__order_Oorder__iff__strict, fact_100_local_Omin_Oleft__commute, fact_138_lfinite__LCons, fact_119_local_Omin_Oleft__idem, fact_44_local_Oantisym__conv1, fact_79_local_OLeast__equality, fact_110_local_Olinfinite__lmerge, fact_111_local_Olfinite__lmergeI, fact_26_step_Oprems_I2_J, fact_4_local_Oless__asym, fact_216_local_Obdd__below__Icc, fact_7_local_Oless__imp__not__eq, fact_32_local_Oeq__iff, fact_58_local_Ole__imp__less__or__eq, fact_88_local_Olsorted__ldistinct__lset__unique, fact_148_lset__induct, fact_155_ldistinct_OLCons, fact_114_local_Omin_Ostrict__order__iff, fact_199_local_Obdd__above__Ico, fact_158_local_Odual__order_Oordering__axioms, fact_160_local_Oorder_Oordering__axioms, fact_81_local_Olsorted__LCons, fact_124_local_Omin__less__iff__conj, fact_6_local_Oless__imp__neq, fact_75_local_Oorder_Ostrict__trans2, fact_146_llist_Oset__intros_I1_J, fact_11_local_Oless__irrefl, fact_60_local_Ole__less__linear, fact_213_local_OIcc__eq__Icc, fact_35_local_Ole__cases3, fact_166_local_Omin_Osemilattice__axioms, fact_122_local_Obdd__belowI, fact_140_local_Obdd__above__Ioc, fact_117_local_Omin_Ostrict__boundedE, fact_106_local_Omin_OboundedI, fact_196_local_OlessThan__iff, fact_34_local_Ole__cases, fact_55_local_Odual__order_Ostrict__trans2, fact_15_local_Olinorder__cases, fact_54_local_Odual__order_Ostrict__trans1, fact_121_local_Omin_Obounded__iff, fact_73_local_Oorder_Ostrict__implies__order, fact_31_local_Odual__order_Otrans, fact_97_local_Omin_OorderI, fact_30_local_Odual__order_Oantisym, fact_3_local_Odual__order_Ostrict__trans, fact_21_local_Oorder_Oasym, fact_71_local_Oorder_Oorder__iff__strict, fact_152_lfinite__LConsI, fact_41_local_Oorder_Otrans, fact_118_local_Omin_Oright__idem, fact_20_local_Oord__less__eq__trans, fact_128_ord_Olfinite__lmergeD, fact_94_local_Omin__le__iff__disj, fact_123_local_Obdd__aboveI, fact_0_local_Oantisym__conv3, fact_103_local_Omin_OcoboundedI1, fact_87_ord_Oin__lset__lmergeD, fact_116_local_Omin_Ostrict__coboundedI1, fact_144_lset__intros_I1_J, fact_212_local_OatLeastAtMost__iff, fact_28_local_Oantisym, fact_61_local_Ole__less__trans, fact_39_local_Oord__le__eq__trans, fact_90_local_Omin_Oabsorb1, fact_127_ord_Olfinite__lmergeI, fact_205_local_Obdd__above__Ioo, fact_86_local_Otransp__le, fact_16_local_OneqE, fact_130_local_OMin_Osemilattice__order__set__axioms, fact_42_local_Oorder__trans, fact_24_local_Oorder_Ostrict__trans, fact_10_local_Oless__imp__triv, fact_43_step_Oprems_I3_J, fact_33_local_Oeq__refl, fact_84_local_Obdd__below__def, fact_23_local_Oorder_Ostrict__implies__not__eq, fact_78_local_OLeastI2__order, conj_0, fact_49_local_Oantisym__conv2, fact_169_local_Obdd__below__Ioi, fact_113_local_Omin__less__iff__disj, fact_25_step_Ohyps_I2_J, fact_150_llist_Oset__cases, fact_137_llist_Oinject, fact_147_lset__cases, fact_38_local_Oord__eq__le__trans, fact_115_local_Omin_Ostrict__coboundedI2, fact_59_local_Ole__less, fact_53_local_Odual__order_Ostrict__implies__order
% 11.53/4.14 % No. of inferences in proof: 352
% 11.53/4.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3777 ms resp. 2890 ms w/o parsing
% 12.18/4.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.18/4.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------