%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP120^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n017.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 08:06:50 AM UTC 2026
% Result : Theorem 28.66s 7.31s
% Output : Refutation 29.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 228
% Syntax : Number of formulae : 475 ( 265 unt; 0 typ; 3 def)
% Number of atoms : 1095 ( 356 equ; 18 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3609 ( 89 ~; 41 |; 48 &;3073 @)
% ( 0 <=>; 358 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 32 usr; 6 con; 0-5 aty)
% Number of variables : 1134 ( 60 ^;1071 !; 0 ?;1134 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(condit1627435690bove_a_decl,type,
condit1627435690bove_a: ( a > a > $o ) > set_a > $o ).
thf(condit1001553558elow_a_decl,type,
condit1001553558elow_a: ( a > a > $o ) > set_a > $o ).
thf(finite40241356em_a_a_decl,type,
finite40241356em_a_a: ( a > a > a ) > $o ).
thf(abel_semigroup_a_decl,type,
abel_semigroup_a: ( a > a > a ) > $o ).
thf(semigroup_a_decl,type,
semigroup_a: ( a > a > a ) > $o ).
thf(inf_inf_set_a_decl,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(semilattice_a_decl,type,
semilattice_a: ( a > a > a ) > $o ).
thf(sup_sup_set_a_decl,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(lattic1885654924_set_a_decl,type,
lattic1885654924_set_a: ( a > a > a ) > $o ).
thf(modula17988509_aux_a_decl,type,
modula17988509_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1373251614_aux_a_decl,type,
modula1373251614_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula581031071_aux_a_decl,type,
modula581031071_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1936294176_aux_a_decl,type,
modula1936294176_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1144073633_aux_a_decl,type,
modula1144073633_aux_a: ( a > a > a ) > ( a > a > a ) > a > a > a > a ).
thf(modula1727524044comp_a_decl,type,
modula1727524044comp_a: ( a > a > $o ) > a > a > $o ).
thf(max_a_decl,type,
max_a: ( a > a > $o ) > a > a > a ).
thf(min_a_decl,type,
min_a: ( a > a > $o ) > a > a > a ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(greatest_a_decl,type,
greatest_a: ( a > a > $o ) > ( a > $o ) > a ).
thf(antimono_a_set_a_decl,type,
antimono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(mono_a_set_a_decl,type,
mono_a_set_a: ( a > a > $o ) > ( a > set_a ) > $o ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(c_decl,type,
c: a ).
thf(inf_decl,type,
inf: a > a > a ).
thf(less_eq_decl,type,
less_eq: a > a > $o ).
thf(sup_decl,type,
sup: a > a > a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: ( a > $o ) > $o ).
thf(sk3_decl,type,
sk3: a > ( a > $o ) > a ).
thf(sk4_decl,type,
sk4: ( a > $o ) > a > ( a > $o ) > a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a,B: a > $o] :
@+[C: a] :
~ ( ( B @ C )
=> ( less_eq @ C @ A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a > $o,B: a,C: a > $o] :
@+[D: a] :
~ ( ( C @ D )
=> ( ! [E: a] :
( ( C @ E )
=> ( less_eq @ E @ D ) )
=> ( A @ D ) ) ) ) ) ).
thf(218,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_local_Osup_Oleft__idem) ).
thf(893,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(6,axiom,
greatest_a = greatest_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_order_OGreatest_Ocong) ).
thf(234,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(140,axiom,
abel_semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_local_Oinf_Oabel__semigroup__axioms) ).
thf(666,plain,
abel_semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(40,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Oantisym) ).
thf(352,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(132,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_local_Osup_Oabsorb1) ).
thf(645,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(217,axiom,
lattic1885654924_set_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_local_OSup__fin_Osemilattice__set__axioms) ).
thf(892,plain,
lattic1885654924_set_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(174,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_local_Ole__iff__sup) ).
thf(777,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(101,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_semilattice__inf__class_Ole__inf__iff) ).
thf(555,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(58,axiom,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_semilattice_Oleft__idem) ).
thf(408,plain,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ ( A @ B @ C ) )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(146,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_local_Oinf_Oassoc) ).
thf(683,plain,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(71,axiom,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_local_OmonoD) ).
thf(449,plain,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(68,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_local_Oorder_Orefl) ).
thf(440,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(161,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_local_Oinf_Oright__idem) ).
thf(730,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(19,axiom,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_local_OmonoE) ).
thf(276,plain,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(181,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_local_Oc__a) ).
thf(797,plain,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(80,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_local_Oeq__iff) ).
thf(472,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(225,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Osup_Oabsorb__iff2) ).
thf(913,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(36,axiom,
! [A: a > a > a] :
( ! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_semigroup_Ointro) ).
thf(340,plain,
! [A: a > a > a] :
( ! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) )
=> ( semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(142,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_local_Oinf_Oabsorb__iff1) ).
thf(670,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(193,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_local_Ob__aux__def) ).
thf(829,plain,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ B @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(197,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_local_Osup__absorb1) ).
thf(841,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(31,axiom,
( semigroup_a
= ( ^ [A: a > a > a] :
! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_semigroup__def) ).
thf(320,plain,
( semigroup_a
= ( ^ [A: a > a > a] :
! [B: a,C: a,D: a] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(134,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ A @ ( inf @ B @ C ) ) @ ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Odistrib__sup__le) ).
thf(651,plain,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ A @ ( inf @ B @ C ) ) @ ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(16,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_order__class_Oeq__iff) ).
thf(257,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(159,axiom,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_local_Ob__a) ).
thf(724,plain,
! [A: a,B: a,C: a] :
( ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C )
= ( modula17988509_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(104,axiom,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( condit1001553558elow_a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_local_Obdd__below__mono) ).
thf(570,plain,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( condit1001553558elow_a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(123,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
=> ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_a__meet__b__eq__d) ).
thf(619,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
=> ( ( inf @ ( modula17988509_aux_a @ inf @ sup @ A @ B @ C ) @ ( modula1373251614_aux_a @ inf @ sup @ A @ B @ C ) )
= ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(196,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_local_Od__b__c__a) ).
thf(838,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(221,axiom,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ord_less_eq_set_a @ ( A @ ( inf @ B @ C ) ) @ ( inf_inf_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_local_Omono__inf) ).
thf(902,plain,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ord_less_eq_set_a @ ( A @ ( inf @ B @ C ) ) @ ( inf_inf_set_a @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(210,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_local_Ole__supE) ).
thf(870,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(118,axiom,
lattic1885654924_set_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_local_OInf__fin_Osemilattice__set__axioms) ).
thf(606,plain,
lattic1885654924_set_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(213,axiom,
! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_local_Oa__aux__def) ).
thf(881,plain,
! [A: a,B: a,C: a] :
( ( modula17988509_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(33,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_equalityD2) ).
thf(325,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
= ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(227,plain,
( ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) )
!= ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(228,plain,
( ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c )
!= ( inf @ ( modula17988509_aux_a @ inf @ sup @ b @ c @ a2 ) @ ( modula581031071_aux_a @ inf @ sup @ a2 @ b @ c ) ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(85,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_subset__trans) ).
thf(492,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(178,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_local_Oe__c__a__b) ).
thf(789,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(112,axiom,
abel_semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_local_Osup_Oabel__semigroup__axioms) ).
thf(591,plain,
abel_semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(48,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_local_Oorder_Oeq__iff) ).
thf(376,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(83,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_8_local_Oord__le__eq__trans) ).
thf(485,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)],[83]) ).
thf(39,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Collect__mono) ).
thf(348,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(190,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_local_Ole__inf__iff) ).
thf(821,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(222,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_local_Osup_Ocobounded2) ).
thf(905,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(117,axiom,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( sup @ D @ ( inf @ E @ F ) )
= ( inf @ ( sup @ D @ E ) @ ( sup @ D @ F ) ) )
=> ( ( inf @ A @ ( sup @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_local_Odistrib__imp2) ).
thf(602,plain,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( sup @ D @ ( inf @ E @ F ) )
= ( inf @ ( sup @ D @ E ) @ ( sup @ D @ F ) ) )
=> ( ( inf @ A @ ( sup @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(54,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_semilattice__inf__class_Oinf_Obounded__iff) ).
thf(397,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(208,axiom,
semilattice_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_local_Osup_Osemilattice__axioms) ).
thf(866,plain,
semilattice_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(173,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_local_Oinf_Oabsorb1) ).
thf(774,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(11,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_order__class_Odual__order_Oeq__iff) ).
thf(243,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( greatest_a @ less_eq @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_local_OGreatestI2__order) ).
thf(259,plain,
! [A: a > $o,B: a,C: a > $o] :
( ( A @ B )
=> ( ! [D: a] :
( ( A @ D )
=> ( less_eq @ D @ B ) )
=> ( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( greatest_a @ less_eq @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(260,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ C @ B ) )
=> ! [C: a > $o] :
( ! [D: a] :
( ( A @ D )
=> ( ! [E: a] :
( ( A @ E )
=> ( less_eq @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( greatest_a @ less_eq @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[259]) ).
thf(261,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk3 @ B @ A ) )
| ( sk2 @ A ) )
& ( ~ ( A @ B )
| ~ ( less_eq @ ( sk3 @ B @ A ) @ B )
| ( sk2 @ A ) )
& ( ~ ( A @ B )
| ~ ( sk2 @ A )
| ( A @ ( sk4 @ C @ B @ A ) )
| ( C @ ( greatest_a @ less_eq @ A ) ) )
& ( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ( A @ D )
| ( less_eq @ D @ ( sk4 @ C @ B @ A ) )
| ( C @ ( greatest_a @ less_eq @ A ) ) )
& ( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ( C @ ( sk4 @ C @ B @ A ) )
| ( C @ ( greatest_a @ less_eq @ A ) ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(265,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ( C @ ( sk4 @ C @ B @ A ) )
| ( C @ ( greatest_a @ less_eq @ A ) ) ),
inference(cnfConj,[status(thm)],[261]) ).
thf(89,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_semilattice__sup__class_Osup_Oleft__idem) ).
thf(507,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(94,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Oeq__refl) ).
thf(527,plain,
! [A: a,B: a] :
( ( A = B )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(212,axiom,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( inf @ D @ ( sup @ E @ F ) )
= ( sup @ ( inf @ D @ E ) @ ( inf @ D @ F ) ) )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_local_Odistrib__imp1) ).
thf(877,plain,
! [A: a,B: a,C: a] :
( ! [D: a,E: a,F: a] :
( ( inf @ D @ ( sup @ E @ F ) )
= ( sup @ ( inf @ D @ E ) @ ( inf @ D @ F ) ) )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ ( sup @ A @ B ) @ ( sup @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(149,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_local_Osup__ge1) ).
thf(692,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(27,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Un__subset__iff) ).
thf(307,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( condit1627435690bove_a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_local_Obdd__above__mono) ).
thf(248,plain,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( condit1627435690bove_a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Collect__mono__iff) ).
thf(380,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(169,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_local_Oinf__absorb2) ).
thf(761,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(186,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_local_Ole__supI) ).
thf(810,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(5,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(231,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(232,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(cnf,[status(esa)],[231]) ).
thf(233,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(72,axiom,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
=> ( semilattice_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_semilattice__set_Oaxioms) ).
thf(452,plain,
! [A: a > a > a] :
( ( lattic1885654924_set_a @ A )
=> ( semilattice_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_Osup_Oabsorb__iff1) ).
thf(910,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( sup @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(206,axiom,
semigroup_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_local_Oinf_Osemigroup__axioms) ).
thf(862,plain,
semigroup_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(103,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ord__eq__le__subst) ).
thf(561,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(127,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_local_Oinf__absorb1) ).
thf(630,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(18,axiom,
modula1373251614_aux_a = modula1373251614_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_lattice_Ob__aux_Ocong) ).
thf(275,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
antimono_a_set_a = antimono_a_set_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_order_Oantimono_Ocong) ).
thf(229,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_semilattice__sup__class_Osup_Obounded__iff) ).
thf(361,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(202,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_local_Od__c__a__b) ).
thf(852,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(34,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_116_local_Omin__def) ).
thf(329,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)],[34]) ).
thf(139,axiom,
modula1936294176_aux_a = modula1936294176_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_lattice_Od__aux_Ocong) ).
thf(665,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(100,axiom,
! [A: a > a > a,B: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_semilattice_Oidem) ).
thf(551,plain,
! [A: a > a > a,B: a] :
( ( semilattice_a @ A )
=> ( ( A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(74,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_order__class_Odual__order_Oantisym) ).
thf(456,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(22,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_subset__refl) ).
thf(285,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(226,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_local_Osup_Obounded__iff) ).
thf(916,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(78,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_semilattice__sup__class_Osup_Oidem) ).
thf(467,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(211,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_local_Ole__supI1) ).
thf(874,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(53,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ C @ B ) )
=> ( ( greatest_a @ less_eq @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_local_OGreatest__equality) ).
thf(388,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ! [C: a] :
( ( A @ C )
=> ( less_eq @ C @ B ) )
=> ( ( greatest_a @ less_eq @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(114,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_local_Ole__infI2) ).
thf(593,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(120,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_local_Oinf_Ocommute) ).
thf(610,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(87,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_order__class_Oantisym) ).
thf(499,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(163,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_local_Oinf_Oabsorb__iff2) ).
thf(742,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(107,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_local_Ole__infI1) ).
thf(578,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(176,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_local_Oa__join__d) ).
thf(783,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(62,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order__class_Oorder_Oantisym) ).
thf(420,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(79,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Odual__order_Oeq__iff) ).
thf(470,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(471,plain,
( ( ^ [A: a,B: a] :
( ( less_eq @ B @ A )
& ( less_eq @ A @ B ) ) )
= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[470]) ).
thf(214,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_local_Oinf_OcoboundedI2) ).
thf(884,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(147,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Osup_Ocommute) ).
thf(686,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(131,axiom,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ ( A @ B ) @ ( A @ C ) ) @ ( A @ ( sup @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_local_Omono__sup) ).
thf(642,plain,
! [A: a > set_a,B: a,C: a] :
( ( mono_a_set_a @ less_eq @ A )
=> ( ord_less_eq_set_a @ ( sup_sup_set_a @ ( A @ B ) @ ( A @ C ) ) @ ( A @ ( sup @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(99,axiom,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_abel__semigroup_Oleft__commute) ).
thf(547,plain,
! [A: a > a > a,B: a,C: a,D: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ ( A @ C @ D ) )
= ( A @ C @ ( A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(124,axiom,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_local_Odistrib__inf__le) ).
thf(622,plain,
! [A: a,B: a,C: a] : ( less_eq @ ( sup @ ( inf @ A @ B ) @ ( inf @ A @ C ) ) @ ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(153,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_local_Ole__supI2) ).
thf(701,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(91,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_ord__class_Oord__eq__le__trans) ).
thf(515,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(158,axiom,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_local_Oc__aux__def) ).
thf(721,plain,
! [A: a,B: a,C: a] :
( ( modula581031071_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( inf @ C @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) ) @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(244,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) )
= ( (=) @ set_a ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(179,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_local_Oinf__le2) ).
thf(792,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(128,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_local_Oinf_Oidem) ).
thf(633,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(180,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_local_Osup_OorderE) ).
thf(794,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_local_Ole__infI) ).
thf(662,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(37,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_11_local_Oorder_Otrans) ).
thf(343,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)],[37]) ).
thf(9,axiom,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_local_Obdd__below__Int1) ).
thf(237,plain,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(102,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_4_local_Odual__order_Otrans) ).
thf(558,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)],[102]) ).
thf(958,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ~ ( C
@ ( sk4
@ ^ [D: a] :
~ ( C @ D )
@ B
@ A ) )
| ~ ( C @ ( greatest_a @ less_eq @ A ) ) ),
inference(prim_subst,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: a] : ~ ( D @ E ) ))]]) ).
thf(1070,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ( C
@ ( sk4
@ ^ [D: a] :
~ ( C @ D )
@ B
@ A ) )
| ~ ( C @ ( greatest_a @ less_eq @ A ) ) ),
inference(cnf,[status(esa)],[958]) ).
thf(1071,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ( C
@ ( sk4
@ ^ [D: a] :
~ ( C @ D )
@ B
@ A ) )
| ~ ( C @ ( greatest_a @ less_eq @ A ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(26,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ord__le__eq__subst) ).
thf(298,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(59,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_order__class_Oantisym__conv) ).
thf(412,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(65,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Int__subset__iff) ).
thf(430,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(191,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_local_Osup_Ocobounded1) ).
thf(824,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(204,axiom,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_Oinf__assoc) ).
thf(856,plain,
! [A: a,B: a,C: a] :
( ( inf @ ( inf @ A @ B ) @ C )
= ( inf @ A @ ( inf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(164,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Oinf_OboundedE) ).
thf(745,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(20,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_order__class_Oorder_Otrans) ).
thf(279,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(105,axiom,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ( semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_abel__semigroup_Oaxioms_I1_J) ).
thf(573,plain,
! [A: a > a > a] :
( ( abel_semigroup_a @ A )
=> ( semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(148,axiom,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_local_Oinf__right__idem) ).
thf(689,plain,
! [A: a,B: a] :
( ( inf @ ( inf @ A @ B ) @ B )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(162,axiom,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ D @ ( A @ D @ E ) )
=> ( ! [D: a,E: a] : ( less_eq @ E @ ( A @ D @ E ) )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ E @ D )
=> ( ( less_eq @ F @ D )
=> ( less_eq @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_local_Osup__unique) ).
thf(733,plain,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ D @ ( A @ D @ E ) )
=> ( ! [D: a,E: a] : ( less_eq @ E @ ( A @ D @ E ) )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ E @ D )
=> ( ( less_eq @ F @ D )
=> ( less_eq @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(109,axiom,
modula581031071_aux_a = modula581031071_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_lattice_Oc__aux_Ocong) ).
thf(584,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(189,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_local_Oinf__le1) ).
thf(819,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(63,axiom,
! [A: a > set_a] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) )
=> ( antimono_a_set_a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_local_OantimonoI) ).
thf(423,plain,
! [A: a > set_a] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) )
=> ( antimono_a_set_a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(150,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_local_Oinf_Ocobounded1) ).
thf(694,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(56,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_lattice__class_Oinf__sup__absorb) ).
thf(402,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(192,axiom,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Osup__commute) ).
thf(826,plain,
! [A: a,B: a] :
( ( sup @ A @ B )
= ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(70,axiom,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_semilattice_Oright__idem) ).
thf(445,plain,
! [A: a > a > a,B: a,C: a] :
( ( semilattice_a @ A )
=> ( ( A @ ( A @ B @ C ) @ C )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(29,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_7_local_Oord__eq__le__trans) ).
thf(313,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)],[29]) ).
thf(155,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_local_Oinf_Oleft__idem) ).
thf(713,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(8,axiom,
min_a = min_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ord_Omin_Ocong) ).
thf(236,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(184,axiom,
! [A: a] :
( ( inf @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_local_Oinf__idem) ).
thf(804,plain,
! [A: a] :
( ( inf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ D )
=> ( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ E )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ D @ E )
=> ( ( less_eq @ D @ F )
=> ( less_eq @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_local_Oinf__unique) ).
thf(704,plain,
! [A: a > a > a,B: a,C: a] :
( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ D )
=> ( ! [D: a,E: a] : ( less_eq @ ( A @ D @ E ) @ E )
=> ( ! [D: a,E: a,F: a] :
( ( less_eq @ D @ E )
=> ( ( less_eq @ D @ F )
=> ( less_eq @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(97,axiom,
! [A: a > a > a,B: a,C: a,D: a] :
( ( semigroup_a @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_semigroup_Oassoc) ).
thf(540,plain,
! [A: a > a > a,B: a,C: a,D: a] :
( ( semigroup_a @ A )
=> ( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(170,axiom,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_local_Osup_OorderI) ).
thf(764,plain,
! [A: a,B: a] :
( ( A
= ( sup @ A @ B ) )
=> ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(61,axiom,
mono_a_set_a = mono_a_set_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_order_Omono_Ocong) ).
thf(419,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(377,plain,
( ( ^ [A: a,B: a] :
( ( less_eq @ A @ B )
& ( less_eq @ B @ A ) ) )
= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(4,axiom,
max_a = max_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_ord_Omax_Ocong) ).
thf(230,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_local_Obdd__above__Int1) ).
thf(245,plain,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
! [A: a] : ( less_eq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_local_Oorder__refl) ).
thf(318,plain,
! [A: a] : ( less_eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(122,axiom,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_local_Osup_Oright__idem) ).
thf(616,plain,
! [A: a,B: a] :
( ( sup @ ( sup @ A @ B ) @ B )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(207,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_local_Osup__mono) ).
thf(863,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(116,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_a__meet__d) ).
thf(599,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1242,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ( C @ ( greatest_a @ less_eq @ A ) )
| ( ( C
@ ( sk4
@ ^ [D: a] :
~ ( C @ D )
@ B
@ A ) )
!= ( ~ ( C @ ( greatest_a @ less_eq @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1071]) ).
thf(1376,plain,
! [C: a > $o,B: a,A: a > $o] :
( ~ ( A @ B )
| ~ ( sk2 @ A )
| ~ ( C @ ( greatest_a @ less_eq @ A ) )
| ( ( C
@ ( sk4
@ ^ [D: a] :
~ ( C @ D )
@ B
@ A ) )
!= ( ~ ( C @ ( greatest_a @ less_eq @ A ) ) ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(216,axiom,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_local_Osup__ge2) ).
thf(890,plain,
! [A: a,B: a] : ( less_eq @ A @ ( sup @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(82,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_local_Omax__def) ).
thf(477,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max_a @ less_eq @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(168,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_local_Ole__iff__inf) ).
thf(758,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( ( inf @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(45,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_semilattice__inf__class_Oinf__left__idem) ).
thf(367,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(188,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Osup_OcoboundedI1) ).
thf(816,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(76,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_preorder__class_Oorder__trans) ).
thf(462,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(200,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Oinf__left__commute) ).
thf(848,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(92,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_preorder__class_Oeq__refl) ).
thf(520,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(10,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_semilattice__inf__class_Oinf_Oleft__idem) ).
thf(240,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__antisym) ).
thf(251,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(129,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( inf @ A @ C ) @ ( inf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_local_Oinf__mono) ).
thf(636,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( inf @ A @ C ) @ ( inf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(175,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_local_Osup__left__commute) ).
thf(780,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(73,axiom,
lattic1885654924_set_a = semilattice_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_semilattice__set__def) ).
thf(454,plain,
lattic1885654924_set_a = semilattice_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(455,plain,
lattic1885654924_set_a = semilattice_a,
inference(lifteq,[status(thm)],[454]) ).
thf(201,axiom,
finite40241356em_a_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_local_Ocomp__fun__idem__inf) ).
thf(851,plain,
finite40241356em_a_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(135,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_local_Oinf_Obounded__iff) ).
thf(653,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
= ( ( less_eq @ A @ B )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(84,axiom,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( abel_semigroup_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_semilattice_Oaxioms_I1_J) ).
thf(490,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( abel_semigroup_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_equalityE) ).
thf(531,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(145,axiom,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_local_Oinf_OorderI) ).
thf(680,plain,
! [A: a,B: a] :
( ( A
= ( inf @ A @ B ) )
=> ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(133,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_local_Oa__meet__e) ).
thf(648,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(165,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_local_Oc__meet__e) ).
thf(749,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ C @ A ) )
= ( inf @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(41,axiom,
! [A: a,B: a] :
( ( modula1727524044comp_a @ less_eq @ A @ B )
= ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Oincomp__def) ).
thf(355,plain,
! [A: a,B: a] :
( ( modula1727524044comp_a @ less_eq @ A @ B )
= ( ~ ( less_eq @ A @ B )
& ~ ( less_eq @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(203,axiom,
modula17988509_aux_a = modula17988509_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_lattice_Oa__aux_Ocong) ).
thf(855,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(25,axiom,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_local_Obdd__above__Int2) ).
thf(295,plain,
! [A: set_a,B: set_a] :
( ( condit1627435690bove_a @ less_eq @ A )
=> ( condit1627435690bove_a @ less_eq @ ( inf_inf_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Oantisym__conv) ).
thf(282,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(215,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_local_Osup__idem) ).
thf(887,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(28,axiom,
! [A: a > set_a] :
( ( antimono_a_set_a @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_local_Oantimono__def) ).
thf(310,plain,
! [A: a > set_a] :
( ( antimono_a_set_a @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(143,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Osup_Oassoc) ).
thf(673,plain,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1607,plain,
! [B: a > $o,A: a] :
( ~ $true
| ~ ( sk2
@ ^ [C: a] : $true )
| ~ ( B
@ ( greatest_a @ less_eq
@ ^ [C: a] : $true ) )
| ( ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C )
@ A
@ ^ [C: a] : $true ) )
!= ( ~ ( B
@ ( greatest_a @ less_eq
@ ^ [C: a] : $true ) ) ) ) ),
inference(prim_subst,[status(thm)],[1376:[bind(A,$thf( ^ [D: a] : $true ))]]) ).
thf(1716,plain,
! [B: a > $o,A: a] :
( ~ ( sk2
@ ^ [C: a] : $true )
| ~ ( B
@ ( greatest_a @ less_eq
@ ^ [C: a] : $true ) )
| ( ( B
@ ( sk4
@ ^ [C: a] :
~ ( B @ C )
@ A
@ ^ [C: a] : $true ) )
!= ( ~ ( B
@ ( greatest_a @ less_eq
@ ^ [C: a] : $true ) ) ) ) ),
inference(simp,[status(thm)],[1607]) ).
thf(88,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_order__subst2) ).
thf(502,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(110,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_local_Oinf__greatest) ).
thf(585,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(46,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_semilattice__sup__class_Osup__idem) ).
thf(370,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(98,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_semilattice__inf__class_Oinf__right__idem) ).
thf(544,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(223,axiom,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Osup__assoc) ).
thf(907,plain,
! [A: a,B: a,C: a] :
( ( sup @ ( sup @ A @ B ) @ C )
= ( sup @ A @ ( sup @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(136,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_local_Osup_OcoboundedI2) ).
thf(656,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(121,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_local_Osup__inf__absorb) ).
thf(613,plain,
! [A: a,B: a] :
( ( sup @ A @ ( inf @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(160,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_c__meet__d) ).
thf(727,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ C @ A ) )
= ( sup @ ( inf @ A @ B ) @ ( inf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(52,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_order__class_Oorder_Oeq__iff) ).
thf(386,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(205,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_local_Osup_OboundedI) ).
thf(859,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(199,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_local_Oe__b__c__a) ).
thf(845,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( modula1144073633_aux_a @ inf @ sup @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(126,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Osup_Oleft__commute) ).
thf(627,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( sup @ B @ C ) )
= ( sup @ B @ ( sup @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(96,axiom,
modula1144073633_aux_a = modula1144073633_aux_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_lattice_Oe__aux_Ocong) ).
thf(539,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(86,axiom,
! [A: a > a > a,B: a,C: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_abel__semigroup_Ocommute) ).
thf(495,plain,
! [A: a > a > a,B: a,C: a] :
( ( abel_semigroup_a @ A )
=> ( ( A @ B @ C )
= ( A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(198,axiom,
semigroup_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_local_Osup_Osemigroup__axioms) ).
thf(844,plain,
semigroup_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(172,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ ( inf @ A @ C ) @ ( inf @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_b__meet__d) ).
thf(771,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ ( inf @ A @ C ) @ ( inf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(77,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_set__eq__subset) ).
thf(465,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(93,axiom,
! [A: a > set_a] :
( ( mono_a_set_a @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_local_Omono__def) ).
thf(524,plain,
! [A: a > set_a] :
( ( mono_a_set_a @ less_eq @ A )
= ( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(108,axiom,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ A @ ( inf @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_local_Ob__join__d) ).
thf(581,plain,
! [A: a,B: a,C: a] :
( ( sup @ A @ ( modula1936294176_aux_a @ inf @ sup @ B @ A @ C ) )
= ( sup @ A @ ( inf @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(187,axiom,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_local_Osup_Omono) ).
thf(813,plain,
! [A: a,B: a,C: a,D: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ D )
=> ( less_eq @ ( sup @ A @ C ) @ ( sup @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(219,axiom,
! [A: a] :
( ( sup @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_local_Osup_Oidem) ).
thf(896,plain,
! [A: a] :
( ( sup @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(258,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) )
= ( (=) @ set_a ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(177,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_local_Oinf__left__idem) ).
thf(786,plain,
! [A: a,B: a] :
( ( inf @ A @ ( inf @ A @ B ) )
= ( inf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(111,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ A @ C ) )
= ( inf @ A @ ( sup @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_local_Ob__meet__e) ).
thf(588,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( modula1144073633_aux_a @ inf @ sup @ B @ A @ C ) )
= ( inf @ A @ ( sup @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(152,axiom,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_local_Oinf_Ocobounded2) ).
thf(699,plain,
! [A: a,B: a] : ( less_eq @ ( inf @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(7,axiom,
modula1727524044comp_a = modula1727524044comp_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_lattice_Oincomp_Ocong) ).
thf(235,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(141,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_local_Oinf_OcoboundedI1) ).
thf(667,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( less_eq @ ( inf @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(51,axiom,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_local_Obdd__below__Int2) ).
thf(383,plain,
! [A: set_a,B: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(220,axiom,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Oinf_Oleft__commute) ).
thf(899,plain,
! [A: a,B: a,C: a] :
( ( inf @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( inf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(194,axiom,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_local_Oinf__sup__absorb) ).
thf(832,plain,
! [A: a,B: a] :
( ( inf @ A @ ( sup @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(38,axiom,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( lattic1885654924_set_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_semilattice__set_Ointro) ).
thf(346,plain,
! [A: a > a > a] :
( ( semilattice_a @ A )
=> ( lattic1885654924_set_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_ord__class_Oord__le__eq__trans) ).
thf(290,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(49,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_preorder__class_Oorder__refl) ).
thf(378,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(66,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_equalityD1) ).
thf(433,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(90,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_order__subst1) ).
thf(510,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(156,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_local_Osup_OboundedE) ).
thf(716,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
=> ~ ( ( less_eq @ A @ C )
=> ~ ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(182,axiom,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_local_Oe__aux__def) ).
thf(800,plain,
! [A: a,B: a,C: a] :
( ( modula1144073633_aux_a @ inf @ sup @ A @ B @ C )
= ( inf @ ( inf @ ( sup @ A @ B ) @ ( sup @ B @ C ) ) @ ( sup @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(23,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_local_Oorder_Oantisym) ).
thf(287,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(166,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_local_Ole__sup__iff) ).
thf(752,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ ( sup @ A @ B ) @ C )
= ( ( less_eq @ A @ C )
& ( less_eq @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(195,axiom,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_local_Od__aux__def) ).
thf(835,plain,
! [A: a,B: a,C: a] :
( ( modula1936294176_aux_a @ inf @ sup @ A @ B @ C )
= ( sup @ ( sup @ ( inf @ A @ B ) @ ( inf @ B @ C ) ) @ ( inf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(57,axiom,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_semilattice__inf__class_Oinf_Oidem) ).
thf(405,plain,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(209,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_local_Oinf_OboundedI) ).
thf(867,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ A @ C )
=> ( less_eq @ A @ ( inf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(47,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_semilattice__sup__class_Osup_Oright__idem) ).
thf(373,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(238,plain,
! [A: set_a] :
( ( condit1001553558elow_a @ less_eq @ A )
=> ! [B: set_a] : ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
inference(miniscope,[status(thm)],[237]) ).
thf(239,plain,
! [B: set_a,A: set_a] :
( ~ ( condit1001553558elow_a @ less_eq @ A )
| ( condit1001553558elow_a @ less_eq @ ( inf_inf_set_a @ A @ B ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(67,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_lattice__class_Osup__inf__absorb) ).
thf(437,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(55,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_order__class_Odual__order_Orefl) ).
thf(400,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(151,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_local_Oinf_OorderE) ).
thf(696,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(157,axiom,
semilattice_a @ inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_local_Oinf_Osemilattice__axioms) ).
thf(720,plain,
semilattice_a @ inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(60,axiom,
! [A: a > set_a] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) )
=> ( mono_a_set_a @ less_eq @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_local_OmonoI) ).
thf(415,plain,
! [A: a > set_a] :
( ! [B: a,C: a] :
( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ B ) @ ( A @ C ) ) )
=> ( mono_a_set_a @ less_eq @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(42,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_order__class_Odual__order_Otrans) ).
thf(358,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(185,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_local_Osup__least) ).
thf(807,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ C @ B )
=> ( less_eq @ ( sup @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(81,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_semilattice__inf__class_Oinf_Oright__idem) ).
thf(474,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(171,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( sup @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_local_Omodular) ).
thf(767,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ ( inf @ B @ C ) )
= ( inf @ B @ ( sup @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(125,axiom,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_local_Osup__left__idem) ).
thf(624,plain,
! [A: a,B: a] :
( ( sup @ A @ ( sup @ A @ B ) )
= ( sup @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(106,axiom,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Oinf__commute) ).
thf(575,plain,
! [A: a,B: a] :
( ( inf @ A @ B )
= ( inf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(64,axiom,
! [A: a > set_a,B: a,C: a] :
( ( antimono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_local_OantimonoD) ).
thf(427,plain,
! [A: a > set_a,B: a,C: a] :
( ( antimono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(115,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_local_Osup_Oabsorb2) ).
thf(596,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(75,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_semilattice__sup__class_Osup__left__idem) ).
thf(459,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(69,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Odual__order_Oantisym) ).
thf(442,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( less_eq @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(119,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_local_Oinf_Oabsorb2) ).
thf(607,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( inf @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(32,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_semilattice__sup__class_Ole__sup__iff) ).
thf(322,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(183,axiom,
finite40241356em_a_a @ sup,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_local_Ocomp__fun__idem__sup) ).
thf(803,plain,
finite40241356em_a_a @ sup,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(35,axiom,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_semilattice__inf__class_Oinf__idem) ).
thf(337,plain,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(137,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Osup_Oorder__iff) ).
thf(659,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( B
= ( sup @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(130,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_local_Osup__absorb2) ).
thf(639,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
=> ( ( sup @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(113,axiom,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(592,plain,
less_eq @ ( modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c ) @ ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(44,axiom,
! [A: a > set_a,B: a,C: a] :
( ( antimono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_local_OantimonoE) ).
thf(364,plain,
! [A: a > set_a,B: a,C: a] :
( ( antimono_a_set_a @ less_eq @ A )
=> ( ( less_eq @ B @ C )
=> ( ord_less_eq_set_a @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(15,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_12_local_Oorder__trans) ).
thf(254,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)],[15]) ).
thf(167,axiom,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_local_Oinf_Oorder__iff) ).
thf(755,plain,
! [A: a,B: a] :
( ( less_eq @ A @ B )
= ( A
= ( inf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(144,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_local_Ole__infE) ).
thf(676,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ ( inf @ B @ C ) )
=> ~ ( ( less_eq @ A @ B )
=> ~ ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(2131,plain,
$false,
inference(e,[status(thm)],[893,234,666,352,645,892,777,555,408,683,449,440,730,276,797,472,913,340,670,829,841,320,651,257,724,570,619,838,902,870,606,881,325,228,492,789,591,376,485,348,821,905,602,397,866,774,243,265,507,527,877,692,307,248,380,761,810,233,452,910,862,561,630,275,229,361,852,329,665,551,456,285,916,467,874,388,593,610,499,742,578,783,420,471,884,686,642,547,622,701,515,721,244,792,633,794,662,343,237,558,1071,298,412,430,824,856,745,279,573,689,733,584,819,423,694,402,826,259,445,313,713,236,804,704,540,764,419,377,230,245,318,616,863,599,1376,890,477,758,367,816,462,848,520,240,251,636,780,455,851,653,490,531,680,648,749,355,855,295,282,887,310,673,1716,502,470,585,370,544,907,656,613,727,386,859,845,627,539,495,844,771,465,231,524,581,813,896,258,786,588,699,235,667,383,899,832,346,290,378,433,510,716,800,287,752,835,405,867,373,239,437,400,696,720,415,358,807,474,767,624,575,427,596,459,442,607,322,803,337,659,639,592,454,364,254,227,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP120^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.08/0.23 % Computer : n017.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 19:51:52 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 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
% 0.64/0.55 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.79 % [INFO] Parsing done (240ms).
% 1.74/0.80 % [INFO] Running in sequential loop mode.
% 2.13/1.03 % [INFO] eprover registered as external prover.
% 2.54/1.03 % [INFO] Scanning for conjecture ...
% 2.83/1.17 % [INFO] Found a conjecture (or negated_conjecture) and 249 axioms. Running axiom selection ...
% 3.34/1.30 % [INFO] Axiom selection finished. Selected 224 axioms (removed 25 axioms).
% 3.99/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 3.99/1.55 % [INFO] Type checking passed.
% 3.99/1.56 % [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 ...
% 28.66/7.30 % External prover 'e' found a proof!
% 28.66/7.30 % [INFO] Killing All external provers ...
% 28.66/7.31 % Time passed: 6979ms (effective reasoning time: 6504ms)
% 28.66/7.31 % 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)>
% 28.66/7.31 % Axioms used in derivation (224): fact_185_order__class_Oorder_Oantisym, fact_169_local_OmonoE, fact_140_local_Osup_Osemilattice__axioms, fact_134_lattice_Od__aux_Ocong, fact_192_order__class_Oantisym, fact_83_local_Ob__join__d, fact_138_local_Osup_Osemigroup__axioms, fact_153_semilattice__set__def, fact_48_local_Ole__iff__inf, fact_207_equalityE, fact_51_local_Ole__infI1, fact_188_order__class_Oorder_Oeq__iff, fact_13_local_Oinf_Oassoc, fact_212_ord_Omin_Ocong, fact_161_semilattice_Oaxioms_I1_J, fact_89_local_Oa__meet__e, fact_60_local_Osup_Oabsorb__iff1, fact_35_local_Oinf_OorderE, fact_33_local_Oinf_OcoboundedI1, fact_54_local_Ole__supE, fact_170_local_OmonoI, fact_49_local_Ole__infE, fact_107_local_Osup_Oidem, fact_171_local_Omono__def, fact_1_local_Oantisym__conv, fact_105_local_Oinf__left__idem, fact_182_order__class_Odual__order_Otrans, fact_195_ord__eq__le__subst, fact_199_set__eq__subset, fact_156_abel__semigroup_Ocommute, fact_57_local_Ole__supI2, fact_237_semilattice__sup__class_Osup__idem, fact_150_lattice_Oincomp_Ocong, fact_55_local_Ole__supI, fact_102_local_Oinf_Oleft__idem, fact_39_local_Oinf__absorb2, fact_183_order__class_Odual__order_Orefl, fact_164_local_Oantimono__def, fact_110_local_Osup__idem, fact_67_local_Osup_OcoboundedI2, fact_8_local_Oord__le__eq__trans, fact_162_local_Obdd__above__mono, fact_235_semilattice__sup__class_Osup__left__idem, fact_158_semigroup_Oassoc, fact_40_local_Oinf__greatest, fact_25_local_Oinf_Oabsorb1, fact_3_local_Odual__order_Oeq__iff, fact_186_ord__class_Oord__le__eq__trans, fact_24_local_Osup__left__commute, fact_30_local_Oinf_OboundedI, fact_92_local_Oe__aux__def, fact_124_local_Osup__inf__absorb, fact_167_local_OantimonoD, fact_94_local_Oe__c__a__b, fact_104_local_Oinf__idem, fact_142_local_Osup_Oabel__semigroup__axioms, fact_80_local_Odistrib__imp2, fact_242_semilattice__sup__class_Osup_Obounded__iff, fact_87_local_Od__b__c__a, fact_165_local_OantimonoI, fact_101_local_Oinf_Oidem, fact_21_local_Osup_Oleft__commute, fact_155_abel__semigroup_Oleft__commute, fact_82_a__meet__d, fact_125_local_Ob__a, fact_143_local_Oinf_Oabel__semigroup__axioms, fact_12_local_Oorder__trans, fact_27_local_Oinf_Oabsorb__iff1, fact_56_local_Ole__supI1, fact_61_local_Osup_Oabsorb__iff2, fact_152_abel__semigroup_Oaxioms_I1_J, fact_106_local_Oinf__right__idem, fact_137_local_Ocomp__fun__idem__inf, fact_159_semigroup__def, fact_59_local_Osup_Oabsorb2, fact_122_local_Osup_Obounded__iff, fact_19_local_Osup_Oassoc, fact_239_semilattice__inf__class_Ole__inf__iff, fact_74_local_Osup__ge1, fact_226_Un__subset__iff, fact_43_local_Oinf__mono, fact_223_local_Obdd__above__Int2, fact_202_subset__refl, fact_73_local_Osup__absorb2, fact_91_local_Oc__meet__e, fact_160_semilattice__set_Oaxioms, fact_117_local_Oa__aux__def, fact_103_local_Oinf_Oright__idem, fact_31_local_Oinf_Ocobounded1, fact_181_order__class_Odual__order_Oeq__iff, fact_88_local_Od__c__a__b, fact_44_local_Oinf__unique, fact_191_preorder__class_Oeq__refl, fact_111_local_Osup__left__idem, fact_166_local_OantimonoE, fact_109_local_Osup_Oright__idem, fact_23_local_Osup__commute, fact_154_semilattice__set_Ointro, fact_180_order__class_Odual__order_Oantisym, fact_130_local_Ob__aux__def, fact_201_Collect__mono, fact_222_local_Obdd__below__Int1, fact_232_semilattice__inf__class_Oinf__idem, fact_50_local_Ole__infI, fact_234_semilattice__sup__class_Osup_Oright__idem, fact_95_local_Odistrib__inf__le, fact_16_local_Oinf__assoc, fact_65_local_Osup_Ocobounded2, fact_15_local_Oinf_Oleft__commute, fact_41_local_Oinf__le1, fact_34_local_Oinf_OcoboundedI2, fact_100_local_Oorder__refl, fact_224_local_Obdd__above__Int1, fact_168_local_OmonoD, fact_139_local_Oinf_Osemigroup__axioms, fact_108_local_Osup_Oleft__idem, fact_2_local_Odual__order_Oantisym, fact_163_local_Obdd__below__mono, fact_64_local_Osup_Ocobounded1, fact_70_local_Osup_OorderI, fact_151_lattice_Ob__aux_Ocong, fact_119_local_Oinf_Obounded__iff, fact_10_local_Oorder_Oeq__iff, fact_77_local_Osup__mono, fact_236_semilattice__sup__class_Osup_Oleft__idem, fact_187_ord__class_Oord__eq__le__trans, fact_113_local_OGreatestI2__order, fact_213_ord_Omax_Ocong, fact_7_local_Oord__eq__le__trans, fact_244_lattice__class_Oinf__sup__absorb, fact_36_local_Oinf_OorderI, fact_17_local_Oinf__commute, fact_228_semilattice__inf__class_Oinf__right__idem, fact_79_local_Odistrib__imp1, fact_5_local_Oeq__iff, fact_179_order_Omono_Ocong, fact_26_local_Oinf_Oabsorb2, fact_115_local_Omax__def, fact_121_local_Ole__sup__iff, fact_120_local_Ole__inf__iff, fact_38_local_Oinf__absorb1, fact_230_semilattice__inf__class_Oinf__left__idem, fact_37_local_Oinf_Oorder__iff, fact_11_local_Oorder_Otrans, fact_47_Collect__cong, fact_176_subset__antisym, fact_75_local_Osup__ge2, fact_211_order_OGreatest_Ocong, fact_66_local_Osup_OcoboundedI1, fact_231_semilattice__inf__class_Oinf_Oleft__idem, fact_98_local_Oincomp__def, fact_112_local_Oc__a, fact_93_local_Oe__b__c__a, fact_84_b__meet__d, fact_71_local_Osup_Oorder__iff, fact_241_semilattice__sup__class_Ole__sup__iff, fact_238_semilattice__sup__class_Osup_Oidem, fact_131_a__meet__b__eq__d, fact_243_lattice__class_Osup__inf__absorb, fact_72_local_Osup__absorb1, fact_133_lattice_Oc__aux_Ocong, fact_18_local_Oinf__left__commute, fact_240_semilattice__inf__class_Oinf_Obounded__iff, fact_28_local_Oinf_Oabsorb__iff2, fact_99_local_Oorder_Orefl, fact_63_local_Osup_OboundedI, fact_233_semilattice__inf__class_Oinf_Oidem, fact_216_local_Omono__inf, fact_68_local_Osup_Omono, fact_85_c__meet__d, fact_205_equalityD1, fact_81_local_Oa__join__d, fact_42_local_Oinf__le2, fact_229_semilattice__inf__class_Oinf_Oright__idem, fact_132_lattice_Oa__aux_Ocong, fact_178_order_Oantimono_Ocong, fact_193_order__class_Oeq__iff, fact_114_local_OGreatest__equality, fact_144_local_OSup__fin_Osemilattice__set__axioms, fact_62_local_Osup_OboundedE, fact_69_local_Osup_OorderE, fact_198_Collect__mono__iff, fact_123_local_Oinf__sup__absorb, fact_172_semilattice_Oidem, fact_194_ord__le__eq__subst, fact_173_semilattice_Oleft__idem, fact_135_lattice_Oe__aux_Ocong, fact_227_Int__subset__iff, fact_184_preorder__class_Oorder__trans, fact_174_semilattice_Oright__idem, fact_118_local_Oc__aux__def, fact_145_local_OInf__fin_Osemilattice__set__axioms, fact_6_local_Oeq__refl, fact_90_local_Ob__meet__e, fact_116_local_Omin__def, fact_177_preorder__class_Oorder__refl, fact_32_local_Oinf_Ocobounded2, fact_29_local_Oinf_OboundedE, fact_22_local_Osup__assoc, fact_78_local_Osup__unique, fact_96_local_Odistrib__sup__le, fact_157_semigroup_Ointro, fact_20_local_Osup_Ocommute, fact_196_order__subst2, fact_190_order__class_Oorder_Otrans, fact_52_local_Ole__infI2, fact_200_subset__trans, fact_189_order__class_Oantisym__conv, fact_86_local_Od__aux__def, fact_197_order__subst1, conj_0, fact_14_local_Oinf_Ocommute, fact_136_local_Ocomp__fun__idem__sup, fact_4_local_Odual__order_Otrans, fact_53_local_Ole__iff__sup, fact_204_equalityD2, fact_58_local_Osup_Oabsorb1, fact_0_local_Oantisym, fact_76_local_Osup__least, fact_141_local_Oinf_Osemilattice__axioms, fact_9_local_Oorder_Oantisym, fact_221_local_Obdd__below__Int2, fact_97_local_Omodular, fact_217_local_Omono__sup
% 28.66/7.31 % No. of inferences in proof: 472
% 28.66/7.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6979 ms resp. 6504 ms w/o parsing
% 29.56/7.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.56/7.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------