%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP075^2 : 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 : n020.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 08:06:40 AM UTC 2026
% Result : Theorem 46.53s 26.16s
% Output : Refutation 47.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 242
% Syntax : Number of formulae : 486 ( 266 unt; 0 typ; 0 def)
% Number of atoms : 1280 ( 507 equ; 6 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4205 ( 154 ~; 8 |; 77 &;3552 @)
% ( 0 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 5 con; 0-4 aty)
% Number of variables : 1306 ( 145 ^;1102 !; 59 ?;1306 :)
% Comments :
%------------------------------------------------------------------------------
thf(hF_Mirabelle_hf_type,type,
hF_Mirabelle_hf: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(hF_Mirabelle_HBall_decl,type,
hF_Mirabelle_HBall: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > $o ).
thf(hF_Mirabelle_HBex_decl,type,
hF_Mirabelle_HBex: hF_Mirabelle_hf > ( hF_Mirabelle_hf > $o ) > $o ).
thf(hF_Mir1687042746ollect_decl,type,
hF_Mir1687042746ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_HF_decl,type,
hF_Mirabelle_HF: ( set @ hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_HInter_decl,type,
hF_Mirabelle_HInter: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_HUnion_decl,type,
hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mir569462966eplace_decl,type,
hF_Mir569462966eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_RepFun_decl,type,
hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_Replace_decl,type,
hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hcard_decl,type,
hF_Mirabelle_hcard: hF_Mirabelle_hf > nat ).
thf(hF_Mirabelle_Abs_hf_decl,type,
hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hfset_decl,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > ( set @ hF_Mirabelle_hf ) ).
thf(hF_Mirabelle_hfst_decl,type,
hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hinsert_decl,type,
hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hmem_decl,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(hF_Mirabelle_hpair_decl,type,
hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hsnd_decl,type,
hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hsplit_decl,type,
hF_Mirabelle_hsplit:
!>[TA: $tType] : ( ( hF_Mirabelle_hf > hF_Mirabelle_hf > TA ) > hF_Mirabelle_hf > TA ) ).
thf(the_decl,type,
the:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(least_decl,type,
least:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a_decl,type,
a: hF_Mirabelle_hf ).
thf(p_decl,type,
p: $o ).
thf(231,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ( hF_Mirabelle_hmem @ B @ C )
=> ( hF_Mirabelle_HBex @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_hbexI) ).
thf(1036,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ( hF_Mirabelle_hmem @ B @ C )
=> ( hF_Mirabelle_HBex @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(121,axiom,
( ( bot_bot @ hF_Mirabelle_hf )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_bot__hf__def) ).
thf(629,plain,
( ( bot_bot @ hF_Mirabelle_hf )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(227,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ A @ B )
=> ~ ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ~ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hbexE) ).
thf(1024,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_HBex @ A @ B )
=> ~ ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ~ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(188,axiom,
( hF_Mirabelle_Replace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( hF_Mir569462966eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ? [E: hF_Mirabelle_hf] :
( ( B @ C @ E )
& ! [F: hF_Mirabelle_hf] :
( ( B @ C @ F )
=> ( F = E ) ) )
& ( B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Replace__def) ).
thf(846,plain,
( hF_Mirabelle_Replace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( hF_Mir569462966eplace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ? [E: hF_Mirabelle_hf] :
( ( B @ C @ E )
& ! [F: hF_Mirabelle_hf] :
( ( B @ C @ F )
=> ( F = E ) ) )
& ( B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(36,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_inf_Ocommute) ).
thf(333,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(243,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( C @ A )
=> ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_HCollectI) ).
thf(1083,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( C @ A )
=> ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(172,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_hpair__iff) ).
thf(777,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(135,axiom,
( ( hF_Mirabelle_hcard @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_hcard__0) ).
thf(666,plain,
( ( hF_Mirabelle_hcard @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(65,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Replace__0) ).
thf(408,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_diffs0__imp__equal) ).
thf(762,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(157,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_theI) ).
thf(730,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(195,axiom,
! [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_union__of__set) ).
thf(873,plain,
! [A: hF_Mirabelle_hf] :
? [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(131,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_not__less0) ).
thf(655,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(139,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_less__nat__zero__code) ).
thf(677,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(158,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_inf_Ostrict__coboundedI1) ).
thf(741,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(239,axiom,
( hF_Mir1687042746ollect
= ( ^ [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( A @ D )
& ( hF_Mirabelle_hmem @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_HCollect__def) ).
thf(1073,plain,
( hF_Mir1687042746ollect
= ( ^ [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( A @ D )
& ( hF_Mirabelle_hmem @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(241,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ord_less @ nat @ ( hF_Mirabelle_hcard @ ( minus_minus @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) @ ( hF_Mirabelle_hcard @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_hcard__hdiff1__less) ).
thf(1078,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ord_less @ nat @ ( hF_Mirabelle_hcard @ ( minus_minus @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) @ ( hF_Mirabelle_hcard @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_equals0I) ).
thf(384,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(92,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_the__eq__trivial) ).
thf(550,plain,
! [TA: $tType,A: TA] :
( ( the @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_DiffI) ).
thf(500,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(147,axiom,
( hF_Mirabelle_RepFun
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( hF_Mirabelle_Replace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( D
= ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_RepFun__def) ).
thf(698,plain,
( hF_Mirabelle_RepFun
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( hF_Mirabelle_Replace @ A
@ ^ [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( D
= ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_inf__fun__def) ).
thf(340,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(137,axiom,
! [TA: $tType] :
( ( if @ TA )
= ( ^ [A: $o,B: TA,C: TA] :
( the @ TA
@ ^ [D: TA] :
( ( A
=> ( D = B ) )
& ( ~ A
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_If__def) ).
thf(670,plain,
! [TA: $tType] :
( ( if @ TA )
= ( ^ [A: $o,B: TA,C: TA] :
( the @ TA
@ ^ [D: TA] :
( ( A
=> ( D = B ) )
& ( ~ A
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(63,axiom,
semilattice_inf @ hF_Mirabelle_hf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HF__Mirabelle__fsbjehakzm_Ohf___Lattices_Osemilattice__inf_30) ).
thf(404,plain,
semilattice_inf @ hF_Mirabelle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(151,axiom,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_theI_H) ).
thf(709,plain,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(68,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) )
= ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ ( zero_zero @ hF_Mirabelle_hf ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_HF__Mirabelle__fsbjehakzm_Odoubleton__eq__iff) ).
thf(417,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) )
= ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ ( zero_zero @ hF_Mirabelle_hf ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(199,axiom,
( hF_Mir569462966eplace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( the @ hF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_PrimReplace__def) ).
thf(885,plain,
( hF_Mir569462966eplace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( the @ hF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(23,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Int__empty__left) ).
thf(301,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(97,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_zero__diff) ).
thf(565,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(7,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Int__assoc) ).
thf(257,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(175,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_6) ).
thf(785,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(50,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(372,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(105,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ B @ A ) )
= ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_HInter @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_HInter__hinsert) ).
thf(587,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ B @ A ) )
= ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_HInter @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(181,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_theI2) ).
thf(802,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(211,axiom,
( ( inf_inf @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_inf__hf__def) ).
thf(949,plain,
( ( inf_inf @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(205,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBall @ A @ B )
=> ( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_hbspec) ).
thf(917,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBall @ A @ B )
=> ( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(162,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Diff__Int__distrib) ).
thf(751,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(89,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_inf @ hF_Mirabelle_hf @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hinter__hempty__left) ).
thf(542,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_inf @ hF_Mirabelle_hf @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(75,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( hF_Mirabelle_hinsert @ A @ B ) @ C )
= ( hF_Mirabelle_hinsert @ ( C @ A ) @ ( hF_Mirabelle_RepFun @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_RepFun__hinsert) ).
thf(460,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( hF_Mirabelle_hinsert @ A @ B ) @ C )
= ( hF_Mirabelle_hinsert @ ( C @ A ) @ ( hF_Mirabelle_RepFun @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(202,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( hF_Mirabelle_hinsert @ A @ ( inf_inf @ hF_Mirabelle_hf @ B @ C ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( inf_inf @ hF_Mirabelle_hf @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_hinter__hinsert__right) ).
thf(902,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( hF_Mirabelle_hinsert @ A @ ( inf_inf @ hF_Mirabelle_hf @ B @ C ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( inf_inf @ hF_Mirabelle_hf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(95,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_diff__zero) ).
thf(559,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(125,axiom,
! [A: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_hdiff__zero) ).
thf(638,plain,
! [A: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(198,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) )
=> ( hF_Mirabelle_HBall @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_hballI) ).
thf(881,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) )
=> ( hF_Mirabelle_HBall @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(33,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_boolean__algebra__cancel_Oinf1) ).
thf(325,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ A @ D )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ex__in__conv) ).
thf(289,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_the1__equality) ).
thf(448,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(29,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Diff__disjoint) ).
thf(316,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_of__nat__0__less__iff) ).
thf(756,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(177,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_RepFun__0) ).
thf(789,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(106,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_12) ).
thf(591,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(128,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_IntD2) ).
thf(646,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_diff__strict__right__mono) ).
thf(514,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(44,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(353,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(237,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( zero_zero @ hF_Mirabelle_hf ) @ ( hF_Mirabelle_hpair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_zero__notin__hpair) ).
thf(1051,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ ( zero_zero @ hF_Mirabelle_hf ) @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(182,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_diff__self) ).
thf(821,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(219,axiom,
! [A: hF_Mirabelle_hf] :
( ( A
= ( zero_zero @ hF_Mirabelle_hf ) )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_hempty__iff) ).
thf(981,plain,
! [A: hF_Mirabelle_hf] :
( ( A
= ( zero_zero @ hF_Mirabelle_hf ) )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(143,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_not__gr0) ).
thf(687,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(123,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_less__iff__diff__less__0) ).
thf(634,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_of__nat__less__0__iff) ).
thf(293,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(66,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_singleton__eq__iff) ).
thf(411,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(25,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_inf_Oidem) ).
thf(307,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(292,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(270,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_inf__right__idem) ).
thf(381,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Int__left__absorb) ).
thf(366,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(235,axiom,
( hF_Mirabelle_HUnion
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_HUnion__def) ).
thf(1047,plain,
( hF_Mirabelle_HUnion
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( hF_Mirabelle_hmem @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(206,axiom,
! [A: hF_Mirabelle_hf,B: $o] :
( ( hF_Mirabelle_HBall @ A
@ ^ [C: hF_Mirabelle_hf] : B )
= ( ? [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ A )
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_hball__triv) ).
thf(920,plain,
! [A: hF_Mirabelle_hf,B: $o] :
( ( hF_Mirabelle_HBall @ A
@ ^ [C: hF_Mirabelle_hf] : B )
= ( ? [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ A )
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(4,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_inf__idem) ).
thf(248,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(203,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HBall @ A
@ ^ [D: hF_Mirabelle_hf] :
~ ( B @ D ) )
=> ( B @ C ) )
=> ( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_HBex @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_HF__Mirabelle__fsbjehakzm_ObexCI) ).
thf(910,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_HBall @ A
@ ^ [D: hF_Mirabelle_hf] :
~ ( B @ D ) )
=> ( B @ C ) )
=> ( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_HBex @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(213,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( C @ A )
=> ( hF_Mirabelle_HBex @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rev__hbexI) ).
thf(957,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( C @ A )
=> ( hF_Mirabelle_HBex @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(160,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_diff__strict__mono) ).
thf(746,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(233,axiom,
( ( minus_minus @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_minus__hf__def) ).
thf(1042,plain,
( ( minus_minus @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_disjoint__iff) ).
thf(392,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(145,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_IntI) ).
thf(693,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(156,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(729,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_empty__Diff) ).
thf(260,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(349,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(120,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_hpair__neq__snd) ).
thf(625,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(197,axiom,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hf__ext) ).
thf(879,plain,
( ( (=) @ hF_Mirabelle_hf )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(190,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HInter @ A ) )
= ( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_HInter__iff) ).
thf(852,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ( hF_Mirabelle_hmem @ B @ ( hF_Mirabelle_HInter @ A ) )
= ( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_of__nat__0__eq__iff) ).
thf(329,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(87,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( A @ ( hF_Mirabelle_hinsert @ D @ C ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_hf__induct__ax) ).
thf(522,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( A @ ( hF_Mirabelle_hinsert @ D @ C ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(79,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_gr0I) ).
thf(493,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(141,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( hF_Mirabelle_hinsert @ B @ ( hF_Mirabelle_hinsert @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_hinsert__commute) ).
thf(682,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( hF_Mirabelle_hinsert @ B @ ( hF_Mirabelle_hinsert @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_equals0D) ).
thf(285,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(32,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(324,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(217,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_hmem__Sup__ne) ).
thf(974,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(86,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( minus_minus @ hF_Mirabelle_hf @ ( minus_minus @ hF_Mirabelle_hf @ A @ C ) @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_hdiff__insert) ).
thf(519,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( minus_minus @ hF_Mirabelle_hf @ ( minus_minus @ hF_Mirabelle_hf @ A @ C ) @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(130,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_zero__less__imp__eq__int) ).
thf(650,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(115,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_diff__right__commute) ).
thf(610,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_psubset__imp__ex__mem) ).
thf(783,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_diff__less) ).
thf(420,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(228,axiom,
( hF_Mirabelle_HBex
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_HBex__def) ).
thf(1028,plain,
( hF_Mirabelle_HBex
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(88,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_pos__int__cases) ).
thf(537,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(124,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_7) ).
thf(637,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(224,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ( A = B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_hmem__hinsert) ).
thf(1016,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ( A = B )
| ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(232,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_hmem__not__sym) ).
thf(1039,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(91,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_gr__zeroI) ).
thf(547,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(240,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_hmem__not__refl) ).
thf(1075,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(78,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_infinite__descent0) ).
thf(476,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(74,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(457,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(220,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_RepFun__iff) ).
thf(984,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_RepFun @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( A
= ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(153,axiom,
( hF_Mirabelle_hfst
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_hfst__def) ).
thf(721,plain,
( hF_Mirabelle_hfst
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(113,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_of__nat__0) ).
thf(605,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(40,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_inf_Oleft__idem) ).
thf(343,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,conjecture,
( ( hF_Mirabelle_HBex @ a
@ ^ [A: hF_Mirabelle_hf] : p )
= ( ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ a )
& p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( hF_Mirabelle_HBex @ a
@ ^ [A: hF_Mirabelle_hf] : p )
!= ( ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ a )
& p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(244,plain,
( ( hF_Mirabelle_HBex @ a
@ ^ [A: hF_Mirabelle_hf] : p )
!= ( ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ a )
& p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_DiffE) ).
thf(792,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(210,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( ( B @ C @ D )
=> ( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_replacement) ).
thf(938,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf,E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( ( B @ C @ D )
=> ( ( B @ C @ E )
=> ( E = D ) ) ) )
=> ? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( B @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(10,axiom,
! [A: int] :
~ ! [B: nat,C: nat] :
( A
!= ( minus_minus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_int__diff__cases) ).
thf(266,plain,
! [A: int] :
~ ! [B: nat,C: nat] :
( A
!= ( minus_minus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_empty__iff) ).
thf(311,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(61,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_boolean__algebra__cancel_Oinf2) ).
thf(398,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( inf_inf @ TA @ B @ C ) )
=> ( ( inf_inf @ TA @ D @ A )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(170,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_less__numeral__extra_I3_J) ).
thf(773,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(133,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_11) ).
thf(662,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(208,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E @ F )
= ( D @ E @ F ) ) )
=> ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Replace__cong) ).
thf(926,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E @ F )
= ( D @ E @ F ) ) )
=> ( ( hF_Mirabelle_Replace @ A @ C )
= ( hF_Mirabelle_Replace @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(167,axiom,
! [TA: $tType] :
( ( least @ TA )
= ( ^ [A: TA > TA > $o,B: TA > $o] :
( the @ TA
@ ^ [C: TA] :
( ( B @ C )
& ! [D: TA] :
( ( B @ D )
=> ( A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ord_OLeast__def) ).
thf(765,plain,
! [TA: $tType] :
( ( least @ TA )
= ( ^ [A: TA > TA > $o,B: TA > $o] :
( the @ TA
@ ^ [C: TA] :
( ( B @ C )
& ! [D: TA] :
( ( B @ D )
=> ( A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(238,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A @ C )
=> ( ( A @ D )
=> ( ~ ( hF_Mirabelle_hmem @ C @ D )
=> ( A @ ( hF_Mirabelle_hinsert @ C @ D ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_hf__induct) ).
thf(1054,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ ( zero_zero @ hF_Mirabelle_hf ) )
=> ( ! [C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A @ C )
=> ( ( A @ D )
=> ( ~ ( hF_Mirabelle_hmem @ C @ D )
=> ( A @ ( hF_Mirabelle_hinsert @ C @ D ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_inf__apply) ).
thf(298,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_diff__commute) ).
thf(618,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(183,axiom,
( ( bot_bot @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_bot__nat__def) ).
thf(824,plain,
( ( bot_bot @ nat )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(191,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( inf_inf @ hF_Mirabelle_hf @ C @ B ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( inf_inf @ hF_Mirabelle_hf @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_hinter__hinsert__left) ).
thf(856,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( inf_inf @ hF_Mirabelle_hf @ C @ B ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_inf @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( inf_inf @ hF_Mirabelle_hf @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(15,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Int__empty__right) ).
thf(279,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(100,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_not__gr__zero) ).
thf(573,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(52,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zero__reorient) ).
thf(375,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(104,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ A
@ ^ [B: hF_Mirabelle_hf] : B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_triv__RepFun) ).
thf(584,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ A
@ ^ [B: hF_Mirabelle_hf] : B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(96,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_inf @ hF_Mirabelle_hf @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_hinter__hempty__right) ).
thf(562,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_inf @ hF_Mirabelle_hf @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(70,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_the1I2) ).
thf(423,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(223,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_RepFun__cong) ).
thf(1007,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf,D: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_RepFun @ A @ C )
= ( hF_Mirabelle_RepFun @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_not__psubset__empty) ).
thf(402,plain,
! [TA: $tType,A: set @ TA] :
~ ( ord_less @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(187,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Diff__Diff__Int) ).
thf(843,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Diff__iff) ).
thf(743,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(184,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_infinite__descent0__measure) ).
thf(826,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_diff__strict__left__mono) ).
thf(579,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(90,axiom,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_hpair__def) ).
thf(545,plain,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(126,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( (=) @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_the__sym__eq__trivial) ).
thf(641,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( (=) @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(58,axiom,
semilattice_inf @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__inf_9) ).
thf(391,plain,
semilattice_inf @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(72,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_inf_Ostrict__order__iff) ).
thf(445,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( A
= ( inf_inf @ TA @ A @ B ) )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(28,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Diff__cancel) ).
thf(313,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(77,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_hpair__inject) ).
thf(466,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ A @ B )
= ( hF_Mirabelle_hpair @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(149,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfset @ ( minus_minus @ hF_Mirabelle_hf @ A @ B ) )
= ( minus_minus @ ( set @ hF_Mirabelle_hf ) @ ( hF_Mirabelle_hfset @ A ) @ ( hF_Mirabelle_hfset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_hfset__hdiff) ).
thf(704,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfset @ ( minus_minus @ hF_Mirabelle_hf @ A @ B ) )
= ( minus_minus @ ( set @ hF_Mirabelle_hf ) @ ( hF_Mirabelle_hfset @ A ) @ ( hF_Mirabelle_hfset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(43,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inf__left__idem) ).
thf(350,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(13,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf_Oright__idem) ).
thf(274,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( F = E ) ) ) )
=> ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_PrimReplace__iff) ).
thf(996,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ! [D: hF_Mirabelle_hf,E: hF_Mirabelle_hf,F: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
=> ( ( B @ D @ E )
=> ( ( B @ D @ F )
=> ( F = E ) ) ) )
=> ( ( hF_Mirabelle_hmem @ C @ ( hF_Mir569462966eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(117,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_not__less__zero) ).
thf(616,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(12,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_all__not__in__conv) ).
thf(271,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_inf_Oassoc) ).
thf(387,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(242,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( D
= ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_replacement__fun) ).
thf(1080,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ? [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ A )
& ( D
= ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(122,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_hsnd__conv) ).
thf(631,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(108,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_8) ).
thf(594,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(119,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_hpair__neq__fst) ).
thf(621,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_inf__assoc) ).
thf(251,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(226,axiom,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_hmem__def) ).
thf(1022,plain,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member @ hF_Mirabelle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(136,axiom,
( ( hF_Mirabelle_HUnion @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_HUnion__hempty) ).
thf(668,plain,
( ( hF_Mirabelle_HUnion @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Int__Diff) ).
thf(799,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(155,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Diff__Int__distrib2) ).
thf(726,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(189,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_hmem__ne) ).
thf(848,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(148,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_inf_Ostrict__boundedE) ).
thf(700,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
=> ~ ( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_DiffD1) ).
thf(685,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(168,axiom,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir1687042746ollect @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_HCollect__hempty) ).
thf(768,plain,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir1687042746ollect @ A @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(193,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_comprehension) ).
thf(868,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(173,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_zero__less__iff__neq__zero) ).
thf(780,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(114,axiom,
( ( hF_Mirabelle_Abs_hf @ ( zero_zero @ nat ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Abs__hf__0) ).
thf(608,plain,
( ( hF_Mirabelle_Abs_hf @ ( zero_zero @ nat ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(83,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_the__equality) ).
thf(505,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(132,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ B )
!= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_hinsert__nonempty) ).
thf(658,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ B )
!= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(234,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBall @ A @ B )
=> ( ~ ( B @ C )
=> ~ ( hF_Mirabelle_hmem @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_hballE) ).
thf(1044,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HBall @ A @ B )
=> ( ~ ( B @ C )
=> ~ ( hF_Mirabelle_hmem @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(146,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_minus__nat_Odiff__0) ).
thf(695,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(140,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inf_Ostrict__coboundedI2) ).
thf(680,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(134,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_diff__0__right) ).
thf(663,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(129,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_less__infI1) ).
thf(648,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(85,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_diff__0__eq__0) ).
thf(516,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(163,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_IntD1) ).
thf(754,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(93,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_less__zeroE) ).
thf(553,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(215,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( minus_minus @ hF_Mirabelle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ~ ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_hdiff__iff) ).
thf(968,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( minus_minus @ hF_Mirabelle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ~ ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(185,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_hpair__nonzero) ).
thf(836,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(236,axiom,
( hF_Mirabelle_HBall
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_HBall__def) ).
thf(1049,plain,
( hF_Mirabelle_HBall
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(144,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_hfst__conv) ).
thf(690,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(21,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Int__absorb) ).
thf(295,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_disjoint__iff__not__equal) ).
thf(282,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_DiffD2) ).
thf(707,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(200,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_HBall @ A @ C )
= ( hF_Mirabelle_HBall @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_hball__cong) ).
thf(887,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_HBall @ A @ C )
= ( hF_Mirabelle_HBall @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(67,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_diff__self__eq__0) ).
thf(414,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(216,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_Replace__iff) ).
thf(971,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_Replace @ B @ C ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ B )
& ( C @ D @ A )
& ! [E: hF_Mirabelle_hf] :
( ( C @ D @ E )
=> ( E = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(9,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Int__commute) ).
thf(263,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(310,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(138,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_gr__implies__not__zero) ).
thf(673,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_diff__less__mono2) ).
thf(502,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(186,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_diff__gt__0__iff__gt) ).
thf(840,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(76,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_bot__nat__0_Onot__eq__extremum) ).
thf(463,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(101,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_bot__nat__0_Oextremum__strict) ).
thf(576,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(212,axiom,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ? [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
& ( ( inf_inf @ hF_Mirabelle_hf @ B @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_foundation) ).
thf(951,plain,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ? [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
& ( ( inf_inf @ hF_Mirabelle_hf @ B @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(37,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(336,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(116,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Diff__Int2) ).
thf(613,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_less__imp__diff__less) ).
thf(600,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(192,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
=> ~ ( ( hF_Mirabelle_hmem @ A @ C )
=> ~ ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_HCollectE) ).
thf(864,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
=> ~ ( ( hF_Mirabelle_hmem @ A @ C )
=> ~ ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(218,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_HCollect__iff) ).
thf(978,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir1687042746ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(99,axiom,
( ( hF_Mirabelle_HInter @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_HInter__hempty) ).
thf(571,plain,
( ( hF_Mirabelle_HInter @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(109,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_16) ).
thf(595,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(196,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_HUnion__iff) ).
thf(876,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mirabelle_HUnion @ B ) )
= ( ? [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(94,axiom,
! [A: int] :
( ( minus_minus @ int @ A @ ( zero_zero @ int ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_minus__int__code_I1_J) ).
thf(556,plain,
! [A: int] :
( ( minus_minus @ int @ A @ ( zero_zero @ int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(103,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_neq0__conv) ).
thf(581,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(165,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_HF__hfset) ).
thf(759,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(169,axiom,
( hF_Mirabelle_hsnd
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_hsnd__def) ).
thf(771,plain,
( hF_Mirabelle_hsnd
= ( ^ [A: hF_Mirabelle_hf] :
( the @ hF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
( A
= ( hF_Mirabelle_hpair @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Int__left__commute) ).
thf(319,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Diff__empty) ).
thf(304,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(57,axiom,
semilattice_inf @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Lattices_Osemilattice__inf_3) ).
thf(390,plain,
semilattice_inf @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_diff__eq__diff__less) ).
thf(786,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(201,axiom,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_hf__cases) ).
thf(896,plain,
! [A: hF_Mirabelle_hf] :
( ( A
!= ( zero_zero @ hF_Mirabelle_hf ) )
=> ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(161,axiom,
! [TA: $tType,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_hsplit) ).
thf(748,plain,
! [TA: $tType,A: hF_Mirabelle_hf > hF_Mirabelle_hf > TA,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsplit @ TA @ A @ ( hF_Mirabelle_hpair @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(229,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( inf_inf @ hF_Mirabelle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_hinter__iff) ).
thf(1030,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( inf_inf @ hF_Mirabelle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(98,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Int__iff) ).
thf(568,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3,axiom,
( ( zero_zero @ hF_Mirabelle_hf )
= ( hF_Mirabelle_HF @ ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Zero__hf__def) ).
thf(246,plain,
( ( zero_zero @ hF_Mirabelle_hf )
= ( hF_Mirabelle_HF @ ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_inf__commute) ).
thf(346,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(204,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hf__equalityI) ).
thf(914,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
= ( hF_Mirabelle_hmem @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_inf_Oleft__commute) ).
thf(378,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(64,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_eq__iff__diff__eq__0) ).
thf(405,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_psubset__trans) ).
thf(373,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(112,axiom,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_hpair__def_H) ).
thf(603,plain,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ A @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ ( zero_zero @ hF_Mirabelle_hf ) ) ) @ ( zero_zero @ hF_Mirabelle_hf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Int__emptyI) ).
thf(358,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(230,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_hemptyE) ).
thf(1033,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(214,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_minus @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( minus_minus @ hF_Mirabelle_hf @ C @ B ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_minus @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( minus_minus @ hF_Mirabelle_hf @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_hinsert__hdiff__if) ).
thf(960,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_minus @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( minus_minus @ hF_Mirabelle_hf @ C @ B ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_minus @ hF_Mirabelle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( minus_minus @ hF_Mirabelle_hf @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(152,axiom,
zero @ hF_Mirabelle_hf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HF__Mirabelle__fsbjehakzm_Ohf___Groups_Ozero_35) ).
thf(720,plain,
zero @ hF_Mirabelle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(179,axiom,
! [A: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zero__hdiff) ).
thf(796,plain,
! [A: hF_Mirabelle_hf] :
( ( minus_minus @ hF_Mirabelle_hf @ ( zero_zero @ hF_Mirabelle_hf ) @ A )
= ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(60,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Diff__idemp) ).
thf(395,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(221,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_HBex @ A @ C )
= ( hF_Mirabelle_HBex @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_hbex__cong) ).
thf(987,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o,D: hF_Mirabelle_hf > $o] :
( ( A = B )
=> ( ! [E: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( hF_Mirabelle_HBex @ A @ C )
= ( hF_Mirabelle_HBex @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(35,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(332,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_IntE) ).
thf(596,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(225,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
= ( ( hF_Mirabelle_hmem @ D @ C )
| ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_hinsert__iff) ).
thf(1019,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
= ( ! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
= ( ( hF_Mirabelle_hmem @ D @ C )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(127,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_psubsetD) ).
thf(644,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_zero__less__diff) ).
thf(723,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(14,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_18) ).
thf(277,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_diff__eq__diff__eq) ).
thf(442,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(194,axiom,
( hF_Mirabelle_HInter
= ( ^ [A: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_hmem @ B @ C ) )
@ ( hF_Mirabelle_HUnion @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_HInter__def) ).
thf(871,plain,
( hF_Mirabelle_HInter
= ( ^ [A: hF_Mirabelle_hf] :
( hF_Mir1687042746ollect
@ ^ [B: hF_Mirabelle_hf] :
! [C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ C @ A )
=> ( hF_Mirabelle_hmem @ B @ C ) )
@ ( hF_Mirabelle_HUnion @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(49,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_of__nat__eq__0__iff) ).
thf(369,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_inf__left__commute) ).
thf(254,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_emptyE) ).
thf(322,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Diff__triv) ).
thf(337,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( zero @ TB )
=> ! [A: ( TC > TB ) > TA,B: TA] :
( ( A
= ( ^ [C: TC > TB] : B ) )
=> ( ( A
@ ^ [C: TC] : ( zero_zero @ TB ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_fun__cong__unused__0) ).
thf(354,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( zero @ TB )
=> ! [A: ( TC > TB ) > TA,B: TA] :
( ( A
= ( ^ [C: TC > TB] : B ) )
=> ( ( A
@ ^ [C: TC] : ( zero_zero @ TB ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(209,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_binary__union) ).
thf(935,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
? [C: hF_Mirabelle_hf] :
! [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ C )
= ( ( hF_Mirabelle_hmem @ D @ A )
| ( hF_Mirabelle_hmem @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(207,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_hmem__hempty) ).
thf(923,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ ( zero_zero @ hF_Mirabelle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(171,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_less__infI2) ).
thf(775,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( inf_inf @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(107,axiom,
( ( hF_Mirabelle_hfset @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_hfset__0) ).
thf(592,plain,
( ( hF_Mirabelle_hfset @ ( zero_zero @ hF_Mirabelle_hf ) )
= ( bot_bot @ ( set @ hF_Mirabelle_hf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_gr__implies__not0) ).
thf(496,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA )
=> ( semilattice_inf @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1086,plain,
$false,
inference(e,[status(thm)],[1036,629,1024,846,333,1083,777,666,408,762,730,873,655,677,741,1073,1078,384,550,500,698,340,670,404,709,417,885,301,565,257,785,372,587,802,949,917,751,542,460,902,559,638,881,325,289,448,316,756,789,591,646,514,353,1051,821,981,687,634,293,411,307,292,270,381,366,1047,920,248,910,957,746,1042,392,693,729,260,349,625,879,852,329,522,493,682,285,324,974,519,650,610,783,420,1028,537,637,1016,1039,547,1075,476,457,984,721,605,343,244,792,938,266,311,398,773,662,926,765,1054,298,618,824,856,279,573,375,584,562,423,1007,402,843,743,826,579,545,641,391,445,313,466,704,350,274,996,616,271,387,1080,631,594,621,251,1022,668,799,726,848,700,685,768,868,780,608,505,658,1044,695,680,663,648,516,754,553,968,836,1049,690,295,282,707,887,414,971,263,310,673,502,840,463,576,951,336,613,600,864,978,571,595,876,556,581,759,771,319,304,390,786,896,748,1030,568,246,346,914,378,405,373,603,358,1033,960,720,796,395,987,332,596,1019,644,723,277,442,871,369,254,322,337,354,935,923,775,592,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP075^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:48:34 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.84/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/1.11 % [INFO] Parsing done (342ms).
% 1.64/1.13 % [INFO] Running in sequential loop mode.
% 3.16/1.50 % [INFO] eprover registered as external prover.
% 3.16/1.51 % [INFO] Scanning for conjecture ...
% 3.34/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 309 axioms. Running axiom selection ...
% 3.54/1.78 % [INFO] Axiom selection finished. Selected 241 axioms (removed 68 axioms).
% 4.29/1.99 % [INFO] Problem is higher-order (TPTP THF).
% 4.29/2.01 % [INFO] Type checking passed.
% 4.29/2.02 % [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 ...
% 46.53/26.15 % External prover 'e' found a proof!
% 46.53/26.16 % [INFO] Killing All external provers ...
% 46.53/26.16 % Time passed: 25817ms (effective reasoning time: 25025ms)
% 46.53/26.16 % 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)>
% 46.53/26.16 % Axioms used in derivation (241): fact_152_equals0I, fact_172_hsnd__conv, fact_81_inf__fun__def, fact_225_gr0I, fact_233_inf_Ostrict__boundedE, fact_123_Diff__disjoint, fact_42_hinter__hempty__right, fact_212_diff__less__mono2, fact_198_PrimReplace__def, fact_125_empty__Diff, fact_201_hsnd__def, fact_69_inf_Oidem, fact_209_diff__gt__0__iff__gt, fact_160_DiffD1, fact_30_Replace__def, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_61_zero__diff, fact_86_inf_Ocommute, fact_68_inf__apply, fact_32_minus__hf__def, fact_114_hf__induct__ax, fact_24_HCollectE, fact_140_Int__commute, fact_65_inf_Oright__idem, fact_97_hfset__0, fact_176_the__sym__eq__trivial, fact_22_hballE, tcon_Int_Oint___Groups_Ozero, fact_55_hemptyE, fact_226_less__iff__diff__less__0, fact_155_disjoint__iff, fact_3_hf__ext, fact_242_of__nat__0__eq__iff, fact_34_HInter__def, fact_202_HUnion__def, fact_223_not__less0, fact_244_psubset__imp__ex__mem, tcon_Int_Oint___Groups_Oordered__ab__group__add, fact_50_RepFun__0, fact_62_diff__0__right, fact_132_IntI, fact_121_hdiff__insert, fact_90_eq__iff__diff__eq__0, fact_56_hempty__iff, fact_192_diffs0__imp__equal, fact_207_less__nat__zero__code, fact_158_disjoint__iff__not__equal, fact_40_hinter__iff, fact_58_RepFun__cong, fact_89_inf__left__commute, tcon_Nat_Onat___Lattices_Osemilattice__inf_9, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_8, fact_213_diff__less, fact_26_hball__cong, tcon_HF__Mirabelle__fsbjehakzm_Ohf___Groups_Ozero_35, fact_51_HUnion__hempty, fact_29_HBall__def, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_6, fact_131_Int__iff, fact_33_inf__hf__def, fact_180_the1__equality, fact_104_hpair__def, fact_163_Diff__Int2, fact_227_zero__less__iff__neq__zero, tcon_Int_Oint___Lattices_Osemilattice__inf_3, fact_16_hballI, fact_164_Diff__Diff__Int, fact_157_Int__empty__right, fact_249_psubsetD, fact_109_hpair__inject, fact_253_minus__int__code_I1_J, fact_92_fun__cong__unused__0, fact_72_hfset__hdiff, fact_52_HInter__hempty, fact_208_neq0__conv, fact_107_hpair__neq__snd, fact_7_rev__hbexI, fact_115_hpair__nonzero, fact_240_of__nat__0__less__iff, fact_236_inf_Ostrict__coboundedI2, tcon_Nat_Onat___Rings_Osemiring__1_12, fact_1_hbexI, fact_230_gr__zeroI, fact_4_hmem__ne, fact_200_hfst__def, fact_224_not__gr0, fact_57_hmem__hempty, fact_211_less__imp__diff__less, fact_101_hmem__hinsert, fact_124_Diff__cancel, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_134_Diff__iff, tcon_Set_Oset___Lattices_Osemilattice__inf_18, fact_232_less__infI2, fact_191_bot__nat__def, fact_18_PrimReplace__iff, fact_10_hmem__not__sym, fact_239_less__numeral__extra_I3_J, fact_19_HCollect__iff, fact_93_HCollect__def, fact_174_the__eq__trivial, fact_122_hsplit, fact_60_diff__zero, tcon_fun___Lattices_Osemilattice__inf, fact_245_of__nat__less__0__iff, fact_31_RepFun__def, fact_84_inf_Oassoc, fact_39_triv__RepFun, fact_25_HCollectI, fact_205_not__gr__zero, fact_214_diff__strict__right__mono, fact_15_HF__Mirabelle__fsbjehakzm_ObexCI, fact_11_union__of__set, tcon_Nat_Onat___Groups_Ozero_16, fact_206_bot__nat__0_Onot__eq__extremum, fact_12_comprehension, fact_75_diff__eq__diff__eq, fact_117_hf__induct, tcon_Nat_Onat___Nat_Osemiring__char__0_11, fact_95_zero__notin__hpair, fact_166_Diff__Int__distrib2, fact_149_bot__hf__def, fact_27_hmem__Sup__ne, tcon_Int_Oint___Rings_Osemiring__1, fact_98_hpair__iff, fact_13_hmem__not__refl, fact_91_HInter__hinsert, fact_231_less__infI1, tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_23_hbspec, fact_94_HF__hfset, fact_70_inf__idem, fact_118_hinter__hinsert__right, fact_66_inf__left__idem, tcon_Int_Oint___Groups_Ogroup__add, fact_193_minus__nat_Odiff__0, fact_111_hinsert__iff, fact_82_boolean__algebra__cancel_Oinf1, fact_113_HF__Mirabelle__fsbjehakzm_Odoubleton__eq__iff, fact_181_the1I2, fact_105_hpair__def_H, fact_235_inf_Ostrict__coboundedI1, fact_243_of__nat__eq__0__iff, fact_215_diff__strict__left__mono, fact_247_pos__int__cases, fact_133_DiffI, fact_116_hf__cases, fact_43_hinter__hempty__left, fact_234_inf_Ostrict__order__iff, fact_76_diff__right__commute, fact_217_diff__strict__mono, fact_188_diff__self__eq__0, fact_6_hbex__cong, fact_96_Abs__hf__0, fact_36_HCollect__hempty, fact_85_inf__assoc, fact_199_hcard__0, fact_162_Int__Diff, fact_54_foundation, fact_135_Diff__idemp, fact_222_less__zeroE, fact_102_singleton__eq__iff, fact_17_hball__triv, fact_35_RepFun__iff, fact_165_Diff__Int__distrib, fact_14_replacement__fun, fact_229_not__less__zero, fact_150_emptyE, fact_185_theI, fact_156_Int__empty__left, fact_161_DiffD2, fact_73_zero__reorient, fact_189_diff__0__eq__0, fact_53_HInter__iff, fact_38_hmem__def, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_7, fact_197_ord_OLeast__def, fact_246_not__psubset__empty, fact_63_diff__self, fact_120_hinsert__hdiff__if, fact_203_hcard__hdiff1__less, fact_20_Replace__iff, fact_248_zero__less__imp__eq__int, tcon_Int_Oint___Nat_Osemiring__char__0, fact_210_zero__less__diff, fact_119_hinter__hinsert__left, fact_173_the__equality, tcon_HF__Mirabelle__fsbjehakzm_Ohf___Lattices_Osemilattice__inf_30, fact_171_hfst__conv, fact_146_IntD1, fact_8_replacement, fact_128_all__not__in__conv, fact_219_bot__nat__0_Oextremum__strict, fact_183_theI2, fact_110_hinsert__commute, fact_49_hdiff__zero, fact_228_gr__implies__not__zero, fact_153_ex__in__conv, fact_184_theI_H, fact_154_Int__emptyI, fact_147_IntE, fact_112_hinsert__nonempty, fact_143_Int__assoc, fact_5_HBex__def, fact_145_IntD2, fact_87_inf__commute, fact_59_cancel__comm__monoid__add__class_Odiff__cancel, fact_28_Replace__cong, fact_103_RepFun__hinsert, fact_88_inf_Oleft__commute, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_71_inf_Oleft__idem, fact_64_inf__right__idem, fact_190_diff__commute, fact_44_zero__hdiff, fact_136_Int__left__commute, fact_108_hpair__neq__fst, fact_159_DiffE, fact_251_psubset__trans, fact_220_infinite__descent0, fact_137_Int__left__absorb, fact_41_hdiff__iff, fact_221_gr__implies__not0, fact_9_binary__union, fact_127_empty__iff, fact_83_boolean__algebra__cancel_Oinf2, fact_126_Diff__empty, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_142_Int__absorb, fact_216_diff__eq__diff__less, fact_37_Replace__0, fact_182_If__def, fact_2_hbexE, fact_170_Diff__triv, fact_106_Zero__hf__def, fact_21_HUnion__iff, fact_252_int__diff__cases, fact_0_hf__equalityI, fact_241_of__nat__0, fact_218_infinite__descent0__measure, fact_151_equals0D
% 46.53/26.16 % No. of inferences in proof: 486
% 46.53/26.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25817 ms resp. 25025 ms w/o parsing
% 47.33/26.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.33/26.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------