%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP075^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 08:06:39 AM UTC 2026
% Result : Theorem 13.84s 4.75s
% Output : Refutation 15.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 166
% Syntax : Number of formulae : 334 ( 242 unt; 0 typ; 0 def)
% Number of atoms : 728 ( 399 equ; 4 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1999 ( 132 ~; 8 |; 69 &;1560 @)
% ( 0 <=>; 230 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 9 con; 0-3 aty)
% Number of variables : 816 ( 125 ^; 636 !; 55 ?; 816 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_HF_Mirabelle_hf_type,type,
set_HF_Mirabelle_hf: $tType ).
thf(hF_Mirabelle_hf_type,type,
hF_Mirabelle_hf: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(minus_1232880740lle_hf_decl,type,
minus_1232880740lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(minus_1450406810lle_hf_decl,type,
minus_1450406810lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(zero_z189798548lle_hf_decl,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
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_Mir818139703ollect_decl,type,
hF_Mir818139703ollect: ( 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_Mir1248913145eplace_decl,type,
hF_Mir1248913145eplace: 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(the_HF_Mirabelle_hf_decl,type,
the_HF_Mirabelle_hf: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(if_HF_Mirabelle_hf_decl,type,
if_HF_Mirabelle_hf: $o > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(inf_in956532509lle_hf_decl,type,
inf_in956532509lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(bot_bo1001194783lle_hf_decl,type,
bot_bo1001194783lle_hf: hF_Mirabelle_hf ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: nat ).
thf(bot_bo53200981lle_hf_decl,type,
bot_bo53200981lle_hf: set_HF_Mirabelle_hf ).
thf(least_917110455lle_hf_decl,type,
least_917110455lle_hf: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(ord_le616625840e_hf_o_decl,type,
ord_le616625840e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_le1344122901lle_hf_decl,type,
ord_le1344122901lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(member1367349282lle_hf_decl,type,
member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(a_decl,type,
a: hF_Mirabelle_hf ).
thf(p_decl,type,
p: $o ).
thf(77,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( A @ B )
=> ( ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the_HF_Mirabelle_hf @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_theI2) ).
thf(433,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf > $o] :
( ( A @ B )
=> ( ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = B ) )
=> ( ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( the_HF_Mirabelle_hf @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(164,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ord_less_nat @ ( hF_Mirabelle_hcard @ ( minus_1232880740lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hcard @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_hcard__hdiff1__less) ).
thf(809,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ord_less_nat @ ( hF_Mirabelle_hcard @ ( minus_1232880740lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hcard @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(56,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_hinter__hempty__right) ).
thf(365,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(93,axiom,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_hpair__def) ).
thf(518,plain,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(83,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfset @ ( minus_1232880740lle_hf @ A @ B ) )
= ( minus_1450406810lle_hf @ ( hF_Mirabelle_hfset @ A ) @ ( hF_Mirabelle_hfset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_hfset__hdiff) ).
thf(468,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfset @ ( minus_1232880740lle_hf @ A @ B ) )
= ( minus_1450406810lle_hf @ ( hF_Mirabelle_hfset @ A ) @ ( hF_Mirabelle_hfset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ A @ A )
= bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Diff__cancel) ).
thf(170,plain,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ A @ A )
= bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_less__numeral__extra_I3_J) ).
thf(276,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(31,axiom,
! [A: set_HF_Mirabelle_hf] :
( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A )
=> ( A = bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_equals0I) ).
thf(269,plain,
! [A: set_HF_Mirabelle_hf] :
( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A )
=> ( A = bot_bo53200981lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(95,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ A
@ ^ [B: hF_Mirabelle_hf] : B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_triv__RepFun) ).
thf(523,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ A
@ ^ [B: hF_Mirabelle_hf] : B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',fact_23_hbspec) ).
thf(762,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)],[153]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_277_hfst__def) ).
thf(385,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)],[62]) ).
thf(102,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_HF_Mirabelle_hf @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_the__equality) ).
thf(550,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_HF_Mirabelle_hf @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(91,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_inf_Oleft__commute) ).
thf(500,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(139,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_hmem__not__refl) ).
thf(715,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(166,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_Mir818139703ollect @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_HCollectI) ).
thf(814,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_Mir818139703ollect @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(148,axiom,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_inf__hf__def) ).
thf(747,plain,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [C: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_35_RepFun__iff) ).
thf(709,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)],[137]) ).
thf(70,axiom,
( ( hF_Mirabelle_hfset @ zero_z189798548lle_hf )
= bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_hfset__0) ).
thf(417,plain,
( ( hF_Mirabelle_hfset @ zero_z189798548lle_hf )
= bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_inf__left__idem) ).
thf(301,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(105,axiom,
( hF_Mirabelle_Replace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( hF_Mir1248913145eplace @ 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/sandbox2/benchmark/theBenchmark.p',fact_30_Replace__def) ).
thf(565,plain,
( hF_Mirabelle_Replace
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( hF_Mir1248913145eplace @ 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)],[105]) ).
thf(107,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_singleton__eq__iff) ).
thf(570,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf )
= ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(8,axiom,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ ( minus_1450406810lle_hf @ A @ B ) @ B )
= ( minus_1450406810lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Diff__idemp) ).
thf(184,plain,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ ( minus_1450406810lle_hf @ A @ B ) @ B )
= ( minus_1450406810lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_278_hsnd__def) ).
thf(357,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)],[53]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_28_Replace__cong) ).
thf(817,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)],[167]) ).
thf(103,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B )
= ( inf_in956532509lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_inf__right__idem) ).
thf(559,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B )
= ( inf_in956532509lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(126,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_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/sandbox2/benchmark/theBenchmark.p',fact_52_HInter__iff) ).
thf(638,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_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)],[126]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_gr__implies__not0) ).
thf(289,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(18,axiom,
! [A: set_HF_Mirabelle_hf] :
~ ( ord_le1344122901lle_hf @ A @ bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_not__psubset__empty) ).
thf(216,plain,
! [A: set_HF_Mirabelle_hf] :
~ ( ord_le1344122901lle_hf @ A @ bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(85,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ? [C: hF_Mirabelle_hf] :
( ( A @ C )
& ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the_HF_Mirabelle_hf @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_the1__equality) ).
thf(475,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ? [C: hF_Mirabelle_hf] :
( ( A @ C )
& ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( the_HF_Mirabelle_hf @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(6,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ~ ( member1367349282lle_hf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_DiffD2) ).
thf(179,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ~ ( member1367349282lle_hf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_20_Replace__iff) ).
thf(591,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)],[114]) ).
thf(86,axiom,
! [A: hF_Mirabelle_hf] :
( ( the_HF_Mirabelle_hf @ ( (=) @ hF_Mirabelle_hf @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_the__sym__eq__trivial) ).
thf(485,plain,
! [A: hF_Mirabelle_hf] :
( ( the_HF_Mirabelle_hf @ ( (=) @ hF_Mirabelle_hf @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(50,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_z189798548lle_hf ) )
= ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ zero_z189798548lle_hf ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_HF__Mirabelle__glliljednj_Odoubleton__eq__iff) ).
thf(348,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_z189798548lle_hf ) )
= ( hF_Mirabelle_hinsert @ C @ ( hF_Mirabelle_hinsert @ D @ zero_z189798548lle_hf ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_5_HBex__def) ).
thf(734,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)],[146]) ).
thf(39,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_bot__nat__def) ).
thf(293,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(78,axiom,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ord_le1344122901lle_hf @ A @ B )
=> ( ( member1367349282lle_hf @ C @ A )
=> ( member1367349282lle_hf @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_psubsetD) ).
thf(453,plain,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ord_le1344122901lle_hf @ A @ B )
=> ( ( member1367349282lle_hf @ C @ A )
=> ( member1367349282lle_hf @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(68,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hfst @ ( hF_Mirabelle_hpair @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_hfst__conv) ).
thf(411,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)],[68]) ).
thf(75,axiom,
( ( hF_Mirabelle_HInter @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_HInter__hempty) ).
thf(428,plain,
( ( hF_Mirabelle_HInter @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(15,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ~ ( ( member1367349282lle_hf @ A @ B )
=> ( member1367349282lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_DiffE) ).
thf(206,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ~ ( ( member1367349282lle_hf @ A @ B )
=> ( member1367349282lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ bot_bot_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_bot_Oextremum__strict) ).
thf(397,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ bot_bot_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(135,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ zero_z189798548lle_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/sandbox2/benchmark/theBenchmark.p',fact_196_hf__induct) ).
thf(687,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ zero_z189798548lle_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)],[135]) ).
thf(23,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ bot_bo53200981lle_hf @ A )
= bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_empty__Diff) ).
thf(233,plain,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ bot_bo53200981lle_hf @ A )
= bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(61,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( inf_in956532509lle_hf @ B @ C ) )
=> ( ( inf_in956532509lle_hf @ A @ D )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_boolean__algebra__cancel_Oinf1) ).
thf(380,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( inf_in956532509lle_hf @ B @ C ) )
=> ( ( inf_in956532509lle_hf @ A @ D )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(97,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_inf__idem) ).
thf(529,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',fact_26_hball__cong) ).
thf(798,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)],[162]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',fact_17_hball__triv) ).
thf(598,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)],[116]) ).
thf(73,axiom,
( if_HF_Mirabelle_hf
= ( ^ [A: $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( the_HF_Mirabelle_hf
@ ^ [D: hF_Mirabelle_hf] :
( ( A
=> ( D = B ) )
& ( ~ A
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_If__def) ).
thf(424,plain,
( if_HF_Mirabelle_hf
= ( ^ [A: $o,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( the_HF_Mirabelle_hf
@ ^ [D: hF_Mirabelle_hf] :
( ( A
=> ( D = B ) )
& ( ~ A
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_11_union__of__set) ).
thf(630,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)],[123]) ).
thf(144,axiom,
( hF_Mir818139703ollect
= ( ^ [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/sandbox2/benchmark/theBenchmark.p',fact_168_HCollect__def) ).
thf(729,plain,
( hF_Mir818139703ollect
= ( ^ [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)],[144]) ).
thf(12,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ A @ bot_bo53200981lle_hf )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Diff__empty) ).
thf(197,plain,
! [A: set_HF_Mirabelle_hf] :
( ( minus_1450406810lle_hf @ A @ bot_bo53200981lle_hf )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(111,axiom,
( ord_le1344122901lle_hf
= ( ^ [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ord_le616625840e_hf_o
@ ^ [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ A )
@ ^ [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_less__set__def) ).
thf(583,plain,
( ord_le1344122901lle_hf
= ( ^ [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ord_le616625840e_hf_o
@ ^ [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ A )
@ ^ [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_182_RepFun__hinsert) ).
thf(456,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)],[79]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_173_hpair__iff) ).
thf(324,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)],[44]) ).
thf(110,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( inf_in956532509lle_hf @ B @ C ) )
=> ( ( inf_in956532509lle_hf @ D @ A )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_boolean__algebra__cancel_Oinf2) ).
thf(578,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf,D: hF_Mirabelle_hf] :
( ( A
= ( inf_in956532509lle_hf @ B @ C ) )
=> ( ( inf_in956532509lle_hf @ D @ A )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(128,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_HCollect__iff) ).
thf(650,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
= ( ( B @ A )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(84,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_hpair__neq__fst) ).
thf(471,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(87,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Replace__0) ).
thf(488,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o] :
( ( hF_Mirabelle_Replace @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(21,axiom,
! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A = bot_bo53200981lle_hf )
=> ~ ( member1367349282lle_hf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_equals0D) ).
thf(225,plain,
! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A = bot_bo53200981lle_hf )
=> ~ ( member1367349282lle_hf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(47,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_inf__left__commute) ).
thf(339,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_16_hballI) ).
thf(669,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)],[132]) ).
thf(127,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( inf_in956532509lle_hf @ C @ B ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( inf_in956532509lle_hf @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_hinter__hinsert__left) ).
thf(642,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( inf_in956532509lle_hf @ C @ B ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( inf_in956532509lle_hf @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_189_hinsert__commute) ).
thf(526,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)],[96]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',fact_21_HUnion__iff) ).
thf(706,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)],[136]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_gr__implies__not__zero) ).
thf(193,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(100,axiom,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_inf__sup__aci_I1_J) ).
thf(537,plain,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(4,axiom,
! [A: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ A @ bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_emptyE) ).
thf(173,plain,
! [A: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ A @ bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(157,axiom,
( hF_Mir1248913145eplace
= ( ^ [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/sandbox2/benchmark/theBenchmark.p',fact_275_PrimReplace__def) ).
thf(779,plain,
( hF_Mir1248913145eplace
= ( ^ [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)],[157]) ).
thf(58,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( minus_1232880740lle_hf @ ( minus_1232880740lle_hf @ A @ C ) @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_hdiff__insert) ).
thf(371,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ A @ ( hF_Mirabelle_hinsert @ B @ C ) )
= ( minus_1232880740lle_hf @ ( minus_1232880740lle_hf @ A @ C ) @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(92,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ zero_z189798548lle_hf )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( A @ ( hF_Mirabelle_hinsert @ D @ C ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_hf__induct__ax) ).
thf(503,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ zero_z189798548lle_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)],[92]) ).
thf(30,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_not__less__zero) ).
thf(266,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(124,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_hmem__hempty) ).
thf(633,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(130,axiom,
! [A: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_hf )
=> ~ ! [B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( A
= ( hF_Mirabelle_hinsert @ B @ C ) )
=> ( hF_Mirabelle_hmem @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_hf__cases) ).
thf(657,plain,
! [A: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_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)],[130]) ).
thf(154,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( hF_Mirabelle_hinsert @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( inf_in956532509lle_hf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_hinter__hinsert__right) ).
thf(765,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( hF_Mirabelle_hinsert @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_hinsert @ A @ C ) )
= ( inf_in956532509lle_hf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(140,axiom,
( hF_Mirabelle_HInter
= ( ^ [A: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [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/sandbox2/benchmark/theBenchmark.p',fact_34_HInter__def) ).
thf(718,plain,
( hF_Mirabelle_HInter
= ( ^ [A: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [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)],[140]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_7_rev__hbexI) ).
thf(773,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)],[155]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',fact_29_HBall__def) ).
thf(794,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)],[160]) ).
thf(41,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( A = bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_all__not__in__conv) ).
thf(298,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( A = bot_bo53200981lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_12_comprehension) ).
thf(618,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)],[119]) ).
thf(76,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inf_Oidem) ).
thf(430,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(29,axiom,
( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Zero__hf__def) ).
thf(264,plain,
( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(108,axiom,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_inf__commute) ).
thf(573,plain,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(117,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( minus_1232880740lle_hf @ C @ B ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( minus_1232880740lle_hf @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_hinsert__hdiff__if) ).
thf(601,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( minus_1232880740lle_hf @ C @ B ) ) )
& ( ~ ( hF_Mirabelle_hmem @ A @ B )
=> ( ( minus_1232880740lle_hf @ ( hF_Mirabelle_hinsert @ A @ C ) @ B )
= ( hF_Mirabelle_hinsert @ A @ ( minus_1232880740lle_hf @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(104,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ bot_bo1001194783lle_hf )
= bot_bo1001194783lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_inf__bot__right) ).
thf(562,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ bot_bo1001194783lle_hf )
= bot_bo1001194783lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(5,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_bot__nat__0_Oextremum__strict) ).
thf(176,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_not__gr0) ).
thf(286,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(35,axiom,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( ord_le1344122901lle_hf @ A @ B )
=> ? [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_psubset__imp__ex__mem) ).
thf(281,plain,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( ord_le1344122901lle_hf @ A @ B )
=> ? [C: hF_Mirabelle_hf] : ( member1367349282lle_hf @ C @ ( minus_1450406810lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(64,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_hinter__hempty__left) ).
thf(391,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(90,axiom,
( ( hF_Mirabelle_hcard @ zero_z189798548lle_hf )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_hcard__0) ).
thf(498,plain,
( ( hF_Mirabelle_hcard @ zero_z189798548lle_hf )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ B )
=> ( ~ ( member1367349282lle_hf @ A @ C )
=> ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_DiffI) ).
thf(236,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ B )
=> ( ~ ( member1367349282lle_hf @ A @ C )
=> ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_zero__less__iff__neq__zero) ).
thf(181,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_gr__zeroI) ).
thf(187,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ A @ bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_empty__iff) ).
thf(219,plain,
! [A: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ A @ bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,axiom,
! [A: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ A @ zero_z189798548lle_hf )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_hdiff__zero) ).
thf(419,plain,
! [A: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ A @ zero_z189798548lle_hf )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(147,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_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_PrimReplace__iff) ).
thf(736,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_Mir1248913145eplace @ A @ B ) )
= ( ? [D: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ D @ A )
& ( B @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(60,axiom,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ bot_bo1001194783lle_hf @ A )
= bot_bo1001194783lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_inf__bot__left) ).
thf(377,plain,
! [A: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ bot_bo1001194783lle_hf @ A )
= bot_bo1001194783lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_neq0__conv) ).
thf(230,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_296_infinite__descent0) ).
thf(245,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)],[27]) ).
thf(55,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_inf_Oassoc) ).
thf(362,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(106,axiom,
! [A: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_zero__hdiff) ).
thf(567,plain,
! [A: hF_Mirabelle_hf] :
( ( minus_1232880740lle_hf @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(89,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_hf )
=> ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ B @ A ) )
= ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_HInter @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_HInter__hinsert) ).
thf(494,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_hf )
=> ( ( hF_Mirabelle_HInter @ ( hF_Mirabelle_hinsert @ B @ A ) )
= ( inf_in956532509lle_hf @ B @ ( hF_Mirabelle_HInter @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(152,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
=> ~ ( ( hF_Mirabelle_hmem @ A @ C )
=> ~ ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_HCollectE) ).
thf(758,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf > $o,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( hF_Mir818139703ollect @ B @ C ) )
=> ~ ( ( hF_Mirabelle_hmem @ A @ C )
=> ~ ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(49,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_inf__sup__aci_I3_J) ).
thf(345,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( inf_in956532509lle_hf @ B @ ( inf_in956532509lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(99,axiom,
bot_bo1001194783lle_hf = zero_z189798548lle_hf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_bot__hf__def) ).
thf(535,plain,
bot_bo1001194783lle_hf = zero_z189798548lle_hf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_57_RepFun__cong) ).
thf(609,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)],[118]) ).
thf(115,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_hmem__ne) ).
thf(594,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(120,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_hinter__iff) ).
thf(621,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( inf_in956532509lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(94,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_HF__hfset) ).
thf(520,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(81,axiom,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_HUnion__hempty) ).
thf(462,plain,
( ( hF_Mirabelle_HUnion @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',fact_22_hballE) ).
thf(811,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)],[165]) ).
thf(63,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ B )
!= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_hinsert__nonempty) ).
thf(387,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hinsert @ A @ B )
!= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(17,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
= ( ( member1367349282lle_hf @ A @ B )
& ~ ( member1367349282lle_hf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_Diff__iff) ).
thf(213,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
= ( ( member1367349282lle_hf @ A @ B )
& ~ ( member1367349282lle_hf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(143,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_hemptyE) ).
thf(726,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(125,axiom,
( minus_1232880740lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_minus__hf__def) ).
thf(636,plain,
( minus_1232880740lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( hF_Mir818139703ollect
@ ^ [C: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(34,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_less__zeroE) ).
thf(278,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(65,axiom,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_zero__reorient) ).
thf(394,plain,
! [A: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = A )
= ( A = zero_z189798548lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_15_HF__Mirabelle__glliljednj_ObexCI) ).
thf(653,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)],[129]) ).
thf(142,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ B )
=> ( ( hF_Mirabelle_HUnion @ A )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_hmem__Sup__ne) ).
thf(722,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)],[142]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_31_RepFun__def) ).
thf(426,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)],[74]) ).
thf(131,axiom,
! [A: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_hf )
=> ? [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
& ( ( inf_in956532509lle_hf @ B @ A )
= zero_z189798548lle_hf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_foundation) ).
thf(663,plain,
! [A: hF_Mirabelle_hf] :
( ( A != zero_z189798548lle_hf )
=> ? [B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ B @ A )
& ( ( inf_in956532509lle_hf @ B @ A )
= zero_z189798548lle_hf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(59,axiom,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_HCollect__hempty) ).
thf(374,plain,
! [A: hF_Mirabelle_hf > $o] :
( ( hF_Mir818139703ollect @ A @ zero_z189798548lle_hf )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(149,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( ( hF_Mirabelle_hmem @ A @ B )
& ( hF_Mirabelle_hmem @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_hmem__not__sym) ).
thf(749,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)],[149]) ).
thf(48,axiom,
! [A: hF_Mirabelle_hf] :
( ( the_HF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_the__eq__trivial) ).
thf(342,plain,
! [A: hF_Mirabelle_hf] :
( ( the_HF_Mirabelle_hf
@ ^ [B: hF_Mirabelle_hf] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
( least_917110455lle_hf
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
( the_HF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
( ( B @ C )
& ! [D: hF_Mirabelle_hf] :
( ( B @ D )
=> ( A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ord_OLeast__def) ).
thf(355,plain,
( least_917110455lle_hf
= ( ^ [A: hF_Mirabelle_hf > hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
( the_HF_Mirabelle_hf
@ ^ [C: hF_Mirabelle_hf] :
( ( B @ C )
& ! [D: hF_Mirabelle_hf] :
( ( B @ D )
=> ( A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_1_hbexI) ).
thf(776,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)],[156]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_180_hmem__hinsert) ).
thf(712,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)],[138]) ).
thf(40,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_zero__reorient) ).
thf(295,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(69,axiom,
! [A: nat] :
( ( A != bot_bot_nat )
= ( ord_less_nat @ bot_bot_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_bot_Onot__eq__extremum) ).
thf(414,plain,
! [A: nat] :
( ( A != bot_bot_nat )
= ( ord_less_nat @ bot_bot_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',fact_188_hpair__inject) ).
thf(327,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)],[45]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_9_binary__union) ).
thf(673,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)],[133]) ).
thf(112,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_inf__assoc) ).
thf(585,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(54,axiom,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_RepFun__0) ).
thf(359,plain,
! [A: hF_Mirabelle_hf > hF_Mirabelle_hf] :
( ( hF_Mirabelle_RepFun @ zero_z189798548lle_hf @ A )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(122,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( minus_1232880740lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ~ ( hF_Mirabelle_hmem @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_hdiff__iff) ).
thf(627,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A @ ( minus_1232880740lle_hf @ B @ C ) )
= ( ( hF_Mirabelle_hmem @ A @ B )
& ~ ( hF_Mirabelle_hmem @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(101,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_HF_Mirabelle_hf @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_theI) ).
thf(539,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf] :
( ( A @ B )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_HF_Mirabelle_hf @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(14,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_gr0I) ).
thf(203,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inf__sup__aci_I4_J) ).
thf(368,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',fact_0_hf__equalityI) ).
thf(588,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)],[113]) ).
thf(43,axiom,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
( ? [C: hF_Mirabelle_hf] :
( ( A @ C )
& ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the_HF_Mirabelle_hf @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_the1I2) ).
thf(304,plain,
! [A: hF_Mirabelle_hf > $o,B: hF_Mirabelle_hf > $o] :
( ? [C: hF_Mirabelle_hf] :
( ( A @ C )
& ! [D: hF_Mirabelle_hf] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( the_HF_Mirabelle_hf @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(51,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_hpair__nonzero) ).
thf(351,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(145,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_zero__notin__hpair) ).
thf(731,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ zero_z189798548lle_hf @ ( hF_Mirabelle_hpair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',fact_6_hbex__cong) ).
thf(781,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)],[158]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_14_replacement__fun) ).
thf(752,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)],[150]) ).
thf(10,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ( member1367349282lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_DiffD1) ).
thf(190,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,C: set_HF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( minus_1450406810lle_hf @ B @ C ) )
=> ( member1367349282lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_bot__nat__0_Onot__eq__extremum) ).
thf(273,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
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/sandbox2/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(168,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(28,axiom,
( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Abs__hf__0) ).
thf(262,plain,
( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
= zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(72,axiom,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inf_Ocommute) ).
thf(422,plain,
( inf_in956532509lle_hf
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( inf_in956532509lle_hf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_2_hbexE) ).
thf(790,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)],[159]) ).
thf(16,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_not__less0) ).
thf(210,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',fact_279_HUnion__def) ).
thf(807,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)],[163]) ).
thf(67,axiom,
! [A: hF_Mirabelle_hf > $o] :
( ? [B: hF_Mirabelle_hf] :
( ( A @ B )
& ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_HF_Mirabelle_hf @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_theI_H) ).
thf(400,plain,
! [A: hF_Mirabelle_hf > $o] :
( ? [B: hF_Mirabelle_hf] :
( ( A @ B )
& ! [C: hF_Mirabelle_hf] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_HF_Mirabelle_hf @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(98,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_inf__sup__aci_I2_J) ).
thf(532,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ C )
= ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(141,axiom,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_hmem__def) ).
thf(720,plain,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(25,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( ? [B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ B @ A ) )
= ( A != bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ex__in__conv) ).
thf(239,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ? [B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ B @ A ) )
= ( A != bot_bo53200981lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(26,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_not__gr__zero) ).
thf(242,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_3_hf__ext) ).
thf(796,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)],[161]) ).
thf(36,axiom,
! [A: set_HF_Mirabelle_hf] :
~ ( ord_le1344122901lle_hf @ A @ bot_bo53200981lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_bot_Oextremum__strict) ).
thf(283,plain,
! [A: set_HF_Mirabelle_hf] :
~ ( ord_le1344122901lle_hf @ A @ bot_bo53200981lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_190_hinsert__iff) ).
thf(624,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)],[121]) ).
thf(82,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_hpair__neq__snd) ).
thf(464,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hpair @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(109,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_inf_Oleft__idem) ).
thf(575,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ A @ ( inf_in956532509lle_hf @ A @ B ) )
= ( inf_in956532509lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hsnd @ ( hF_Mirabelle_hpair @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_hsnd__conv) ).
thf(459,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)],[80]) ).
thf(13,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( A != bot_bo53200981lle_hf )
= ( ord_le1344122901lle_hf @ bot_bo53200981lle_hf @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_bot_Onot__eq__extremum) ).
thf(200,plain,
! [A: set_HF_Mirabelle_hf] :
( ( A != bot_bo53200981lle_hf )
= ( ord_le1344122901lle_hf @ bot_bo53200981lle_hf @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_hpair__def_H) ).
thf(337,plain,
( hF_Mirabelle_hpair
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ A @ zero_z189798548lle_hf ) ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ A @ ( hF_Mirabelle_hinsert @ B @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B )
= ( inf_in956532509lle_hf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_inf_Oright__idem) ).
thf(491,plain,
! [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( inf_in956532509lle_hf @ ( inf_in956532509lle_hf @ A @ B ) @ B )
= ( inf_in956532509lle_hf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(20,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_less__nat__zero__code) ).
thf(222,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(151,axiom,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_hempty__iff) ).
thf(755,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
= ( ! [B: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_8_replacement) ).
thf(676,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)],[134]) ).
thf(859,plain,
$false,
inference(e,[status(thm)],[433,809,365,518,468,170,276,269,523,762,385,550,500,715,814,747,709,417,301,565,570,184,357,817,559,638,289,216,475,179,591,485,348,734,293,453,411,428,206,397,687,233,380,529,798,598,424,630,729,197,583,456,324,578,650,471,488,225,339,669,642,526,706,193,537,173,779,371,503,266,633,657,765,718,773,794,298,618,430,264,573,601,562,176,286,281,391,498,236,181,187,219,419,736,377,230,245,362,567,494,758,345,535,609,594,621,520,462,811,387,213,726,636,278,394,653,722,426,663,374,749,342,355,776,712,295,414,327,673,585,359,627,539,203,368,588,304,351,731,781,752,190,273,168,262,422,790,210,807,400,532,720,239,242,796,283,624,464,575,459,200,337,491,222,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP075^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:50:12 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.05/1.18 % [INFO] Parsing done (394ms).
% 2.05/1.19 % [INFO] Running in sequential loop mode.
% 3.31/1.57 % [INFO] eprover registered as external prover.
% 3.31/1.58 % [INFO] Scanning for conjecture ...
% 3.69/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ...
% 3.88/1.85 % [INFO] Axiom selection finished. Selected 165 axioms (removed 189 axioms).
% 4.52/2.03 % [INFO] Problem is higher-order (TPTP THF).
% 4.52/2.05 % [INFO] Type checking passed.
% 4.52/2.06 % [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 ...
% 13.84/4.74 % External prover 'e' found a proof!
% 13.84/4.74 % [INFO] Killing All external provers ...
% 13.84/4.74 % Time passed: 4417ms (effective reasoning time: 3546ms)
% 13.84/4.74 % 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)>
% 13.84/4.75 % Axioms used in derivation (165): fact_249_hfst__conv, fact_211_DiffI, fact_42_hinter__hempty__right, fact_229_equals0D, fact_183_hpair__def, fact_280_hcard__hdiff1__less, fact_303_zero__less__iff__neq__zero, fact_305_not__less__zero, fact_91_inf__idem, fact_86_inf_Oidem, fact_160_inf_Oleft__commute, fact_145_inf__assoc, fact_189_hinsert__commute, fact_167_HInter__hinsert, fact_195_hf__cases, fact_30_Replace__def, fact_204_Diff__empty, fact_32_minus__hf__def, fact_109_inf__sup__aci_I4_J, fact_24_HCollectE, fact_22_hballE, fact_48_hdiff__zero, fact_140_inf_Oassoc, fact_298_less__zeroE, fact_51_HInter__hempty, fact_213_Diff__idemp, fact_3_hf__ext, fact_34_HInter__def, fact_49_RepFun__0, fact_52_HInter__iff, fact_258_the1__equality, fact_198_hinter__hinsert__left, fact_55_hempty__iff, fact_277_hfst__def, fact_191_hinsert__nonempty, fact_250_hsnd__conv, fact_40_hinter__iff, fact_26_hball__cong, fact_238_DiffD1, fact_261_theI2, fact_227_bot__hf__def, fact_29_HBall__def, fact_99_zero__reorient, fact_74_inf_Oright__idem, fact_181_singleton__eq__iff, fact_124_inf__sup__aci_I1_J, fact_33_inf__hf__def, fact_173_hpair__iff, fact_285_neq0__conv, fact_69_inf__right__idem, fact_185_Zero__hf__def, fact_251_the__equality, fact_16_hballI, fact_295_bot__nat__0_Oextremum__strict, fact_331_less__numeral__extra_I3_J, fact_188_hpair__inject, fact_50_HUnion__hempty, fact_259_the1I2, fact_1_hbexI, fact_282_not__gr__zero, fact_4_hmem__ne, fact_231_ex__in__conv, fact_330_bot_Onot__eq__extremum, fact_7_rev__hbexI, fact_135_boolean__algebra__cancel_Oinf2, fact_299_not__less0, fact_283_bot__nat__0_Onot__eq__extremum, fact_155_inf__commute, fact_274_ord_OLeast__def, fact_79_inf__left__idem, fact_239_DiffD2, fact_182_RepFun__hinsert, fact_10_hmem__not__sym, fact_300_not__gr0, fact_252_the__eq__trivial, fact_19_HCollect__iff, fact_18_PrimReplace__iff, fact_301_gr0I, fact_341_psubset__imp__ex__mem, fact_262_theI_H, fact_31_RepFun__def, fact_325_bot_Oextremum__strict, fact_347_psubsetD, fact_192_HF__Mirabelle__glliljednj_Odoubleton__eq__iff, fact_304_gr__implies__not__zero, fact_278_hsnd__def, fact_25_HCollectI, fact_39_triv__RepFun, fact_186_hpair__neq__snd, fact_184_hpair__def_H, fact_11_union__of__set, fact_119_inf__sup__aci_I2_J, fact_12_comprehension, fact_197_hinter__hinsert__right, fact_172_hfset__0, fact_27_hmem__Sup__ne, fact_13_hmem__not__refl, fact_344_not__psubset__empty, fact_56_hmem__hempty, fact_23_hbspec, fact_169_HF__hfset, fact_96_inf_Oleft__idem, fact_171_Abs__hf__0, fact_187_hpair__neq__fst, fact_200_hdiff__insert, fact_212_Diff__iff, fact_98_zero__reorient, fact_196_hf__induct, fact_228_emptyE, fact_43_hinter__hempty__left, fact_260_If__def, fact_6_hbex__cong, fact_36_HCollect__hempty, fact_170_zero__notin__hpair, fact_179_inf__bot__left, fact_269_bot__nat__def, fact_97_hfset__hdiff, fact_14_replacement__fun, fact_17_hball__triv, fact_276_hcard__0, fact_202_Diff__cancel, fact_328_bot_Onot__eq__extremum, fact_35_RepFun__iff, fact_205_empty__iff, fact_306_gr__zeroI, fact_176_inf__bot__right, fact_38_hmem__def, fact_284_less__nat__zero__code, fact_130_boolean__algebra__cancel_Oinf1, fact_206_all__not__in__conv, fact_194_hpair__nonzero, fact_150_inf_Ocommute, fact_20_Replace__iff, fact_190_hinsert__iff, fact_8_replacement, fact_296_infinite__descent0, fact_254_the__sym__eq__trivial, fact_5_HBex__def, fact_180_hmem__hinsert, fact_28_Replace__cong, fact_15_HF__Mirabelle__glliljednj_ObexCI, fact_44_zero__hdiff, fact_279_HUnion__def, fact_230_equals0I, fact_193_hf__induct__ax, fact_53_foundation, fact_54_hemptyE, fact_165_inf__left__commute, fact_41_hdiff__iff, fact_9_binary__union, fact_203_empty__Diff, fact_114_inf__sup__aci_I3_J, fact_348_less__set__def, fact_199_hinsert__hdiff__if, fact_275_PrimReplace__def, fact_263_theI, fact_168_HCollect__def, fact_57_RepFun__cong, fact_37_Replace__0, fact_237_DiffE, fact_2_hbexE, fact_21_HUnion__iff, fact_297_gr__implies__not0, fact_0_hf__equalityI, fact_327_bot_Oextremum__strict
% 13.84/4.75 % No. of inferences in proof: 334
% 13.84/4.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4417 ms resp. 3546 ms w/o parsing
% 15.17/4.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.17/4.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------