TSTP Solution File: ITP072^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:27:51 EDT 2024
% Result : Theorem 217.01s 39.53s
% Output : Refutation 217.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 38
% Syntax : Number of formulae : 134 ( 66 unt; 21 typ; 0 def)
% Number of atoms : 263 ( 133 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 533 ( 98 ~; 56 |; 0 &; 363 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 127 ( 6 ^ 120 !; 1 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_se933006839lle_hf_type,type,
set_se933006839lle_hf: $tType ).
thf(set_HF_Mirabelle_hf_type,type,
set_HF_Mirabelle_hf: $tType ).
thf(hF_Mirabelle_hf_type,type,
hF_Mirabelle_hf: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(finite1213132899lle_hf_type,type,
finite1213132899lle_hf: set_HF_Mirabelle_hf > nat ).
thf(finite586181922lle_hf_type,type,
finite586181922lle_hf: set_HF_Mirabelle_hf > $o ).
thf(zero_z189798548lle_hf_type,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(hF_Mirabelle_HF_type,type,
hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(hF_Mirabelle_hfset_type,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(hF_Mirabelle_hmem_type,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(bot_bot_nat_type,type,
bot_bot_nat: nat ).
thf(bot_bo53200981lle_hf_type,type,
bot_bo53200981lle_hf: set_HF_Mirabelle_hf ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le432112161lle_hf_type,type,
ord_le432112161lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(insert9649339lle_hf_type,type,
insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(member1367349282lle_hf_type,type,
member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(z_type,type,
z: hF_Mirabelle_hf ).
thf(sk60_type,type,
sk60: hF_Mirabelle_hf ).
thf(sk561_type,type,
sk561: hF_Mirabelle_hf ).
thf(98,axiom,
! [A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ A )
=> ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_card_Oinfinite) ).
thf(583,plain,
! [A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ A )
=> ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(584,plain,
! [A: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
| ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) ),
inference(cnf,[status(esa)],[583]) ).
thf(585,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ A )
= zero_zero_nat )
| ( finite586181922lle_hf @ A ) ),
inference(lifteq,[status(thm)],[584]) ).
thf(131,axiom,
! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_finite__hfset) ).
thf(706,plain,
! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(707,plain,
! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) ),
inference(cnf,[status(esa)],[706]) ).
thf(24,axiom,
! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_card__insert__le) ).
thf(220,plain,
! [A: set_HF_Mirabelle_hf,B: hF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(221,plain,
! [A: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ! [B: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[220]) ).
thf(222,plain,
! [B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ A )
| ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(8350,plain,
! [C: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ B ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ C @ B ) ) )
| ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) )
!= ( finite586181922lle_hf @ B ) ) ),
inference(paramod_ordered,[status(thm)],[707,222]) ).
thf(8351,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[8350:[bind(A,$thf( D )),bind(B,$thf( hF_Mirabelle_hfset @ D ))]]) ).
thf(8427,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] : ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(simp,[status(thm)],[8351]) ).
thf(21,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_bot_Oextremum__uniqueI) ).
thf(213,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(214,plain,
! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ bot_bot_nat )
| ( A = bot_bot_nat ) ),
inference(cnf,[status(esa)],[213]) ).
thf(215,plain,
! [A: nat] :
( ( A = bot_bot_nat )
| ~ ( ord_less_eq_nat @ A @ bot_bot_nat ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(129,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_bot__nat__def) ).
thf(700,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(701,plain,
bot_bot_nat = zero_zero_nat,
inference(lifteq,[status(thm)],[700]) ).
thf(1764,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ~ ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
inference(rewrite,[status(thm)],[215,701]) ).
thf(6,axiom,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ( ( ord_le432112161lle_hf @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_card__seteq) ).
thf(160,plain,
! [A: set_HF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ( ( ord_le432112161lle_hf @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(161,plain,
! [A: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
=> ! [B: set_HF_Mirabelle_hf] :
( ( ord_le432112161lle_hf @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
=> ( B = A ) ) ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ A )
| ~ ( ord_le432112161lle_hf @ B @ A )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
| ( B = A ) ),
inference(cnf,[status(esa)],[161]) ).
thf(163,plain,
! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ( B = A )
| ~ ( finite586181922lle_hf @ A )
| ~ ( ord_le432112161lle_hf @ B @ A )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(122,axiom,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_HF__hfset) ).
thf(680,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(681,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(cnf,[status(esa)],[680]) ).
thf(682,plain,
! [A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
= A ),
inference(lifteq,[status(thm)],[681]) ).
thf(140,axiom,
( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Zero__hf__def) ).
thf(728,plain,
( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(729,plain,
( ( hF_Mirabelle_HF @ bot_bo53200981lle_hf )
= zero_z189798548lle_hf ),
inference(lifteq,[status(thm)],[728]) ).
thf(1520,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_HF @ ( hF_Mirabelle_hfset @ A ) )
!= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[682,729]) ).
thf(1526,plain,
! [A: hF_Mirabelle_hf] :
( ( A = zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hfset @ A )
!= bot_bo53200981lle_hf ) ),
inference(simp,[status(thm)],[1520]) ).
thf(1,conjecture,
( ( z = zero_z189798548lle_hf )
= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( z = zero_z189798548lle_hf )
!= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(149,plain,
( ( z = zero_z189798548lle_hf )
!= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(150,plain,
( ( z = zero_z189798548lle_hf )
!= ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(754,plain,
( ( z != zero_z189798548lle_hf )
| ~ ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ),
inference(bool_ext,[status(thm)],[150]) ).
thf(756,plain,
( ( z != zero_z189798548lle_hf )
| ~ ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ),
inference(lifteq,[status(thm)],[754]) ).
thf(758,plain,
( ( hF_Mirabelle_hmem @ sk60 @ z )
| ( z != zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[756]) ).
thf(143,axiom,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hmem__hempty) ).
thf(735,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(736,plain,
~ ? [A: hF_Mirabelle_hf] : ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(miniscope,[status(thm)],[735]) ).
thf(737,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ),
inference(cnf,[status(esa)],[736]) ).
thf(834,plain,
! [A: hF_Mirabelle_hf] :
( ( z != zero_z189798548lle_hf )
| ( ( hF_Mirabelle_hmem @ sk60 @ z )
!= ( hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[758,737]) ).
thf(836,plain,
! [A: hF_Mirabelle_hf] :
( ( z != zero_z189798548lle_hf )
| ( sk60 != A )
| ( z != zero_z189798548lle_hf ) ),
inference(simp,[status(thm)],[834]) ).
thf(838,plain,
z != zero_z189798548lle_hf,
inference(simp,[status(thm)],[836]) ).
thf(2298,plain,
! [A: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hfset @ A )
!= bot_bo53200981lle_hf )
| ( A != z ) ),
inference(paramod_ordered,[status(thm)],[1526,838]) ).
thf(2299,plain,
( ( hF_Mirabelle_hfset @ z )
!= bot_bo53200981lle_hf ),
inference(pattern_uni,[status(thm)],[2298:[bind(A,$thf( z ))]]) ).
thf(2403,plain,
! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ A )
| ~ ( ord_le432112161lle_hf @ B @ A )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ A ) @ ( finite1213132899lle_hf @ B ) )
| ( B != bot_bo53200981lle_hf )
| ( A
!= ( hF_Mirabelle_hfset @ z ) ) ),
inference(paramod_ordered,[status(thm)],[163,2299]) ).
thf(2404,plain,
! [A: set_HF_Mirabelle_hf] :
( ~ ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
| ~ ( ord_le432112161lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ ( finite1213132899lle_hf @ A ) )
| ( A != bot_bo53200981lle_hf ) ),
inference(pattern_uni,[status(thm)],[2403:[bind(A,$thf( hF_Mirabelle_hfset @ z )),bind(B,$thf( B ))]]) ).
thf(2406,plain,
( ~ ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
| ~ ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ ( hF_Mirabelle_hfset @ z ) )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ ( finite1213132899lle_hf @ bot_bo53200981lle_hf ) ) ),
inference(simp,[status(thm)],[2404]) ).
thf(71,axiom,
! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__subsetI) ).
thf(438,plain,
! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(439,plain,
! [A: set_HF_Mirabelle_hf] : ( ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A ),
inference(cnf,[status(esa)],[438]) ).
thf(115,axiom,
( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_card_Oempty) ).
thf(654,plain,
( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(655,plain,
( ( finite1213132899lle_hf @ bot_bo53200981lle_hf )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[654]) ).
thf(2464,plain,
( ~ $true
| ~ $true
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ zero_zero_nat ) ),
inference(rewrite,[status(thm)],[2406,707,439,655]) ).
thf(2465,plain,
~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ zero_zero_nat ),
inference(simp,[status(thm)],[2464]) ).
thf(2476,plain,
! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A )
| ( zero_zero_nat != zero_zero_nat ) ),
inference(paramod_ordered,[status(thm)],[1764,2465]) ).
thf(2477,plain,
! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[2476:[]]) ).
thf(3,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_bot_Oextremum__unique) ).
thf(151,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(152,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ bot_bot_nat )
= ( A = bot_bot_nat ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(773,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(rewrite,[status(thm)],[153,701]) ).
thf(2949,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
inference(rewrite,[status(thm)],[2477,773]) ).
thf(2950,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ~ ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ A ) ),
inference(lifteq,[status(thm)],[2949]) ).
thf(12415,plain,
! [C: nat,B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( C != zero_zero_nat )
| ( ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ B ) ) @ ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) )
!= ( ord_less_eq_nat @ ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8427,2950]) ).
thf(12416,plain,
! [A: hF_Mirabelle_hf] :
( ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
!= zero_zero_nat ),
inference(pattern_uni,[status(thm)],[12415:[bind(A,$thf( E )),bind(B,$thf( z )),bind(C,$thf( finite1213132899lle_hf @ ( insert9649339lle_hf @ E @ ( hF_Mirabelle_hfset @ z ) ) ))]]) ).
thf(12524,plain,
! [A: hF_Mirabelle_hf] :
( ( finite1213132899lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
!= zero_zero_nat ),
inference(simp,[status(thm)],[12416]) ).
thf(12575,plain,
! [B: hF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ A )
| ( ( finite1213132899lle_hf @ A )
!= ( finite1213132899lle_hf @ ( insert9649339lle_hf @ B @ ( hF_Mirabelle_hfset @ z ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,12524]) ).
thf(12576,plain,
! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) ),
inference(pattern_uni,[status(thm)],[12575:[bind(A,$thf( insert9649339lle_hf @ C @ ( hF_Mirabelle_hfset @ z ) )),bind(B,$thf( C ))]]) ).
thf(12591,plain,
! [A: hF_Mirabelle_hf] : ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) ),
inference(simp,[status(thm)],[12576]) ).
thf(99,axiom,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
= ( finite586181922lle_hf @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_finite__insert) ).
thf(586,plain,
! [A: hF_Mirabelle_hf,B: set_HF_Mirabelle_hf] :
( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
= ( finite586181922lle_hf @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(587,plain,
! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
= ( finite586181922lle_hf @ B ) ),
inference(cnf,[status(esa)],[586]) ).
thf(588,plain,
! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( finite586181922lle_hf @ ( insert9649339lle_hf @ A @ B ) )
= ( finite586181922lle_hf @ B ) ),
inference(lifteq,[status(thm)],[587]) ).
thf(12618,plain,
finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ),
inference(rewrite,[status(thm)],[12591,588]) ).
thf(116,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( A = bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_all__not__in__conv) ).
thf(656,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)],[116]) ).
thf(657,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( A = bot_bo53200981lle_hf ) ),
inference(cnf,[status(esa)],[656]) ).
thf(658,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( A = bot_bo53200981lle_hf ) ),
inference(lifteq,[status(thm)],[657]) ).
thf(63,axiom,
! [A: set_HF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ A )
= zero_zero_nat )
= ( ( A = bot_bo53200981lle_hf )
| ~ ( finite586181922lle_hf @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_card__eq__0__iff) ).
thf(412,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ A )
= zero_zero_nat )
= ( ( A = bot_bo53200981lle_hf )
| ~ ( finite586181922lle_hf @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(413,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ A )
= zero_zero_nat )
= ( ( A = bot_bo53200981lle_hf )
| ~ ( finite586181922lle_hf @ A ) ) ),
inference(cnf,[status(esa)],[412]) ).
thf(414,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ( A = bot_bo53200981lle_hf )
| ~ ( finite586181922lle_hf @ A ) )
= ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) ),
inference(lifteq,[status(thm)],[413]) ).
thf(17471,plain,
! [B: set_HF_Mirabelle_hf,A: set_HF_Mirabelle_hf] :
( ( ( ! [C: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ C @ A )
| ~ ( finite586181922lle_hf @ B ) )
= ( ( finite1213132899lle_hf @ B )
= zero_zero_nat ) )
| ( ( A = bot_bo53200981lle_hf )
!= ( B = bot_bo53200981lle_hf ) ) ),
inference(paramod_ordered,[status(thm)],[658,414]) ).
thf(17472,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A )
| ~ ( finite586181922lle_hf @ A ) )
= ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) ),
inference(pattern_uni,[status(thm)],[17471:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(35334,plain,
! [A: set_HF_Mirabelle_hf] :
( ( ( ! [B: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ B @ A ) )
= ( ( finite1213132899lle_hf @ A )
= zero_zero_nat ) )
| ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ z ) )
!= ( finite586181922lle_hf @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12618,17472]) ).
thf(35335,plain,
( ( ! [A: hF_Mirabelle_hf] :
~ ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ z ) ) )
= ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ z ) )
= zero_zero_nat ) ),
inference(pattern_uni,[status(thm)],[35334:[bind(A,$thf( hF_Mirabelle_hfset @ z ))]]) ).
thf(141,axiom,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hmem__def) ).
thf(730,plain,
( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(731,plain,
( ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) )
= hF_Mirabelle_hmem ),
inference(lifteq,[status(thm)],[730]) ).
thf(785,plain,
! [B: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) )
= ( hF_Mirabelle_hmem @ A @ B ) ),
inference(func_ext,[status(esa)],[731]) ).
thf(17479,plain,
! [B: set_HF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( ( B = bot_bo53200981lle_hf )
= ( ( finite1213132899lle_hf @ B )
= zero_zero_nat ) )
| ( ( finite586181922lle_hf @ ( hF_Mirabelle_hfset @ A ) )
!= ( finite586181922lle_hf @ B ) ) ),
inference(paramod_ordered,[status(thm)],[707,414]) ).
thf(17480,plain,
! [A: hF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ A ) )
= zero_zero_nat )
= ( ( hF_Mirabelle_hfset @ A )
= bot_bo53200981lle_hf ) ),
inference(pattern_uni,[status(thm)],[17479:[bind(A,$thf( C )),bind(B,$thf( hF_Mirabelle_hfset @ C ))]]) ).
thf(17721,plain,
! [A: hF_Mirabelle_hf] :
( ( ( finite1213132899lle_hf @ ( hF_Mirabelle_hfset @ A ) )
= zero_zero_nat )
= ( ( hF_Mirabelle_hfset @ A )
= bot_bo53200981lle_hf ) ),
inference(simp,[status(thm)],[17480]) ).
thf(35753,plain,
( ( ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) )
= ( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf ) ),
inference(rewrite,[status(thm)],[35335,785,17721]) ).
thf(35754,plain,
( ~ ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z )
| ( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf ) ),
inference(bool_ext,[status(thm)],[35753]) ).
thf(35941,plain,
( ( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf )
| ~ ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ),
inference(lifteq,[status(thm)],[35754]) ).
thf(36026,plain,
( ( hF_Mirabelle_hmem @ sk561 @ z )
| ( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf ) ),
inference(cnf,[status(esa)],[35941]) ).
thf(755,plain,
( ( z = zero_z189798548lle_hf )
| ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ),
inference(bool_ext,[status(thm)],[150]) ).
thf(757,plain,
( ( z = zero_z189798548lle_hf )
| ! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ) ),
inference(lifteq,[status(thm)],[755]) ).
thf(759,plain,
! [A: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ A @ z )
| ( z = zero_z189798548lle_hf ) ),
inference(cnf,[status(esa)],[757]) ).
thf(842,plain,
! [A: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A @ z ),
inference(simplifyReflect,[status(thm)],[759,838]) ).
thf(38993,plain,
( $false
| ( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf ) ),
inference(rewrite,[status(thm)],[36026,842]) ).
thf(38994,plain,
( ( hF_Mirabelle_hfset @ z )
= bot_bo53200981lle_hf ),
inference(simp,[status(thm)],[38993]) ).
thf(38995,plain,
$false,
inference(simplifyReflect,[status(thm)],[38994,2299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP072^1 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat May 18 18:19:54 EDT 2024
% 0.20/0.35 % CPUTime :
% 0.99/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.30 % [INFO] Parsing done (357ms).
% 2.21/1.31 % [INFO] Running in sequential loop mode.
% 3.05/1.66 % [INFO] nitpick registered as external prover.
% 3.05/1.66 % [INFO] Scanning for conjecture ...
% 3.42/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ...
% 3.69/1.92 % [INFO] Axiom selection finished. Selected 146 axioms (removed 205 axioms).
% 3.95/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 4.18/2.07 % [INFO] Type checking passed.
% 4.18/2.08 % [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 ...
% 216.76/39.36 % [INFO] Killing All external provers ...
% 217.01/39.53 % Time passed: 38883ms (effective reasoning time: 38051ms)
% 217.01/39.53 % 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)>
% 217.01/39.53 % Axioms used in derivation (16): fact_9_Zero__hf__def, fact_14_HF__hfset, fact_106_bot__nat__def, fact_2_hmem__hempty, fact_117_finite__insert, fact_168_card_Oempty, fact_5_hmem__def, fact_169_card_Oinfinite, fact_20_all__not__in__conv, fact_164_empty__subsetI, fact_248_card__insert__le, fact_244_card__seteq, fact_107_finite__hfset, fact_208_bot_Oextremum__unique, fact_210_bot_Oextremum__uniqueI, fact_228_card__eq__0__iff
% 217.01/39.53 % No. of inferences in proof: 113
% 217.01/39.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 38883 ms resp. 38051 ms w/o parsing
% 217.40/39.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 217.40/39.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------