%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP072^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:23:59 AM UTC 2026
% Result : Theorem 1.22s 0.43s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 243 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 1931 ( 829 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2392 ( 333 ~; 434 |; 0 &;1619 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 12 con; 0-2 aty)
% Number of variables : 577 ( 33 ^; 544 !; 0 ?; 577 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_hF_Mirabelle_hf,type,
hF_Mirabelle_hf: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_set_HF_Mirabelle_hf,type,
set_HF_Mirabelle_hf: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_se933006839lle_hf,type,
set_se933006839lle_hf: $tType ).
thf(tp_bot_bo1263054448e_hf_o,type,
bot_bo1263054448e_hf_o: hF_Mirabelle_hf > $o ).
thf(tp_bot_bo2093393035lle_hf,type,
bot_bo2093393035lle_hf: set_se933006839lle_hf ).
thf(tp_bot_bo53200981lle_hf,type,
bot_bo53200981lle_hf: set_HF_Mirabelle_hf ).
thf(tp_bot_bo554042810e_hf_o,type,
bot_bo554042810e_hf_o: set_HF_Mirabelle_hf > $o ).
thf(tp_bot_bot_nat,type,
bot_bot_nat: nat ).
thf(tp_bot_bot_nat_o,type,
bot_bot_nat_o: nat > $o ).
thf(tp_bot_bot_o,type,
bot_bot_o: $o ).
thf(tp_bot_bot_set_nat,type,
bot_bot_set_nat: set_nat ).
thf(tp_collec1758573718lle_hf,type,
collec1758573718lle_hf: ( set_HF_Mirabelle_hf > $o ) > set_se933006839lle_hf ).
thf(tp_collec2046588256lle_hf,type,
collec2046588256lle_hf: ( hF_Mirabelle_hf > $o ) > set_HF_Mirabelle_hf ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_finite1213132899lle_hf,type,
finite1213132899lle_hf: set_HF_Mirabelle_hf > nat ).
thf(tp_finite1450550360lle_hf,type,
finite1450550360lle_hf: set_se933006839lle_hf > $o ).
thf(tp_finite586181922lle_hf,type,
finite586181922lle_hf: set_HF_Mirabelle_hf > $o ).
thf(tp_finite90088345lle_hf,type,
finite90088345lle_hf: set_se933006839lle_hf > nat ).
thf(tp_finite_card_nat,type,
finite_card_nat: set_nat > nat ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_hF_Mirabelle_Abs_hf,type,
hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_HF,type,
hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hfset,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hinsert,type,
hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hmem,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(tp_image_131453538hf_nat,type,
image_131453538hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > set_nat ).
thf(tp_image_1514960916lle_hf,type,
image_1514960916lle_hf: ( set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ) > set_se933006839lle_hf > set_se933006839lle_hf ).
thf(tp_image_1743964010lle_hf,type,
image_1743964010lle_hf: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_image_246164834lle_hf,type,
image_246164834lle_hf: ( nat > hF_Mirabelle_hf ) > set_nat > set_HF_Mirabelle_hf ).
thf(tp_image_899003828lle_hf,type,
image_899003828lle_hf: ( set_HF_Mirabelle_hf > hF_Mirabelle_hf ) > set_se933006839lle_hf > set_HF_Mirabelle_hf ).
thf(tp_image_nat_nat,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(tp_inj_on1874279374hf_nat,type,
inj_on1874279374hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > $o ).
thf(tp_inj_on1988990670lle_hf,type,
inj_on1988990670lle_hf: ( nat > hF_Mirabelle_hf ) > set_nat > $o ).
thf(tp_inj_on755450110lle_hf,type,
inj_on755450110lle_hf: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > set_HF_Mirabelle_hf > $o ).
thf(tp_inj_on811196232lle_hf,type,
inj_on811196232lle_hf: ( set_HF_Mirabelle_hf > hF_Mirabelle_hf ) > set_se933006839lle_hf > $o ).
thf(tp_inj_on_nat_nat,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(tp_insert1636143089lle_hf,type,
insert1636143089lle_hf: set_HF_Mirabelle_hf > set_se933006839lle_hf > set_se933006839lle_hf ).
thf(tp_insert9649339lle_hf,type,
insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_insert_nat,type,
insert_nat: nat > set_nat > set_nat ).
thf(tp_is_emp566801209lle_hf,type,
is_emp566801209lle_hf: set_HF_Mirabelle_hf > $o ).
thf(tp_is_sin1448700567lle_hf,type,
is_sin1448700567lle_hf: set_HF_Mirabelle_hf > $o ).
thf(tp_lattic1974000059at_nat,type,
lattic1974000059at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_lattic710307446hf_nat,type,
lattic710307446hf_nat: ( hF_Mirabelle_hf > nat ) > set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_member1367349282lle_hf,type,
member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(tp_member1490636632lle_hf,type,
member1490636632lle_hf: set_HF_Mirabelle_hf > set_se933006839lle_hf > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_minus_1450406810lle_hf,type,
minus_1450406810lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_minus_500612048lle_hf,type,
minus_500612048lle_hf: set_se933006839lle_hf > set_se933006839lle_hf > set_se933006839lle_hf ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(tp_minus_minus_set_nat,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(tp_ord_le2016357975lle_hf,type,
ord_le2016357975lle_hf: set_se933006839lle_hf > set_se933006839lle_hf > $o ).
thf(tp_ord_le432112161lle_hf,type,
ord_le432112161lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_sK1_SY23,type,
sK1_SY23: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK2_SY32,type,
sK2_SY32: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK3_X,type,
sK3_X: hF_Mirabelle_hf ).
thf(tp_sK4_SY31,type,
sK4_SY31: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_semiri2013084963it_nat,type,
semiri2013084963it_nat: nat > nat > nat ).
thf(tp_semiri2115134414it_nat,type,
semiri2115134414it_nat: nat > nat > nat ).
thf(tp_semiring_1_Nats_nat,type,
semiring_1_Nats_nat: set_nat ).
thf(tp_the_el1104322134lle_hf,type,
the_el1104322134lle_hf: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_z,type,
z: hF_Mirabelle_hf ).
thf(tp_zero_z189798548lle_hf,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(342,axiom,
( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Zero__hf__def) ).
thf(343,axiom,
( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
= zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Abs__hf__0) ).
thf(345,axiom,
! [X2: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = X2 )
= ( X2 = zero_z189798548lle_hf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__reorient) ).
thf(346,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_5_hmem__def) ).
thf(347,axiom,
! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A2 @ ( hF_Mirabelle_hinsert @ B3 @ C ) )
= ( ( A2 = B3 )
| ( hF_Mirabelle_hmem @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_hmem__hinsert) ).
thf(348,axiom,
! [Y2: hF_Mirabelle_hf] :
( ( Y2 != zero_z189798548lle_hf )
=> ~ ! [A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
( ( Y2
= ( hF_Mirabelle_hinsert @ A3 @ B2 ) )
=> ( hF_Mirabelle_hmem @ A3 @ B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hf__cases) ).
thf(349,axiom,
! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hmem__hempty) ).
thf(350,axiom,
! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hemptyE) ).
thf(351,axiom,
( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [X: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X @ A )
= ( hF_Mirabelle_hmem @ X @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hf__ext) ).
thf(352,conjecture,
( ( z = zero_z189798548lle_hf )
= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(353,negated_conjecture,
( ( ( z = zero_z189798548lle_hf )
= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[352]) ).
thf(354,plain,
( ( ( z = zero_z189798548lle_hf )
= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(unfold_def,[status(thm)],[353]) ).
thf(355,plain,
( ( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(356,plain,
( ( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
= zero_z189798548lle_hf )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(357,plain,
( ( ! [X2: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = X2 )
= ( X2 = zero_z189798548lle_hf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(358,plain,
( ( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(359,plain,
( ( ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A2 @ ( hF_Mirabelle_hinsert @ B3 @ C ) )
= ( ( A2 = B3 )
| ( hF_Mirabelle_hmem @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(360,plain,
( ( ! [Y2: hF_Mirabelle_hf] :
( ( Y2 != zero_z189798548lle_hf )
=> ~ ! [A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
( ( Y2
= ( hF_Mirabelle_hinsert @ A3 @ B2 ) )
=> ( hF_Mirabelle_hmem @ A3 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(361,plain,
( ( ! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(362,plain,
( ( ! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(363,plain,
( ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [X: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X @ A )
= ( hF_Mirabelle_hmem @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(364,plain,
( ( ( z = zero_z189798548lle_hf )
!= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[354]) ).
thf(365,plain,
( ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [X: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X @ A )
= ( hF_Mirabelle_hmem @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(366,plain,
( ( ! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(367,plain,
( ( ! [A2: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ A2 @ zero_z189798548lle_hf ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(368,plain,
( ( ! [Y2: hF_Mirabelle_hf] :
( ( Y2 != zero_z189798548lle_hf )
=> ~ ! [A3: hF_Mirabelle_hf,B2: hF_Mirabelle_hf] :
( ( Y2
= ( hF_Mirabelle_hinsert @ A3 @ B2 ) )
=> ( hF_Mirabelle_hmem @ A3 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(369,plain,
( ( ! [A2: hF_Mirabelle_hf,B3: hF_Mirabelle_hf,C: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ A2 @ ( hF_Mirabelle_hinsert @ B3 @ C ) )
= ( ( A2 = B3 )
| ( hF_Mirabelle_hmem @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(370,plain,
( ( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(371,plain,
( ( ! [X2: hF_Mirabelle_hf] :
( ( zero_z189798548lle_hf = X2 )
= ( X2 = zero_z189798548lle_hf ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(372,plain,
( ( ( hF_Mirabelle_Abs_hf @ zero_zero_nat )
= zero_z189798548lle_hf )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(373,plain,
( ( zero_z189798548lle_hf
= ( hF_Mirabelle_HF @ bot_bo53200981lle_hf ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(374,plain,
( ( ( z = zero_z189798548lle_hf )
!= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(375,plain,
( ( ! [SX0: hF_Mirabelle_hf] :
( ~ ( ( SX0 != zero_z189798548lle_hf ) )
| ~ ! [SX1: hF_Mirabelle_hf,SX2: hF_Mirabelle_hf] :
( ( SX0
!= ( hF_Mirabelle_hinsert @ SX1 @ SX2 ) )
| ( hF_Mirabelle_hmem @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(376,plain,
( ( ! [SV1: hF_Mirabelle_hf] :
( ( ^ [SY17: hF_Mirabelle_hf] : ( SV1 = SY17 ) )
= ( ^ [SY18: hF_Mirabelle_hf] :
! [SY19: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY19 @ SV1 )
= ( hF_Mirabelle_hmem @ SY19 @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[365]) ).
thf(377,plain,
( ( ( ^ [Y: hF_Mirabelle_hf,Z: hF_Mirabelle_hf] : ( Y = Z ) )
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] :
! [X: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X @ A )
= ( hF_Mirabelle_hmem @ X @ B ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[365]) ).
thf(378,plain,
! [SV2: hF_Mirabelle_hf] :
( ( ~ ( hF_Mirabelle_hmem @ SV2 @ zero_z189798548lle_hf ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(379,plain,
! [SV3: hF_Mirabelle_hf] :
( ( ~ ( hF_Mirabelle_hmem @ SV3 @ zero_z189798548lle_hf ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(380,plain,
! [SV4: hF_Mirabelle_hf] :
( ( ! [SY20: hF_Mirabelle_hf,SY21: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SY20 @ SY21 ) )
= ( ( SV4 = SY20 )
| ( hF_Mirabelle_hmem @ SV4 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(381,plain,
( ( ! [SV5: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV5 )
= ( ^ [SY22: hF_Mirabelle_hf] : ( member1367349282lle_hf @ SV5 @ ( hF_Mirabelle_hfset @ SY22 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[370]) ).
thf(382,plain,
( ( hF_Mirabelle_hmem
= ( ^ [A: hF_Mirabelle_hf,B: hF_Mirabelle_hf] : ( member1367349282lle_hf @ A @ ( hF_Mirabelle_hfset @ B ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[370]) ).
thf(383,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf = SV6 )
= ( SV6 = zero_z189798548lle_hf ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(384,plain,
( ( ( z = zero_z189798548lle_hf )
= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(385,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ~ ( ( SV7 != zero_z189798548lle_hf ) )
| ~ ! [SY23: hF_Mirabelle_hf,SY24: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ SY23 @ SY24 ) )
| ( hF_Mirabelle_hmem @ SY23 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(386,plain,
! [SV8: hF_Mirabelle_hf] :
( ( ( ^ [SY25: hF_Mirabelle_hf] : ( SV8 = SY25 ) )
= ( ^ [SY26: hF_Mirabelle_hf] :
! [SY27: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY27 @ SV8 )
= ( hF_Mirabelle_hmem @ SY27 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(387,plain,
! [SV2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV2 @ zero_z189798548lle_hf )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(388,plain,
! [SV3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV3 @ zero_z189798548lle_hf )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(389,plain,
! [SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ! [SY28: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SY28 ) )
= ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(390,plain,
! [SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 )
= ( ^ [SY29: hF_Mirabelle_hf] : ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(391,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ~ ( ( zero_z189798548lle_hf = SV6 )
| ( SV6 = zero_z189798548lle_hf ) )
| ~ ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[383]) ).
thf(392,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf = SV6 )
= ( SV6 = zero_z189798548lle_hf ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[383]) ).
thf(393,plain,
( ( ~ ( ( z = zero_z189798548lle_hf )
| ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
| ~ ( ( z != zero_z189798548lle_hf )
| ~ ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[384]) ).
thf(394,plain,
( ( ( z = zero_z189798548lle_hf )
= ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[384]) ).
thf(395,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV7 != zero_z189798548lle_hf ) ) )
= $true )
| ( ( ~ ! [SY23: hF_Mirabelle_hf,SY24: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ SY23 @ SY24 ) )
| ( hF_Mirabelle_hmem @ SY23 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(396,plain,
! [SV8: hF_Mirabelle_hf] :
( ( ! [SV11: hF_Mirabelle_hf] :
( ( SV8 = SV11 )
= ( ! [SY30: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY30 @ SV8 )
= ( hF_Mirabelle_hmem @ SY30 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[386]) ).
thf(397,plain,
! [SV8: hF_Mirabelle_hf] :
( ( ( ^ [SY25: hF_Mirabelle_hf] : ( SV8 = SY25 ) )
= ( ^ [SY26: hF_Mirabelle_hf] :
! [SY27: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY27 @ SV8 )
= ( hF_Mirabelle_hmem @ SY27 @ SY26 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[386]) ).
thf(398,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(399,plain,
! [SV10: hF_Mirabelle_hf] :
( ( ! [SV13: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV10 @ SV13 )
= ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV13 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[390]) ).
thf(400,plain,
! [SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 )
= ( ^ [SY29: hF_Mirabelle_hf] : ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SY29 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[390]) ).
thf(401,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( ( zero_z189798548lle_hf = SV6 )
| ( SV6 = zero_z189798548lle_hf ) ) )
= $true )
| ( ( ~ ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(402,plain,
( ( ~ ( ( z = zero_z189798548lle_hf )
| ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(403,plain,
( ( ~ ( ( z != zero_z189798548lle_hf )
| ~ ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(404,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( SV7 != zero_z189798548lle_hf )
= $false )
| ( ( ~ ! [SY23: hF_Mirabelle_hf,SY24: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ SY23 @ SY24 ) )
| ( hF_Mirabelle_hmem @ SY23 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(405,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(406,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ~ ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[398]) ).
thf(407,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[398]) ).
thf(408,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(409,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ( zero_z189798548lle_hf = SV6 )
| ( SV6 = zero_z189798548lle_hf ) )
= $false )
| ( ( ~ ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(410,plain,
( ( ( z = zero_z189798548lle_hf )
| ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(411,plain,
( ( ( z != zero_z189798548lle_hf )
| ~ ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(412,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( SV7 = zero_z189798548lle_hf )
= $true )
| ( ( ~ ! [SY23: hF_Mirabelle_hf,SY24: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ SY23 @ SY24 ) )
| ( hF_Mirabelle_hmem @ SY23 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(413,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ~ ( ( SV8 = SV14 )
| ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
| ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[405]) ).
thf(414,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[405]) ).
thf(415,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(416,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ~ ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[408]) ).
thf(417,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[408]) ).
thf(418,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf = SV6 )
= $false )
| ( ( ~ ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(419,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( SV6 = zero_z189798548lle_hf )
= $false )
| ( ( ~ ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(420,plain,
( ( ( z = zero_z189798548lle_hf )
= $true )
| ( ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(421,plain,
( ( ( z != zero_z189798548lle_hf )
= $true )
| ( ( ~ ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(422,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( ! [SY23: hF_Mirabelle_hf,SY24: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ SY23 @ SY24 ) )
| ( hF_Mirabelle_hmem @ SY23 @ SY24 ) ) )
= $false )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(423,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV8 = SV14 )
| ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(424,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(426,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) )
= $false )
| ( ( zero_z189798548lle_hf = SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(427,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ( zero_z189798548lle_hf != SV6 )
| ( SV6 != zero_z189798548lle_hf ) )
= $false )
| ( ( SV6 = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(428,plain,
! [SV16: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV16 @ z ) )
= $true )
| ( ( z = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(429,plain,
( ( ( z = zero_z189798548lle_hf )
= $false )
| ( ( ~ ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( ! [SY32: hF_Mirabelle_hf] :
( ( SV7
!= ( hF_Mirabelle_hinsert @ ( sK1_SY23 @ SV7 ) @ SY32 ) )
| ( hF_Mirabelle_hmem @ ( sK1_SY23 @ SV7 ) @ SY32 ) ) )
= $false )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[422]) ).
thf(431,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ( SV8 = SV14 )
| ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(432,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(433,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(434,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(435,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf != SV6 )
= $false )
| ( ( zero_z189798548lle_hf = SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(436,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( SV6 != zero_z189798548lle_hf )
= $false )
| ( ( zero_z189798548lle_hf = SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(437,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf != SV6 )
= $false )
| ( ( SV6 = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(438,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( SV6 != zero_z189798548lle_hf )
= $false )
| ( ( SV6 = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(439,plain,
! [SV16: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV16 @ z )
= $false )
| ( ( z = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(440,plain,
( ( ( ! [X: hF_Mirabelle_hf] :
~ ( hF_Mirabelle_hmem @ X @ z ) )
= $false )
| ( ( z = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(441,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( ( SV7
!= ( hF_Mirabelle_hinsert @ ( sK1_SY23 @ SV7 ) @ ( sK2_SY32 @ SV7 ) ) )
| ( hF_Mirabelle_hmem @ ( sK1_SY23 @ SV7 ) @ ( sK2_SY32 @ SV7 ) ) )
= $false )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(442,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(443,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(444,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(445,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( SV4 = SV9 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(446,plain,
! [SV9: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(447,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(448,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(449,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf = SV6 )
= $true )
| ( ( zero_z189798548lle_hf = SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(450,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( SV6 = zero_z189798548lle_hf )
= $true )
| ( ( zero_z189798548lle_hf = SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(451,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( zero_z189798548lle_hf = SV6 )
= $true )
| ( ( SV6 = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(452,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( SV6 = zero_z189798548lle_hf )
= $true )
| ( ( SV6 = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(453,plain,
( ( ( ~ ( hF_Mirabelle_hmem @ sK3_X @ z ) )
= $false )
| ( ( z = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[440]) ).
thf(454,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( SV7
!= ( hF_Mirabelle_hinsert @ ( sK1_SY23 @ SV7 ) @ ( sK2_SY32 @ SV7 ) ) )
= $false )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(455,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK1_SY23 @ SV7 ) @ ( sK2_SY32 @ SV7 ) )
= $false )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(456,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(457,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[443]) ).
thf(458,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(459,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(460,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(461,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
| ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(462,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(463,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 )
| ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $false )
| ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(464,plain,
( ( ( hF_Mirabelle_hmem @ sK3_X @ z )
= $true )
| ( ( z = zero_z189798548lle_hf )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(465,plain,
! [SV7: hF_Mirabelle_hf] :
( ( ( SV7
= ( hF_Mirabelle_hinsert @ ( sK1_SY23 @ SV7 ) @ ( sK2_SY32 @ SV7 ) ) )
= $true )
| ( ( SV7 = zero_z189798548lle_hf )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(466,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 != SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(467,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(468,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[457]) ).
thf(469,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[457]) ).
thf(470,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(471,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(472,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) ) )
= $false )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(473,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(474,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(475,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(476,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(477,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(478,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV15 ) )
= $false )
| ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(479,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( ~ ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) ) )
= $false )
| ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(480,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(481,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(482,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(483,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) ) )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(484,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(485,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( SV4 = SV9 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(486,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(487,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(488,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV4 @ ( hF_Mirabelle_hinsert @ SV9 @ SV12 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(489,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( ( SV4 = SV9 )
| ( hF_Mirabelle_hmem @ SV4 @ SV12 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(490,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(491,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(492,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV15 )
= $true )
| ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(493,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $true )
| ( ( member1367349282lle_hf @ SV10 @ ( hF_Mirabelle_hfset @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(494,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(495,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(496,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(497,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 != SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(498,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(499,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( SV4 = SV9 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(500,plain,
! [SV12: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV4: hF_Mirabelle_hf] :
( ( ( SV4 = SV9 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV4 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(501,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[494]) ).
thf(502,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[494]) ).
thf(503,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(504,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 ) )
= $true )
| ( ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(505,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(506,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(507,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(508,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(509,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $true )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(510,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(511,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(512,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 != SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(513,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(514,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( ~ ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(515,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[510]) ).
thf(516,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[510]) ).
thf(517,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(518,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) ) )
= $true )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(519,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(520,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(521,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ( SV8 != SV14 )
| ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(522,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(523,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(524,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(525,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(526,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 != SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(527,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(528,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(529,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(530,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(531,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(532,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV17 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(533,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[525]) ).
thf(534,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[525]) ).
thf(535,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( SV8 = SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(536,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY31: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SY31 @ SV8 )
= ( hF_Mirabelle_hmem @ SY31 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(537,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(538,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) ) )
= $true )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(539,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(540,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(541,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(542,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV17 @ SV14 )
= $false )
| ( ( SV8 = SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(543,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(544,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(545,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(546,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(547,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(548,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(549,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(550,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(551,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(552,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(553,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV18 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(554,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(555,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(556,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(557,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(558,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(559,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(560,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV18 @ SV14 )
= $false )
| ( ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(561,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(562,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(563,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(564,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(565,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(566,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(567,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV19 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(568,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(569,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(570,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(571,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(572,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(573,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV19 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(574,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(575,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 )
| ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(576,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(577,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(578,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV8 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(579,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV20 @ SV14 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(580,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(581,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(582,plain,
! [SV14: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV8 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(583,plain,
! [SV8: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV20 @ SV14 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV8 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( sK4_SY31 @ SV14 @ SV8 ) @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(584,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[372,583,582,581,580,573,572,571,570,560,559,558,557,549,542,541,540,539,535,534,519,516,505,502,500,499,493,492,491,490,488,486,485,480,470,465,464,455,452,451,450,449,439,417,414,407,400,397,394,392,388,387,382,377,373]) ).
thf(585,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP072^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n014.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 11:15:57 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.22/0.43 ..
% 1.22/0.43
% 1.22/0.43 No.of.Axioms: 9
% 1.22/0.43
% 1.22/0.43 Length.of.Defs: 0
% 1.22/0.43
% 1.22/0.43 Contains.Choice.Funs: false
% 1.22/0.43 .......
% 1.22/0.43
% 1.22/0.43 ********************************
% 1.22/0.43 * All subproblems solved! *
% 1.22/0.43 ********************************
% 1.22/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:584,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.22/0.43
% 1.22/0.43 %**** Beginning of derivation protocol ****
% 1.22/0.43 % SZS output start CNFRefutation
% See solution above
% 1.22/0.44
% 1.22/0.44 %**** End of derivation protocol ****
% 1.22/0.44 %**** no. of clauses in derivation: 243 ****
% 1.22/0.44 %**** clause counter: 584 ****
% 1.22/0.44
% 1.22/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:9,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:584,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------