%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP076^1 : 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 : n003.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 10:24:01 AM UTC 2026
% Result : Theorem 1.64s 0.54s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 155 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 1371 ( 551 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 3014 ( 763 ~; 460 |; 6 &;1779 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 9 con; 0-5 aty)
% Number of variables : 655 ( 5 ^; 644 !; 6 ?; 655 :)
% 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_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_hF_Mir1248913145eplace,type,
hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(tp_hF_Mir137170979_hpair,type,
hF_Mir137170979_hpair: hF_Mirabelle_hf > $o ).
thf(tp_hF_Mir1653039215strict,type,
hF_Mir1653039215strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mir199975595nction,type,
hF_Mir199975595nction: hF_Mirabelle_hf > $o ).
thf(tp_hF_Mir434065167lation,type,
hF_Mir434065167lation: hF_Mirabelle_hf > $o ).
thf(tp_hF_Mir818139703ollect,type,
hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
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_HInter,type,
hF_Mirabelle_HInter: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_HUnion,type,
hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_RepFun,type,
hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_Rep_hf,type,
hF_Mirabelle_Rep_hf: hF_Mirabelle_hf > nat ).
thf(tp_hF_Mirabelle_Replace,type,
hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hcard,type,
hF_Mirabelle_hcard: hF_Mirabelle_hf > nat ).
thf(tp_hF_Mirabelle_hfset,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hfst,type,
hF_Mirabelle_hfst: hF_Mirabelle_hf > 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_hF_Mirabelle_hpair,type,
hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_hF_Mirabelle_hsnd,type,
hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_inf_in307783154e_hf_o,type,
inf_in307783154e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
thf(tp_inf_in923488851lle_hf,type,
inf_in923488851lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_inf_in956532509lle_hf,type,
inf_in956532509lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_inf_inf_nat_o,type,
inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(tp_inf_inf_set_nat,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
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_member1367349282lle_hf,type,
member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_r,type,
r: hF_Mirabelle_hf ).
thf(tp_sK1_SY22,type,
sK1_SY22: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK2_SY27,type,
sK2_SY27: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK3_SY29,type,
sK3_SY29: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK4_SY25,type,
sK4_SY25: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK5_SY36,type,
sK5_SY36: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK6_SY25,type,
sK6_SY25: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sK7_SY44,type,
sK7_SY44: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_sup_su1199008216e_hf_o,type,
sup_su1199008216e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
thf(tp_sup_su1790843629lle_hf,type,
sup_su1790843629lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(tp_sup_su638957495lle_hf,type,
sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(tp_sup_sup_nat_o,type,
sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(tp_sup_sup_set_nat,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(tp_top_to22270292e_hf_o,type,
top_to22270292e_hf_o: hF_Mirabelle_hf > $o ).
thf(tp_top_to489427057lle_hf,type,
top_to489427057lle_hf: set_HF_Mirabelle_hf ).
thf(tp_top_top_nat_o,type,
top_top_nat_o: nat > $o ).
thf(tp_top_top_o,type,
top_top_o: $o ).
thf(tp_top_top_set_nat,type,
top_top_set_nat: set_nat ).
thf(tp_type_d1794767497hf_nat,type,
type_d1794767497hf_nat: ( hF_Mirabelle_hf > nat ) > ( nat > hF_Mirabelle_hf ) > set_nat > $o ).
thf(tp_x,type,
x: 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(352,axiom,
! [Z: hF_Mirabelle_hf,R: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ Z @ ( hF_Mir1653039215strict @ R @ A ) )
= ( ( hF_Mirabelle_hmem @ Z @ R )
& ? [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( Z
= ( hF_Mirabelle_hpair @ X2 @ Y ) )
& ( hF_Mirabelle_hmem @ X2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hrestrict__iff) ).
thf(353,axiom,
( hF_Mir199975595nction
= ( ^ [R2: hF_Mirabelle_hf] :
! [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y ) @ R2 )
=> ! [Y2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y2 ) @ R2 )
=> ( Y = Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hfunction__def) ).
thf(354,axiom,
! [R: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ R @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hrelation__restr) ).
thf(355,axiom,
hF_Mir199975595nction @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(356,conjecture,
hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(357,negated_conjecture,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
= $false ),
inference(negate_conjecture,[status(cth)],[356]) ).
thf(358,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
= $false ),
inference(unfold_def,[status(thm)],[357]) ).
thf(359,plain,
( ( ! [Z: hF_Mirabelle_hf,R: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ Z @ ( hF_Mir1653039215strict @ R @ A ) )
= ( ( hF_Mirabelle_hmem @ Z @ R )
& ? [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( Z
= ( hF_Mirabelle_hpair @ X2 @ Y ) )
& ( hF_Mirabelle_hmem @ X2 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(360,plain,
( ( hF_Mir199975595nction
= ( ^ [R2: hF_Mirabelle_hf] :
! [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y ) @ R2 )
=> ! [Y2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y2 ) @ R2 )
=> ( Y = Y2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(361,plain,
( ( ! [R: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ R @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(362,plain,
( ( hF_Mir199975595nction @ r )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(363,plain,
( ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[358]) ).
thf(364,plain,
( ( hF_Mir199975595nction @ r )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(365,plain,
( ( ! [R: hF_Mirabelle_hf,X: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ R @ X ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(366,plain,
( ( hF_Mir199975595nction
= ( ^ [R2: hF_Mirabelle_hf] :
! [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y ) @ R2 )
=> ! [Y2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X2 @ Y2 ) @ R2 )
=> ( Y = Y2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(367,plain,
( ( ! [Z: hF_Mirabelle_hf,R: hF_Mirabelle_hf,A: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ Z @ ( hF_Mir1653039215strict @ R @ A ) )
= ( ( hF_Mirabelle_hmem @ Z @ R )
& ? [X2: hF_Mirabelle_hf,Y: hF_Mirabelle_hf] :
( ( Z
= ( hF_Mirabelle_hpair @ X2 @ Y ) )
& ( hF_Mirabelle_hmem @ X2 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(368,plain,
( ( ~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(369,plain,
( ( ! [SX0: hF_Mirabelle_hf,SX1: hF_Mirabelle_hf,SX2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SX0 @ ( hF_Mir1653039215strict @ SX1 @ SX2 ) )
= ( ~ ( ~ ( hF_Mirabelle_hmem @ SX0 @ SX1 )
| ~ ~ ! [SX3: hF_Mirabelle_hf] :
~ ~ ! [SX4: hF_Mirabelle_hf] :
~ ~ ( ( SX0
!= ( hF_Mirabelle_hpair @ SX3 @ SX4 ) )
| ~ ( hF_Mirabelle_hmem @ SX3 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(370,plain,
( ( hF_Mir199975595nction
= ( ^ [SX0: hF_Mirabelle_hf] :
! [SX1: hF_Mirabelle_hf,SX2: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SX1 @ SX2 ) @ SX0 )
| ! [SX3: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(371,plain,
! [SV1: hF_Mirabelle_hf] :
( ( ! [SY11: hF_Mirabelle_hf] : ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ SV1 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(372,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(373,plain,
! [SV2: hF_Mirabelle_hf] :
( ( ! [SY12: hF_Mirabelle_hf,SY13: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SY12 @ SY13 ) )
= ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SY12 )
| ~ ~ ! [SY14: hF_Mirabelle_hf] :
~ ~ ! [SY15: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY14 @ SY15 ) )
| ~ ( hF_Mirabelle_hmem @ SY14 @ SY13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(374,plain,
( ( ! [SV3: hF_Mirabelle_hf] :
( ( hF_Mir199975595nction @ SV3 )
= ( ! [SY16: hF_Mirabelle_hf,SY17: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY16 @ SY17 ) @ SV3 )
| ! [SY18: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY16 @ SY18 ) @ SV3 )
| ( SY17 = SY18 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[370]) ).
thf(375,plain,
( ( hF_Mir199975595nction
= ( ^ [SX0: hF_Mirabelle_hf] :
! [SX1: hF_Mirabelle_hf,SX2: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SX1 @ SX2 ) @ SX0 )
| ! [SX3: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[370]) ).
thf(376,plain,
! [SV4: hF_Mirabelle_hf,SV1: hF_Mirabelle_hf] :
( ( hF_Mir434065167lation @ ( hF_Mir1653039215strict @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(377,plain,
! [SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ! [SY19: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SY19 ) )
= ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY14: hF_Mirabelle_hf] :
~ ~ ! [SY15: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY14 @ SY15 ) )
| ~ ( hF_Mirabelle_hmem @ SY14 @ SY19 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(378,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(379,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(380,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ~ ( ( hF_Mir199975595nction @ SV6 )
| ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
| ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[378]) ).
thf(381,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[378]) ).
thf(382,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ~ ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[379]) ).
thf(383,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[379]) ).
thf(384,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mir199975595nction @ SV6 )
| ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(385,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(386,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ( hF_Mir199975595nction @ SV6 )
| ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(387,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(388,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(389,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(390,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(391,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(392,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(393,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY27: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ SY27 ) @ SV6 )
| ! [SY28: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ SY28 ) @ SV6 )
| ( SY27 = SY28 ) ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[389]) ).
thf(394,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(395,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(396,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 ) )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(397,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(398,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
| ! [SY29: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ SY29 ) @ SV6 )
| ( ( sK2_SY27 @ SV6 )
= SY29 ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[393]) ).
thf(399,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(400,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(401,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(402,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(403,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(404,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(405,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY29: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ SY29 ) @ SV6 )
| ( ( sK2_SY27 @ SV6 )
= SY29 ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(406,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(407,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(408,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(409,plain,
! [SV6: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ! [SY30: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SY30 ) @ SV6 )
| ! [SY31: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SY31 ) @ SV6 )
| ( SY30 = SY31 ) ) ) )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(410,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(411,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
| ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[405]) ).
thf(412,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(413,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(414,plain,
! [SV6: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 )
| ! [SY32: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SY32 ) @ SV6 )
| ( SV9 = SY32 ) ) )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(415,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(416,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(417,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(418,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(419,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(420,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(421,plain,
! [SV6: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 ) )
= $true )
| ( ( ! [SY32: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SY32 ) @ SV6 )
| ( SV9 = SY32 ) ) )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(422,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(423,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(424,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true )
| ( ( ~ ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(425,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(426,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(427,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(428,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ! [SY33: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SY33 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(429,plain,
! [SV6: hF_Mirabelle_hf,SV9: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 )
= $false )
| ( ( ! [SY32: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SY32 ) @ SV6 )
| ( SV9 = SY32 ) ) )
= $true )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(431,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(432,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 )
| ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(433,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 ) )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(434,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(435,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(436,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY33: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SY33 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(437,plain,
! [SV9: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV11: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV11 ) @ SV6 )
| ( SV9 = SV11 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(438,plain,
! [SV6: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( ! [SY34: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SY34 ) @ SV6 )
| ! [SY35: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SY35 ) @ SV6 )
| ( SY34 = SY35 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(439,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mir199975595nction @ SV6 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(440,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ~ ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(441,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(442,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(443,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ! [SY36: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SY36 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[435]) ).
thf(444,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY33: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SY33 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(445,plain,
! [SV9: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV11: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV11 ) @ SV6 ) )
= $true )
| ( ( SV9 = SV11 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(446,plain,
! [SV6: hF_Mirabelle_hf,SV13: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 )
| ! [SY37: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SY37 ) @ SV6 )
| ( SV13 = SY37 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(447,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( hF_Mir199975595nction @ SV6 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(448,plain,
! [SV6: hF_Mirabelle_hf] :
( ( ( ! [SY22: hF_Mirabelle_hf,SY23: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY23 ) @ SV6 )
| ! [SY24: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SY22 @ SY24 ) @ SV6 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(449,plain,
! [SV6: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ! [SY38: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SY38 ) @ SV6 )
| ! [SY39: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SY39 ) @ SV6 )
| ( SY38 = SY39 ) ) ) )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(450,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY36: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SY36 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(451,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(452,plain,
! [SV9: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV11: hF_Mirabelle_hf,SV8: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV11 ) @ SV6 )
= $false )
| ( ( SV9 = SV11 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV8 @ SV9 ) @ SV6 )
= $false )
| ( ( hF_Mir199975595nction @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(453,plain,
! [SV6: hF_Mirabelle_hf,SV13: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 ) )
= $true )
| ( ( ! [SY37: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SY37 ) @ SV6 )
| ( SV13 = SY37 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(454,plain,
! [SV6: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( ! [SY40: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SY40 ) @ SV6 )
| ! [SY41: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SY41 ) @ SV6 )
| ( SY40 = SY41 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(455,plain,
! [SV6: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 )
| ! [SY42: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SY42 ) @ SV6 )
| ( SV17 = SY42 ) ) )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(456,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY36: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SY36 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV6: hF_Mirabelle_hf,SV13: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 )
= $false )
| ( ( ! [SY37: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SY37 ) @ SV6 )
| ( SV13 = SY37 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(459,plain,
! [SV6: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 )
| ! [SY43: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SY43 ) @ SV6 )
| ( SV18 = SY43 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(460,plain,
! [SV6: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 ) )
= $true )
| ( ( ! [SY42: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SY42 ) @ SV6 )
| ( SV17 = SY42 ) ) )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(461,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ ( sK5_SY36 @ SV7 @ SV5 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[456]) ).
thf(462,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
| ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(463,plain,
! [SV13: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV19 ) @ SV6 )
| ( SV13 = SV19 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(464,plain,
! [SV6: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 ) )
= $true )
| ( ( ! [SY43: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SY43 ) @ SV6 )
| ( SV18 = SY43 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(465,plain,
! [SV6: hF_Mirabelle_hf,SV17: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 )
= $false )
| ( ( ! [SY42: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SY42 ) @ SV6 )
| ( SV17 = SY42 ) ) )
= $true )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(466,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ ( sK5_SY36 @ SV7 @ SV5 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(467,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
!= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(468,plain,
! [SV13: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV19 ) @ SV6 ) )
= $true )
| ( ( SV13 = SV19 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(469,plain,
! [SV6: hF_Mirabelle_hf,SV18: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 )
= $false )
| ( ( ! [SY43: hF_Mirabelle_hf] :
( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SY43 ) @ SV6 )
| ( SV18 = SY43 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(470,plain,
! [SV17: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV20 ) @ SV6 )
| ( SV17 = SV20 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(471,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ ( sK5_SY36 @ SV7 @ SV5 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(472,plain,
! [SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( ~ ( hF_Mirabelle_hmem @ SV10 @ SV7 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(473,plain,
! [SV13: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV19: hF_Mirabelle_hf,SV12: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV19 ) @ SV6 )
= $false )
| ( ( SV13 = SV19 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV12 @ SV13 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK2_SY27 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(474,plain,
! [SV18: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV21: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV21 ) @ SV6 )
| ( SV18 = SV21 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(475,plain,
! [SV17: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV20 ) @ SV6 ) )
= $true )
| ( ( SV17 = SV20 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(476,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ ( sK5_SY36 @ SV7 @ SV5 @ SV2 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(477,plain,
! [SV2: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(478,plain,
! [SV5: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(479,plain,
! [SV18: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV21: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV21 ) @ SV6 ) )
= $true )
| ( ( SV18 = SV21 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(480,plain,
! [SV17: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV20: hF_Mirabelle_hf,SV14: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV20 ) @ SV6 )
= $false )
| ( ( SV17 = SV20 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV14 @ SV17 ) @ SV6 )
= $false )
| ( ( ( sK2_SY27 @ SV6 )
= ( sK3_SY29 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(481,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
= ( hF_Mirabelle_hpair @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ ( sK5_SY36 @ SV7 @ SV5 @ SV2 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(482,plain,
! [SV2: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK4_SY25 @ SV5 @ SV7 @ SV2 ) @ SV7 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(483,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
| ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(484,plain,
! [SV18: hF_Mirabelle_hf,SV6: hF_Mirabelle_hf,SV21: hF_Mirabelle_hf,SV16: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV21 ) @ SV6 )
= $false )
| ( ( SV18 = SV21 )
= $true )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ SV16 @ SV18 ) @ SV6 )
= $false )
| ( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ ( sK1_SY22 @ SV6 ) @ ( sK3_SY29 @ SV6 ) ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(485,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(486,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(487,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ ( hF_Mir1653039215strict @ SV5 @ SV7 ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(488,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(489,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 )
| ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(490,plain,
! [SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ SV2 @ SV5 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(491,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(492,plain,
! [SV7: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(493,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(494,plain,
! [SV15: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY25: hF_Mirabelle_hf] :
~ ~ ! [SY26: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ SY25 @ SY26 ) )
| ~ ( hF_Mirabelle_hmem @ SY25 @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(495,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ! [SY44: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SY44 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[494]) ).
thf(496,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ! [SY44: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SY44 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(497,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ! [SY44: hF_Mirabelle_hf] :
~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SY44 ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(498,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ ( sK7_SY44 @ SV7 @ SV5 @ SV10 @ SV15 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[497]) ).
thf(499,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ~ ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ ( sK7_SY44 @ SV7 @ SV5 @ SV10 @ SV15 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(500,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ ( sK7_SY44 @ SV7 @ SV5 @ SV10 @ SV15 @ SV2 ) ) )
| ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(501,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
!= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ ( sK7_SY44 @ SV7 @ SV5 @ SV10 @ SV15 @ SV2 ) ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(502,plain,
! [SV2: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf] :
( ( ( ~ ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(503,plain,
! [SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf,SV2: hF_Mirabelle_hf] :
( ( ( SV2
= ( hF_Mirabelle_hpair @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ ( sK7_SY44 @ SV7 @ SV5 @ SV10 @ SV15 @ SV2 ) ) )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(504,plain,
! [SV2: hF_Mirabelle_hf,SV7: hF_Mirabelle_hf,SV5: hF_Mirabelle_hf,SV10: hF_Mirabelle_hf,SV15: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ ( sK6_SY25 @ SV15 @ SV10 @ SV5 @ SV7 @ SV2 ) @ SV7 )
= $true )
| ( ( hF_Mirabelle_hmem @ SV2 @ SV5 )
= $false )
| ( ( SV2
= ( hF_Mirabelle_hpair @ SV10 @ SV15 ) )
= $false )
| ( ( hF_Mirabelle_hmem @ SV10 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(505,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[364,504,503,492,487,484,482,481,480,473,452,447,441,430,426,406,402,383,381,376,375,372]) ).
thf(506,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP076^1 : 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
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 11:19:12 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.64/0.54 ..
% 1.64/0.54
% 1.64/0.54 No.of.Axioms: 4
% 1.64/0.54
% 1.64/0.54 Length.of.Defs: 0
% 1.64/0.54
% 1.64/0.54 Contains.Choice.Funs: false
% 1.64/0.54 .......
% 1.64/0.54
% 1.64/0.54 ********************************
% 1.64/0.54 * All subproblems solved! *
% 1.64/0.54 ********************************
% 1.64/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:505,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.64/0.54
% 1.64/0.54 %**** Beginning of derivation protocol ****
% 1.64/0.54 % SZS output start CNFRefutation
% See solution above
% 1.64/0.54
% 1.64/0.54 %**** End of derivation protocol ****
% 1.64/0.54 %**** no. of clauses in derivation: 155 ****
% 1.64/0.54 %**** clause counter: 505 ****
% 1.64/0.54
% 1.64/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:505,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------