%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% 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 : n007.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 10:36:09 AM UTC 2026
% Result : Theorem 154.63s 26.14s
% Output : CNFRefutation 154.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 31
% Syntax : Number of formulae : 304 ( 122 unt; 0 typ; 25 def)
% Number of atoms : 2051 ( 592 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 7084 ( 932 ~; 510 |; 14 &;5564 @)
% ( 4 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 929 ( 929 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 6 con; 0-3 aty)
% Number of variables : 2855 (2236 ^; 612 !; 7 ?;2855 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_essence,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(tp_god,type,
god: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $o ) > $i > $o ).
thf(tp_mbox_generic,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia,type,
mdia: ( $i > $o ) > $i > $o ).
thf(tp_mdia_generic,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_indset,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_indset,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_necessary_existence,type,
necessary_existence: mu > $i > $o ).
thf(tp_positive,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(tp_rel,type,
rel: $i > $i > $o ).
thf(tp_sK10_SY391,type,
sK10_SY391: $i > ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(tp_sK11_E,type,
sK11_E: ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(tp_sK12_E,type,
sK12_E: ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > mu > $i > $o ) > mu ).
thf(tp_sK14_E,type,
sK14_E: ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > mu > $i > $o ) > $i ).
thf(tp_sK15_E,type,
sK15_E: ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(tp_sK16_E,type,
sK16_E: ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > $i ).
thf(tp_sK17_E,type,
sK17_E: ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > mu > $i > $o ) > mu ).
thf(tp_sK18_E,type,
sK18_E: ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > mu > $i > $o ) > $i ).
thf(tp_sK1_SY97,type,
sK1_SY97: $i ).
thf(tp_sK2_SY307,type,
sK2_SY307: mu ).
thf(tp_sK3_SX0,type,
sK3_SX0: mu > $i > $o ).
thf(tp_sK4_SY350,type,
sK4_SY350: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(tp_sK5_SY352,type,
sK5_SY352: $i > ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).
thf(tp_sK6_SX0,type,
sK6_SX0: mu > $i > $o ).
thf(tp_sK7_SY380,type,
sK7_SY380: $i ).
thf(tp_sK8_SY388,type,
sK8_SY388: mu ).
thf(tp_sK9_SY386,type,
sK9_SY386: ( mu > $i > $o ) > ( mu > $i > $o ) > $i > $i ).
thf(essence,definition,
( essence
= ( ^ [Phi: mu > $i > $o,X: mu] :
( mand @ ( Phi @ X )
@ ( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies @ ( Psi @ X )
@ ( mbox
@ ( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( Phi @ Y ) @ ( Psi @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD2) ).
thf(god,definition,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD1) ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
& ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_generic,definition,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_generic) ).
thf(mdia,definition,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_generic,definition,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( R @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_generic) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_ind) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_indset,definition,
( mexists_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
? [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_indset) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
? [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( ^ [W: $i] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_indset,definition,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_indset) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Psi @ W )
=> ( Phi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( ( Phi @ W )
& ~ ( Psi @ W ) )
| ( ~ ( Phi @ W )
& ( Psi @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(necessary_existence,definition,
( necessary_existence
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( essence @ Phi @ X )
@ ( mbox
@ ( mexists_ind
@ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD3) ).
thf(1,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5) ).
thf(2,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( mbox @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA4) ).
thf(3,axiom,
mvalid @ ( positive @ god ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA3) ).
thf(4,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Phi )
@ ( mbox
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) )
@ ( positive @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA2) ).
thf(5,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
@ ( mnot @ ( positive @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1) ).
thf(6,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT2) ).
thf(7,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [SY97: $i,SY98: mu] :
( ! [SY99: mu > $i > $o] :
( ( positive @ SY99 @ SY97 )
=> ( SY99 @ SY98 @ SY97 ) )
=> ( ! [SY100: mu > $i > $o] :
( ( positive @ SY100 @ SY97 )
=> ( SY100 @ SY98 @ SY97 ) )
& ! [SY101: mu > $i > $o] :
( ( SY101 @ SY98 @ SY97 )
=> ! [SY102: $i] :
( ~ ( rel @ SY97 @ SY102 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY102 )
=> ( SY56 @ SY55 @ SY102 ) )
=> ( SY101 @ SY55 @ SY102 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(9,plain,
( ( ! [SY114: $i] :
( positive
@ ^ [SY115: mu,SY166: $i] :
! [SY167: mu > $i > $o] :
( ( ( SY167 @ SY115 @ SY166 )
& ! [SY182: mu > $i > $o] :
( ( SY182 @ SY115 @ SY166 )
=> ! [SY183: $i] :
( ~ ( rel @ SY166 @ SY183 )
| ! [SY171: mu] :
( ( SY167 @ SY171 @ SY183 )
=> ( SY182 @ SY171 @ SY183 ) ) ) ) )
=> ! [SY185: $i] :
( ~ ( rel @ SY166 @ SY185 )
| ? [SY179: mu] : ( SY167 @ SY179 @ SY185 ) ) )
@ SY114 ) )
= $true ),
inference(unfold_def,[status(thm)],[1,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(10,plain,
( ( ! [SY210: $i,SY211: mu > $i > $o] :
( ( positive @ SY211 @ SY210 )
=> ! [SY212: $i] :
( ~ ( rel @ SY210 @ SY212 )
| ( positive @ SY211 @ SY212 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(11,plain,
( ( ! [SY217: $i] :
( positive
@ ^ [SY218: mu,SY223: $i] :
! [SY224: mu > $i > $o] :
( ( positive @ SY224 @ SY223 )
=> ( SY224 @ SY218 @ SY223 ) )
@ SY217 ) )
= $true ),
inference(unfold_def,[status(thm)],[3,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(12,plain,
( ( ! [SY273: $i,SY274: mu > $i > $o,SY275: mu > $i > $o] :
( ( ( positive @ SY274 @ SY273 )
& ! [SY276: $i] :
( ~ ( rel @ SY273 @ SY276 )
| ! [SY269: mu] :
( ( SY274 @ SY269 @ SY276 )
=> ( SY275 @ SY269 @ SY276 ) ) ) )
=> ( positive @ SY275 @ SY273 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(13,plain,
( ( ! [SY299: $i,SY300: mu > $i > $o] :
( ( positive
@ ^ [SY295: mu,SY296: $i] :
~ ( SY300 @ SY295 @ SY296 )
@ SY299 )
<=> ~ ( positive @ SY300 @ SY299 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(14,plain,
( ( ! [SY307: mu] :
( ! [SY308: mu > $i > $o] :
( ( positive @ SY308 @ sK1_SY97 )
=> ( SY308 @ SY307 @ sK1_SY97 ) )
=> ( ! [SY309: mu > $i > $o] :
( ( positive @ SY309 @ sK1_SY97 )
=> ( SY309 @ SY307 @ sK1_SY97 ) )
& ! [SY310: mu > $i > $o] :
( ( SY310 @ SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY310 @ SY55 @ SY311 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY314: mu > $i > $o] :
( ( positive @ SY314 @ sK1_SY97 )
=> ( SY314 @ sK2_SY307 @ sK1_SY97 ) )
=> ( ! [SY315: mu > $i > $o] :
( ( positive @ SY315 @ sK1_SY97 )
=> ( SY315 @ sK2_SY307 @ sK1_SY97 ) )
& ! [SY316: mu > $i > $o] :
( ( SY316 @ sK2_SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY316 @ SY55 @ SY311 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY314: mu > $i > $o] :
( ( positive @ SY314 @ sK1_SY97 )
=> ( SY314 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [SY315: mu > $i > $o] :
( ( positive @ SY315 @ sK1_SY97 )
=> ( SY315 @ sK2_SY307 @ sK1_SY97 ) )
& ! [SY316: mu > $i > $o] :
( ( SY316 @ sK2_SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY316 @ SY55 @ SY311 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY315: mu > $i > $o] :
( ( positive @ SY315 @ sK1_SY97 )
=> ( SY315 @ sK2_SY307 @ sK1_SY97 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[17]) ).
thf(19,plain,
( ( ! [SY316: mu > $i > $o] :
( ( SY316 @ sK2_SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY316 @ SY55 @ SY311 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[17]) ).
thf(20,plain,
( ( ~ ! [SY315: mu > $i > $o] :
( ( positive @ SY315 @ sK1_SY97 )
=> ( SY315 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ! [SY316: mu > $i > $o] :
( ( SY316 @ sK2_SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY316 @ SY55 @ SY311 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(22,plain,
( ( ! [SY299: $i,SY300: mu > $i > $o] :
( ( positive
@ ^ [SY295: mu,SY296: $i] :
~ ( SY300 @ SY295 @ SY296 )
@ SY299 )
<=> ~ ( positive @ SY300 @ SY299 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(23,plain,
( ( ! [SY273: $i,SY274: mu > $i > $o,SY275: mu > $i > $o] :
( ( ( positive @ SY274 @ SY273 )
& ! [SY276: $i] :
( ~ ( rel @ SY273 @ SY276 )
| ! [SY269: mu] :
( ( SY274 @ SY269 @ SY276 )
=> ( SY275 @ SY269 @ SY276 ) ) ) )
=> ( positive @ SY275 @ SY273 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(24,plain,
( ( ! [SY217: $i] :
( positive
@ ^ [SY218: mu,SY223: $i] :
! [SY224: mu > $i > $o] :
( ( positive @ SY224 @ SY223 )
=> ( SY224 @ SY218 @ SY223 ) )
@ SY217 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(25,plain,
( ( ! [SY210: $i,SY211: mu > $i > $o] :
( ( positive @ SY211 @ SY210 )
=> ! [SY212: $i] :
( ~ ( rel @ SY210 @ SY212 )
| ( positive @ SY211 @ SY212 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [SY114: $i] :
( positive
@ ^ [SY115: mu,SY166: $i] :
! [SY167: mu > $i > $o] :
( ( ( SY167 @ SY115 @ SY166 )
& ! [SY182: mu > $i > $o] :
( ( SY182 @ SY115 @ SY166 )
=> ! [SY183: $i] :
( ~ ( rel @ SY166 @ SY183 )
| ! [SY171: mu] :
( ( SY167 @ SY171 @ SY183 )
=> ( SY182 @ SY171 @ SY183 ) ) ) ) )
=> ! [SY185: $i] :
( ~ ( rel @ SY166 @ SY185 )
| ? [SY179: mu] : ( SY167 @ SY179 @ SY185 ) ) )
@ SY114 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [SY314: mu > $i > $o] :
( ( positive @ SY314 @ sK1_SY97 )
=> ( SY314 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(28,plain,
( ( ~ ! [SY315: mu > $i > $o] :
( ( positive @ SY315 @ sK1_SY97 )
=> ( SY315 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[26,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(30,plain,
( ( ! [SX0: mu > $i > $o] :
( ~ ( positive @ SX0 @ sK1_SY97 )
| ( SX0 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(31,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[24,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel @ SX0 @ SX2 )
| ( positive @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(33,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o,SX2: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
( ~ ( rel @ SX0 @ SX3 )
| ! [SX4: mu] :
( ~ ( SX1 @ SX4 @ SX3 )
| ( SX2 @ SX4 @ SX3 ) ) ) )
| ( positive @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(34,plain,
( ( ~ ! [SX0: mu > $i > $o] :
( ~ ( positive @ SX0 @ sK1_SY97 )
| ( SX0 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(35,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(36,plain,
! [SV1: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV2: mu > $i > $o] :
( ( ~ ( positive @ SV2 @ sK1_SY97 )
| ( SV2 @ sK2_SY307 @ sK1_SY97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV3: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV4: $i] :
( ( ! [SY331: mu > $i > $o] :
( ~ ( positive @ SY331 @ SV4 )
| ! [SY332: $i] :
( ~ ( rel @ SV4 @ SY332 )
| ( positive @ SY331 @ SY332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV5: $i] :
( ( ! [SY333: mu > $i > $o,SY334: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SY333 @ SV5 )
| ~ ! [SY335: $i] :
( ~ ( rel @ SV5 @ SY335 )
| ! [SX4: mu] :
( ~ ( SY333 @ SX4 @ SY335 )
| ( SY334 @ SX4 @ SY335 ) ) ) )
| ( positive @ SY334 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [SX0: mu > $i > $o] :
( ~ ( positive @ SX0 @ sK1_SY97 )
| ( SX0 @ sK2_SY307 @ sK1_SY97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV6: $i] :
( ( ! [SY337: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY337 @ SX2 @ SX3 )
@ SV6 )
| ~ ( positive @ SY337 @ SV6 ) )
| ~ ( ~ ~ ( positive @ SY337 @ SV6 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY337 @ SX2 @ SX3 )
@ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV2: mu > $i > $o] :
( ( ( ~ ( positive @ SV2 @ sK1_SY97 ) )
= $true )
| ( ( SV2 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ~ ( positive @ SV7 @ SV4 )
| ! [SY342: $i] :
( ~ ( rel @ SV4 @ SY342 )
| ( positive @ SV7 @ SY342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV5: $i,SV8: mu > $i > $o] :
( ( ! [SY343: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SV8 @ SV5 )
| ~ ! [SY344: $i] :
( ~ ( rel @ SV5 @ SY344 )
| ! [SY345: mu] :
( ~ ( SV8 @ SY345 @ SY344 )
| ( SY343 @ SY345 @ SY344 ) ) ) )
| ( positive @ SY343 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
( ( ~ ( positive @ sK3_SX0 @ sK1_SY97 )
| ( sK3_SX0 @ sK2_SY307 @ sK1_SY97 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(47,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ( ~ ( ~ ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
| ~ ( positive @ SV9 @ SV6 ) )
| ~ ( ~ ~ ( positive @ SV9 @ SV6 )
| ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: mu > $i > $o] :
( ( ( positive @ SV2 @ sK1_SY97 )
= $false )
| ( ( SV2 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( ~ ( positive @ SV7 @ SV4 ) )
= $true )
| ( ( ! [SY342: $i] :
( ~ ( rel @ SV4 @ SY342 )
| ( positive @ SV7 @ SY342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ~ ~ ( ~ ( positive @ SV8 @ SV5 )
| ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) )
| ( positive @ SV10 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
( ( ~ ( positive @ sK3_SX0 @ sK1_SY97 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
( ( sK3_SX0 @ sK2_SY307 @ sK1_SY97 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
| ~ ( positive @ SV9 @ SV6 ) )
| ~ ( ~ ~ ( positive @ SV9 @ SV6 )
| ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV4: $i,SV7: mu > $i > $o] :
( ( ( positive @ SV7 @ SV4 )
= $false )
| ( ( ! [SY342: $i] :
( ~ ( rel @ SV4 @ SY342 )
| ( positive @ SV7 @ SY342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ~ ( ~ ( positive @ SV8 @ SV5 )
| ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) ) )
= $true )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( positive @ sK3_SX0 @ sK1_SY97 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
| ~ ( positive @ SV9 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ( ~ ~ ( positive @ SV9 @ SV6 )
| ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV7: mu > $i > $o,SV11: $i,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ SV11 )
| ( positive @ SV7 @ SV11 ) )
= $true )
| ( ( positive @ SV7 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ( ~ ( positive @ SV8 @ SV5 )
| ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) ) )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
| ~ ( positive @ SV9 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ~ ~ ( positive @ SV9 @ SV6 )
| ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: mu > $i > $o,SV11: $i,SV4: $i] :
( ( ( ~ ( rel @ SV4 @ SV11 ) )
= $true )
| ( ( positive @ SV7 @ SV11 )
= $true )
| ( ( positive @ SV7 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ( positive @ SV8 @ SV5 )
| ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) )
= $true )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 ) )
= $true )
| ( ( ~ ( positive @ SV9 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( ~ ~ ( positive @ SV9 @ SV6 ) )
= $true )
| ( ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV7: mu > $i > $o,SV11: $i,SV4: $i] :
( ( ( rel @ SV4 @ SV11 )
= $false )
| ( ( positive @ SV7 @ SV11 )
= $true )
| ( ( positive @ SV7 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ( positive @ SV8 @ SV5 ) )
= $true )
| ( ( ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) )
= $true )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
= $false )
| ( ( ~ ( positive @ SV9 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( ~ ( positive @ SV9 @ SV6 ) )
= $false )
| ( ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( ~ ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) )
= $true )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( positive @ SV9 @ SV6 )
= $false )
| ( ( positive
@ ^ [SY346: mu,SY347: $i] :
~ ( SV9 @ SY346 @ SY347 )
@ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV6: $i,SV9: mu > $i > $o] :
( ( ( positive @ SV9 @ SV6 )
= $true )
| ( ( positive
@ ^ [SY348: mu,SY349: $i] :
~ ( SV9 @ SY348 @ SY349 )
@ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV10: mu > $i > $o,SV8: mu > $i > $o,SV5: $i] :
( ( ( ! [SY350: $i] :
( ~ ( rel @ SV5 @ SY350 )
| ! [SY351: mu] :
( ~ ( SV8 @ SY351 @ SY350 )
| ( SV10 @ SY351 @ SY350 ) ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV8: mu > $i > $o,SV10: mu > $i > $o,SV5: $i] :
( ( ( ~ ( rel @ SV5 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
| ! [SY352: mu] :
( ~ ( SV8 @ SY352 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
| ( SV10 @ SY352 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(76,plain,
! [SV8: mu > $i > $o,SV10: mu > $i > $o,SV5: $i] :
( ( ( ~ ( rel @ SV5 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(77,plain,
! [SV5: $i,SV10: mu > $i > $o,SV8: mu > $i > $o] :
( ( ( ! [SY352: mu] :
( ~ ( SV8 @ SY352 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
| ( SV10 @ SY352 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(78,plain,
! [SV8: mu > $i > $o,SV10: mu > $i > $o,SV5: $i] :
( ( ( rel @ SV5 @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
= $true )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ( SV8 @ ( sK5_SY352 @ SV5 @ SV10 @ SV8 ) @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
| ( SV10 @ ( sK5_SY352 @ SV5 @ SV10 @ SV8 ) @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(80,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( ~ ( SV8 @ ( sK5_SY352 @ SV5 @ SV10 @ SV8 ) @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(81,plain,
! [SV8: mu > $i > $o,SV5: $i,SV10: mu > $i > $o] :
( ( ( SV10 @ ( sK5_SY352 @ SV5 @ SV10 @ SV8 ) @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
= $false )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(82,plain,
! [SV10: mu > $i > $o,SV5: $i,SV8: mu > $i > $o] :
( ( ( SV8 @ ( sK5_SY352 @ SV5 @ SV10 @ SV8 ) @ ( sK4_SY350 @ SV10 @ SV8 @ SV5 ) )
= $true )
| ( ( positive @ SV8 @ SV5 )
= $false )
| ( ( positive @ SV10 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(83,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,82,81,78,73,72,67,56,52,48,38]) ).
thf(84,plain,
( ( ! [SY299: $i,SY300: mu > $i > $o] :
( ( positive
@ ^ [SY295: mu,SY296: $i] :
~ ( SY300 @ SY295 @ SY296 )
@ SY299 )
<=> ~ ( positive @ SY300 @ SY299 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(85,plain,
( ( ! [SY273: $i,SY274: mu > $i > $o,SY275: mu > $i > $o] :
( ( ( positive @ SY274 @ SY273 )
& ! [SY276: $i] :
( ~ ( rel @ SY273 @ SY276 )
| ! [SY269: mu] :
( ( SY274 @ SY269 @ SY276 )
=> ( SY275 @ SY269 @ SY276 ) ) ) )
=> ( positive @ SY275 @ SY273 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(86,plain,
( ( ! [SY217: $i] :
( positive
@ ^ [SY218: mu,SY223: $i] :
! [SY224: mu > $i > $o] :
( ( positive @ SY224 @ SY223 )
=> ( SY224 @ SY218 @ SY223 ) )
@ SY217 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(87,plain,
( ( ! [SY210: $i,SY211: mu > $i > $o] :
( ( positive @ SY211 @ SY210 )
=> ! [SY212: $i] :
( ~ ( rel @ SY210 @ SY212 )
| ( positive @ SY211 @ SY212 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(88,plain,
( ( ! [SY114: $i] :
( positive
@ ^ [SY115: mu,SY166: $i] :
! [SY167: mu > $i > $o] :
( ( ( SY167 @ SY115 @ SY166 )
& ! [SY182: mu > $i > $o] :
( ( SY182 @ SY115 @ SY166 )
=> ! [SY183: $i] :
( ~ ( rel @ SY166 @ SY183 )
| ! [SY171: mu] :
( ( SY167 @ SY171 @ SY183 )
=> ( SY182 @ SY171 @ SY183 ) ) ) ) )
=> ! [SY185: $i] :
( ~ ( rel @ SY166 @ SY185 )
| ? [SY179: mu] : ( SY167 @ SY179 @ SY185 ) ) )
@ SY114 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(89,plain,
( ( ! [SY314: mu > $i > $o] :
( ( positive @ SY314 @ sK1_SY97 )
=> ( SY314 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(90,plain,
( ( ~ ! [SY316: mu > $i > $o] :
( ( SY316 @ sK2_SY307 @ sK1_SY97 )
=> ! [SY311: $i] :
( ~ ( rel @ sK1_SY97 @ SY311 )
| ! [SY55: mu] :
( ! [SY56: mu > $i > $o] :
( ( positive @ SY56 @ SY311 )
=> ( SY56 @ SY55 @ SY311 ) )
=> ( SY316 @ SY55 @ SY311 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[86,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[88,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 )
| ~ ( positive @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( positive @ SX1 @ SX0 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SX1 @ SX2 @ SX3 )
@ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel @ SX0 @ SX2 )
| ( positive @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(95,plain,
( ( ~ ! [SX0: mu > $i > $o] :
( ~ ( SX0 @ sK2_SY307 @ sK1_SY97 )
| ! [SX1: $i] :
( ~ ( rel @ sK1_SY97 @ SX1 )
| ! [SX2: mu] :
( ~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX1 )
| ( SX3 @ SX2 @ SX1 ) )
| ( SX0 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: mu > $i > $o,SX2: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SX1 @ SX0 )
| ~ ! [SX3: $i] :
( ~ ( rel @ SX0 @ SX3 )
| ! [SX4: mu] :
( ~ ( SX1 @ SX4 @ SX3 )
| ( SX2 @ SX4 @ SX3 ) ) ) )
| ( positive @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(97,plain,
( ( ! [SX0: mu > $i > $o] :
( ~ ( positive @ SX0 @ sK1_SY97 )
| ( SX0 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89,essence,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,mtrue,mvalid,mxor,necessary_existence]) ).
thf(98,plain,
! [SV12: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX2 )
| ( SX3 @ SX1 @ SX2 ) )
@ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV13: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ~ ( ~ ( SX3 @ SX1 @ SX2 )
| ~ ! [SX4: mu > $i > $o] :
( ~ ( SX4 @ SX1 @ SX2 )
| ! [SX5: $i] :
( ~ ( rel @ SX2 @ SX5 )
| ! [SX6: mu] :
( ~ ( SX3 @ SX6 @ SX5 )
| ( SX4 @ SX6 @ SX5 ) ) ) ) )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV14: $i] :
( ( ! [SY364: mu > $i > $o] :
~ ( ~ ( ~ ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY364 @ SX2 @ SX3 )
@ SV14 )
| ~ ( positive @ SY364 @ SV14 ) )
| ~ ( ~ ~ ( positive @ SY364 @ SV14 )
| ( positive
@ ^ [SX2: mu,SX3: $i] :
~ ( SY364 @ SX2 @ SX3 )
@ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV15: $i] :
( ( ! [SY369: mu > $i > $o] :
( ~ ( positive @ SY369 @ SV15 )
| ! [SY370: $i] :
( ~ ( rel @ SV15 @ SY370 )
| ( positive @ SY369 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
( ( ! [SX0: mu > $i > $o] :
( ~ ( SX0 @ sK2_SY307 @ sK1_SY97 )
| ! [SX1: $i] :
( ~ ( rel @ sK1_SY97 @ SX1 )
| ! [SX2: mu] :
( ~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX1 )
| ( SX3 @ SX2 @ SX1 ) )
| ( SX0 @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV16: $i] :
( ( ! [SY371: mu > $i > $o,SY372: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SY371 @ SV16 )
| ~ ! [SY373: $i] :
( ~ ( rel @ SV16 @ SY373 )
| ! [SX4: mu] :
( ~ ( SY371 @ SX4 @ SY373 )
| ( SY372 @ SX4 @ SY373 ) ) ) )
| ( positive @ SY372 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV17: mu > $i > $o] :
( ( ~ ( positive @ SV17 @ sK1_SY97 )
| ( SV17 @ sK2_SY307 @ sK1_SY97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ( ~ ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
| ~ ( positive @ SV18 @ SV14 ) )
| ~ ( ~ ~ ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV15: $i,SV19: mu > $i > $o] :
( ( ~ ( positive @ SV19 @ SV15 )
| ! [SY379: $i] :
( ~ ( rel @ SV15 @ SY379 )
| ( positive @ SV19 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(107,plain,
( ( ~ ( sK6_SX0 @ sK2_SY307 @ sK1_SY97 )
| ! [SY380: $i] :
( ~ ( rel @ sK1_SY97 @ SY380 )
| ! [SY381: mu] :
( ~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY380 )
| ( SX3 @ SY381 @ SY380 ) )
| ( sK6_SX0 @ SY381 @ SY380 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(108,plain,
! [SV16: $i,SV20: mu > $i > $o] :
( ( ! [SY383: mu > $i > $o] :
( ~ ~ ( ~ ( positive @ SV20 @ SV16 )
| ~ ! [SY384: $i] :
( ~ ( rel @ SV16 @ SY384 )
| ! [SY385: mu] :
( ~ ( SV20 @ SY385 @ SY384 )
| ( SY383 @ SY385 @ SY384 ) ) ) )
| ( positive @ SY383 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV17: mu > $i > $o] :
( ( ( ~ ( positive @ SV17 @ sK1_SY97 ) )
= $true )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
| ~ ( positive @ SV18 @ SV14 ) )
| ~ ( ~ ~ ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV15: $i,SV19: mu > $i > $o] :
( ( ( ~ ( positive @ SV19 @ SV15 ) )
= $true )
| ( ( ! [SY379: $i] :
( ~ ( rel @ SV15 @ SY379 )
| ( positive @ SV19 @ SY379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(112,plain,
( ( ~ ( sK6_SX0 @ sK2_SY307 @ sK1_SY97 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(113,plain,
( ( ! [SY380: $i] :
( ~ ( rel @ sK1_SY97 @ SY380 )
| ! [SY381: mu] :
( ~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY380 )
| ( SX3 @ SY381 @ SY380 ) )
| ( sK6_SX0 @ SY381 @ SY380 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(114,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ~ ~ ( ~ ( positive @ SV20 @ SV16 )
| ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) )
| ( positive @ SV21 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV17: mu > $i > $o] :
( ( ( positive @ SV17 @ sK1_SY97 )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(116,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
| ~ ( positive @ SV18 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(117,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ( ~ ~ ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(118,plain,
! [SV15: $i,SV19: mu > $i > $o] :
( ( ( positive @ SV19 @ SV15 )
= $false )
| ( ( ! [SY379: $i] :
( ~ ( rel @ SV15 @ SY379 )
| ( positive @ SV19 @ SY379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
( ( sK6_SX0 @ sK2_SY307 @ sK1_SY97 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(120,plain,
( ( ~ ( rel @ sK1_SY97 @ sK7_SY380 )
| ! [SY388: mu] :
( ~ ! [SY389: mu > $i > $o] :
( ~ ( positive @ SY389 @ sK7_SY380 )
| ( SY389 @ SY388 @ sK7_SY380 ) )
| ( sK6_SX0 @ SY388 @ sK7_SY380 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(121,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ~ ( ~ ( positive @ SV20 @ SV16 )
| ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) ) )
= $true )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
| ~ ( positive @ SV18 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(123,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ~ ~ ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV19: mu > $i > $o,SV22: $i,SV15: $i] :
( ( ( ~ ( rel @ SV15 @ SV22 )
| ( positive @ SV19 @ SV22 ) )
= $true )
| ( ( positive @ SV19 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
( ( ~ ( rel @ sK1_SY97 @ sK7_SY380 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(126,plain,
( ( ! [SY388: mu] :
( ~ ! [SY389: mu > $i > $o] :
( ~ ( positive @ SY389 @ sK7_SY380 )
| ( SY389 @ SY388 @ sK7_SY380 ) )
| ( sK6_SX0 @ SY388 @ sK7_SY380 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(127,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ( ~ ( positive @ SV20 @ SV16 )
| ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) ) )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
= $true )
| ( ( ~ ( positive @ SV18 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ~ ( positive @ SV18 @ SV14 ) )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV19: mu > $i > $o,SV22: $i,SV15: $i] :
( ( ( ~ ( rel @ SV15 @ SV22 ) )
= $true )
| ( ( positive @ SV19 @ SV22 )
= $true )
| ( ( positive @ SV19 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(131,plain,
( ( rel @ sK1_SY97 @ sK7_SY380 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
( ( ~ ! [SY390: mu > $i > $o] :
( ~ ( positive @ SY390 @ sK7_SY380 )
| ( SY390 @ sK8_SY388 @ sK7_SY380 ) )
| ( sK6_SX0 @ sK8_SY388 @ sK7_SY380 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(133,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ( positive @ SV20 @ SV16 )
| ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) )
= $true )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false )
| ( ( ~ ( positive @ SV18 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( positive @ SV18 @ SV14 ) )
= $false )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV19: mu > $i > $o,SV22: $i,SV15: $i] :
( ( ( rel @ SV15 @ SV22 )
= $false )
| ( ( positive @ SV19 @ SV22 )
= $true )
| ( ( positive @ SV19 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
( ( ~ ! [SY390: mu > $i > $o] :
( ~ ( positive @ SY390 @ sK7_SY380 )
| ( SY390 @ sK8_SY388 @ sK7_SY380 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(138,plain,
( ( sK6_SX0 @ sK8_SY388 @ sK7_SY380 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(139,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ( positive @ SV20 @ SV16 ) )
= $true )
| ( ( ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) )
= $true )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive @ SV18 @ SV14 )
= $false )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive @ SV18 @ SV14 )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
( ( ! [SY390: mu > $i > $o] :
( ~ ( positive @ SY390 @ sK7_SY380 )
| ( SY390 @ sK8_SY388 @ sK7_SY380 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(143,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( ~ ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) )
= $true )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV23: mu > $i > $o] :
( ( ~ ( positive @ SV23 @ sK7_SY380 )
| ( SV23 @ sK8_SY388 @ sK7_SY380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(145,plain,
! [SV21: mu > $i > $o,SV20: mu > $i > $o,SV16: $i] :
( ( ( ! [SY386: $i] :
( ~ ( rel @ SV16 @ SY386 )
| ! [SY387: mu] :
( ~ ( SV20 @ SY387 @ SY386 )
| ( SV21 @ SY387 @ SY386 ) ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(146,plain,
! [SV23: mu > $i > $o] :
( ( ( ~ ( positive @ SV23 @ sK7_SY380 ) )
= $true )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(147,plain,
! [SV20: mu > $i > $o,SV21: mu > $i > $o,SV16: $i] :
( ( ( ~ ( rel @ SV16 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
| ! [SY391: mu] :
( ~ ( SV20 @ SY391 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
| ( SV21 @ SY391 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(148,plain,
! [SV23: mu > $i > $o] :
( ( ( positive @ SV23 @ sK7_SY380 )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(149,plain,
! [SV20: mu > $i > $o,SV21: mu > $i > $o,SV16: $i] :
( ( ( ~ ( rel @ SV16 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(150,plain,
! [SV16: $i,SV21: mu > $i > $o,SV20: mu > $i > $o] :
( ( ( ! [SY391: mu] :
( ~ ( SV20 @ SY391 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
| ( SV21 @ SY391 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(151,plain,
! [SV20: mu > $i > $o,SV21: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16 @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(152,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ( SV20 @ ( sK10_SY391 @ SV16 @ SV21 @ SV20 ) @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
| ( SV21 @ ( sK10_SY391 @ SV16 @ SV21 @ SV20 ) @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(153,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( ~ ( SV20 @ ( sK10_SY391 @ SV16 @ SV21 @ SV20 ) @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(154,plain,
! [SV20: mu > $i > $o,SV16: $i,SV21: mu > $i > $o] :
( ( ( SV21 @ ( sK10_SY391 @ SV16 @ SV21 @ SV20 ) @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(155,plain,
! [SV21: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( SV20 @ ( sK10_SY391 @ SV16 @ SV21 @ SV20 ) @ ( sK9_SY386 @ SV21 @ SV20 @ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(157,plain,
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ sK1_SY97 )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[115:[bind(SV17,$thf( ^ [SV48: mu] : ^ [SV49: $i] : $false ))]]) ).
thf(158,plain,
! [SV47: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV47 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( SV47 @ sK2_SY307 @ sK1_SY97 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[115:[bind(SV17,$thf( ^ [SV45: mu] : ^ [SV46: $i] : ~ ( SV47 @ SV45 @ SV46 ) ))]]) ).
thf(160,plain,
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ sK7_SY380 )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[148:[bind(SV23,$thf( ^ [SV41: mu] : ^ [SV42: $i] : $false ))]]) ).
thf(161,plain,
! [SV40: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV40 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( SV40 @ sK8_SY388 @ sK7_SY380 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[148:[bind(SV23,$thf( ^ [SV38: mu] : ^ [SV39: $i] : ~ ( SV40 @ SV38 @ SV39 ) ))]]) ).
thf(162,plain,
! [SV21: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV20,$thf( ^ [SV29: mu] : ^ [SV30: $i] : $true ))]]) ).
thf(163,plain,
! [SV21: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV20,$thf( ^ [SV27: mu] : ^ [SV28: $i] : $false ))]]) ).
thf(164,plain,
! [SV26: mu > $i > $o,SV21: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV20,$thf( ^ [SV24: mu] : ^ [SV25: $i] : ~ ( SV26 @ SV24 @ SV25 ) ))]]) ).
thf(165,plain,
! [SV20: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] : $true
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV21,$thf( ^ [SV36: mu] : ^ [SV37: $i] : $true ))]]) ).
thf(166,plain,
! [SV20: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] : $false
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV21,$thf( ^ [SV34: mu] : ^ [SV35: $i] : $false ))]]) ).
thf(167,plain,
! [SV20: mu > $i > $o,SV33: mu > $i > $o,SV16: $i] :
( ( ( rel @ SV16
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[151:[bind(SV21,$thf( ^ [SV31: mu] : ^ [SV32: $i] : ~ ( SV33 @ SV31 @ SV32 ) ))]]) ).
thf(168,plain,
! [SV16: $i,SV21: mu > $i > $o] :
( ( ( SV21
@ ( sK10_SY391 @ SV16 @ SV21
@ ^ [SX0: mu,SX1: $i] : $true )
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[154:[bind(SV20,$thf( ^ [SV29: mu] : ^ [SV30: $i] : $true ))]]) ).
thf(169,plain,
! [SV16: $i,SV21: mu > $i > $o] :
( ( ( SV21
@ ( sK10_SY391 @ SV16 @ SV21
@ ^ [SX0: mu,SX1: $i] : $false )
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[154:[bind(SV20,$thf( ^ [SV27: mu] : ^ [SV28: $i] : $false ))]]) ).
thf(170,plain,
! [SV26: mu > $i > $o,SV16: $i,SV21: mu > $i > $o] :
( ( ( SV21
@ ( sK10_SY391 @ SV16 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 ) )
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[154:[bind(SV20,$thf( ^ [SV24: mu] : ^ [SV25: $i] : ~ ( SV26 @ SV24 @ SV25 ) ))]]) ).
thf(171,plain,
! [SV16: $i,SV20: mu > $i > $o] :
( ( $true = $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[154:[bind(SV21,$thf( ^ [SV36: mu] : ^ [SV37: $i] : $true ))]]) ).
thf(173,plain,
! [SV20: mu > $i > $o,SV16: $i,SV33: mu > $i > $o] :
( ( ( ~ ( SV33
@ ( sK10_SY391 @ SV16
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20 )
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20
@ SV16 ) ) )
= $false )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[154:[bind(SV21,$thf( ^ [SV31: mu] : ^ [SV32: $i] : ~ ( SV33 @ SV31 @ SV32 ) ))]]) ).
thf(175,plain,
! [SV21: mu > $i > $o,SV16: $i] :
( ( $false = $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[155:[bind(SV20,$thf( ^ [SV27: mu] : ^ [SV28: $i] : $false ))]]) ).
thf(176,plain,
! [SV21: mu > $i > $o,SV16: $i,SV26: mu > $i > $o] :
( ( ( ~ ( SV26
@ ( sK10_SY391 @ SV16 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 ) )
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[155:[bind(SV20,$thf( ^ [SV24: mu] : ^ [SV25: $i] : ~ ( SV26 @ SV24 @ SV25 ) ))]]) ).
thf(177,plain,
! [SV16: $i,SV20: mu > $i > $o] :
( ( ( SV20
@ ( sK10_SY391 @ SV16
@ ^ [SX0: mu,SX1: $i] : $true
@ SV20 )
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] : $true
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[155:[bind(SV21,$thf( ^ [SV36: mu] : ^ [SV37: $i] : $true ))]]) ).
thf(178,plain,
! [SV16: $i,SV20: mu > $i > $o] :
( ( ( SV20
@ ( sK10_SY391 @ SV16
@ ^ [SX0: mu,SX1: $i] : $false
@ SV20 )
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] : $false
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[155:[bind(SV21,$thf( ^ [SV34: mu] : ^ [SV35: $i] : $false ))]]) ).
thf(179,plain,
! [SV33: mu > $i > $o,SV16: $i,SV20: mu > $i > $o] :
( ( ( SV20
@ ( sK10_SY391 @ SV16
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20 )
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV16 )
= $true ) ),
inference(prim_subst,[status(thm)],[155:[bind(SV21,$thf( ^ [SV31: mu] : ^ [SV32: $i] : ~ ( SV33 @ SV31 @ SV32 ) ))]]) ).
thf(180,plain,
! [SV17: mu > $i > $o] :
( ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true )
| ( ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= ( ~ ( positive @ SV17 @ sK1_SY97 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[115]) ).
thf(181,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false )
| ( ( ( positive @ SV18 @ SV14 )
= ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[140]) ).
thf(182,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true )
| ( ( ( positive @ SV18 @ SV14 )
= ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[141]) ).
thf(183,plain,
! [SV23: mu > $i > $o] :
( ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true )
| ( ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= ( ~ ( positive @ SV23 @ sK7_SY380 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[148]) ).
thf(184,plain,
! [SV17: mu > $i > $o] :
( ( ( ~ ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
| ~ ( positive @ SV17 @ sK1_SY97 ) )
| ~ ( ~ ( SV17 @ sK2_SY307 @ sK1_SY97 )
| ~ ~ ( positive @ SV17 @ sK1_SY97 ) ) )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[180]) ).
thf(185,plain,
! [SV17: mu > $i > $o] :
( ( ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= ( ~ ( positive @ SV17 @ sK1_SY97 ) ) )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[180]) ).
thf(186,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
| ~ ( ~ ( positive @ SV18 @ SV14 )
| ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) ) )
= $false )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[181]) ).
thf(188,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) )
| ~ ( ~ ( positive @ SV18 @ SV14 )
| ~ ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) ) )
= $false )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[182]) ).
thf(190,plain,
! [SV23: mu > $i > $o] :
( ( ( ~ ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
| ~ ( positive @ SV23 @ sK7_SY380 ) )
| ~ ( ~ ( SV23 @ sK8_SY388 @ sK7_SY380 )
| ~ ~ ( positive @ SV23 @ sK7_SY380 ) ) )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[183]) ).
thf(191,plain,
! [SV23: mu > $i > $o] :
( ( ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= ( ~ ( positive @ SV23 @ sK7_SY380 ) ) )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[183]) ).
thf(192,plain,
! [SV17: mu > $i > $o] :
( ( ( ~ ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
| ~ ( positive @ SV17 @ sK1_SY97 ) ) )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(195,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( ~ ( positive @ SV18 @ SV14 )
| ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) ) )
= $false )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(196,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) ) )
= $false )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(198,plain,
! [SV23: mu > $i > $o] :
( ( ( ~ ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
| ~ ( positive @ SV23 @ sK7_SY380 ) ) )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(200,plain,
! [SV17: mu > $i > $o] :
( ( ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
| ~ ( positive @ SV17 @ sK1_SY97 ) )
= $true )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(203,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( positive @ SV18 @ SV14 )
| ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
= $true )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(204,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ( positive @ SV18 @ SV14 )
| ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 ) )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(206,plain,
! [SV23: mu > $i > $o] :
( ( ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
| ~ ( positive @ SV23 @ sK7_SY380 ) )
= $true )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(208,plain,
! [SV17: mu > $i > $o] :
( ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true )
| ( ( ~ ( positive @ SV17 @ sK1_SY97 ) )
= $true )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(211,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( ~ ( positive @ SV18 @ SV14 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
= $true )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive @ SV18 @ SV14 )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV23: mu > $i > $o] :
( ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true )
| ( ( ~ ( positive @ SV23 @ sK7_SY380 ) )
= $true )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV17: mu > $i > $o] :
( ( ( positive @ SV17 @ sK1_SY97 )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive @ SV18 @ SV14 )
= $false )
| ( ( ~ ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 ) )
= $true )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV23: mu > $i > $o] :
( ( ( positive @ SV23 @ sK7_SY380 )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false )
| ( ( positive @ SV18 @ SV14 )
= $false )
| ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(228,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 ) )
= $true )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX1 ) ))]]) ).
thf(229,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 ) )
= $true )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK1_SY97 )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ sK1_SY97 ) ))]]) ).
thf(230,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 ) )
= $true )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX1 ) ))]]) ).
thf(231,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 ) )
= $true )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK1_SY97 )
= $false ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ sK1_SY97 ) ))]]) ).
thf(232,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ))]]) ).
thf(233,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) @ sK1_SY97 ) ))]]) ).
thf(234,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ))]]) ).
thf(235,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $false ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) @ sK1_SY97 ) ))]]) ).
thf(237,plain,
! [SV62: mu > $i > $i,SV61: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive @ ( SV61 @ sK2_SY307 @ sK1_SY97 ) @ ( SV62 @ sK2_SY307 @ sK1_SY97 ) ) )
= $true )
| ( ( positive @ ( SV61 @ sK2_SY307 @ sK1_SY97 ) @ ( SV62 @ sK2_SY307 @ sK1_SY97 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV61 @ SX0 @ SX1 ) @ ( SV62 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ( SV61 @ SX0 @ SX1 ) @ ( SV62 @ SX0 @ SX1 ) ) ))]]) ).
thf(238,plain,
! [SV56: mu > $i > $o] :
( ( ( ~ ( SV56 @ sK2_SY307 @ sK1_SY97 ) )
= $true )
| ( ( ~ ( SV56 @ sK2_SY307 @ sK1_SY97 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV56 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extuni,[status(esa)],[185:[bind(SV17,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( SV56 @ SX0 @ SX1 ) ))]]) ).
thf(240,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 ) )
= $true )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX1 ) ))]]) ).
thf(241,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 ) )
= $true )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK7_SY380 )
= $true ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ sK7_SY380 ) ))]]) ).
thf(242,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 ) )
= $true )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX1 ) ))]]) ).
thf(243,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 ) )
= $true )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK7_SY380 )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ sK7_SY380 ) ))]]) ).
thf(244,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ))]]) ).
thf(245,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) @ sK7_SY380 ) ))]]) ).
thf(246,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ))]]) ).
thf(247,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ^ [SX2: mu] : ^ [SX3: $i] : ~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) @ sK7_SY380 ) ))]]) ).
thf(249,plain,
! [SV143: mu > $i > $i,SV142: mu > $i > mu > $i > $o] :
( ( ( ~ ( positive @ ( SV142 @ sK8_SY388 @ sK7_SY380 ) @ ( SV143 @ sK8_SY388 @ sK7_SY380 ) ) )
= $true )
| ( ( positive @ ( SV142 @ sK8_SY388 @ sK7_SY380 ) @ ( SV143 @ sK8_SY388 @ sK7_SY380 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV142 @ SX0 @ SX1 ) @ ( SV143 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( positive @ ( SV142 @ SX0 @ SX1 ) @ ( SV143 @ SX0 @ SX1 ) ) ))]]) ).
thf(250,plain,
! [SV137: mu > $i > $o] :
( ( ( ~ ( SV137 @ sK8_SY388 @ sK7_SY380 ) )
= $true )
| ( ( ~ ( SV137 @ sK8_SY388 @ sK7_SY380 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV137 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extuni,[status(esa)],[191:[bind(SV23,$thf( ^ [SX0: mu] : ^ [SX1: $i] : ~ ( SV137 @ SX0 @ SX1 ) ))]]) ).
thf(253,plain,
! [SV56: mu > $i > $o] :
( ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false )
| ( ( ~ ( SV56 @ sK2_SY307 @ sK1_SY97 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV56 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV62: mu > $i > $i,SV61: mu > $i > mu > $i > $o] :
( ( ( positive @ ( SV61 @ sK2_SY307 @ sK1_SY97 ) @ ( SV62 @ sK2_SY307 @ sK1_SY97 ) )
= $false )
| ( ( positive @ ( SV61 @ sK2_SY307 @ sK1_SY97 ) @ ( SV62 @ sK2_SY307 @ sK1_SY97 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV61 @ SX0 @ SX1 ) @ ( SV62 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(256,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(258,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(259,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(260,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK1_SY97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(261,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(262,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK1_SY97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV81: mu > $i > mu > $i > $i,SV80: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV80 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) @ ( SV81 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false )
| ( ( positive
@ ( SV80 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV81 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV80
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV81
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV80 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV81 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV80 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV81 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(265,plain,
! [SV137: mu > $i > $o] :
( ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false )
| ( ( ~ ( SV137 @ sK8_SY388 @ sK7_SY380 ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV137 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV143: mu > $i > $i,SV142: mu > $i > mu > $i > $o] :
( ( ( positive @ ( SV142 @ sK8_SY388 @ sK7_SY380 ) @ ( SV143 @ sK8_SY388 @ sK7_SY380 ) )
= $false )
| ( ( positive @ ( SV142 @ sK8_SY388 @ sK7_SY380 ) @ ( SV143 @ sK8_SY388 @ sK7_SY380 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV142 @ SX0 @ SX1 ) @ ( SV143 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(268,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(269,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(270,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(271,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(272,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK7_SY380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(273,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ sK7_SY380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(275,plain,
! [SV162: mu > $i > mu > $i > $i,SV161: mu > $i > mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV161 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) @ ( SV162 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false )
| ( ( positive
@ ( SV161 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
@ ( SV162 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive
@ ( SV161
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 )
@ ( SV162
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( positive @ ( SV161 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( SV162 @ SX2 @ SX3 @ SX4 @ SX5 ) ) )
@ SX0
@ SX1 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( positive @ ( SV161 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( SV162 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(277,plain,
! [SV56: mu > $i > $o] :
( ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false )
| ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV56 @ SX0 @ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(278,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(279,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(280,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(281,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(283,plain,
! [SV137: mu > $i > $o] :
( ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false )
| ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV137 @ SX0 @ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(284,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(285,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(286,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(287,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( ~ ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(289,plain,
! [SV56: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV56 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false )
| ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(290,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(291,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(292,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : sK1_SY97
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK1_SY97 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : sK1_SY97
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(293,plain,
! [SV71: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71
@ ( sK11_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK12_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV71 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV71 @ sK2_SY307 @ sK1_SY97 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV71 @ sK2_SY307 @ sK1_SY97
@ ( sK11_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK12_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV71 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(295,plain,
! [SV137: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV137 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false )
| ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(297,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(298,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : sK7_SY380
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ sK7_SY380 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : sK7_SY380
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV152: mu > $i > mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152
@ ( sK15_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ ( sK16_E
@ ^ [SX2: mu,SX3: $i] : SX3
@ ^ [SX2: mu,SX3: $i,SX4: mu,SX5: $i] :
~ ( SV152 @ SX2 @ SX3 @ SX4 @ SX5 ) )
@ SX0
@ SX1 )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV152 @ sK8_SY388 @ sK7_SY380 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV152 @ sK8_SY388 @ sK7_SY380
@ ( sK15_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) )
@ ( sK16_E
@ ^ [SX0: mu,SX1: $i] : SX1
@ ^ [SX0: mu,SX1: $i,SX2: mu,SX3: $i] :
~ ( SV152 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV47: mu > $i > $o] :
( ( ( SV47 @ sK2_SY307 @ sK1_SY97 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV47 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(301,plain,
! [SV40: mu > $i > $o] :
( ( ( SV40 @ sK8_SY388 @ sK7_SY380 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV40 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(302,plain,
! [SV20: mu > $i > $o,SV16: $i,SV33: mu > $i > $o] :
( ( ( SV33
@ ( sK10_SY391 @ SV16
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20 )
@ ( sK9_SY386
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV20
@ SV16 ) )
= $true )
| ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV33 @ SX0 @ SX1 )
@ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(303,plain,
! [SV21: mu > $i > $o,SV16: $i,SV26: mu > $i > $o] :
( ( ( SV26
@ ( sK10_SY391 @ SV16 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 ) )
@ ( sK9_SY386 @ SV21
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV26 @ SX0 @ SX1 )
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(304,plain,
! [SV17: mu > $i > $o] :
( ( ( positive @ SV17 @ sK1_SY97 )
= $false )
| ( ( SV17 @ sK2_SY307 @ sK1_SY97 )
= $true ) ),
inference(sim,[status(thm)],[216]) ).
thf(305,plain,
! [SV56: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV56 @ SX0 @ SX1 )
@ sK1_SY97 )
= $false )
| ( ( SV56 @ sK2_SY307 @ sK1_SY97 )
= $false ) ),
inference(sim,[status(thm)],[289]) ).
thf(306,plain,
! [SV62: mu > $i > $i,SV61: mu > $i > mu > $i > $o] :
( ( ( positive @ ( SV61 @ sK2_SY307 @ sK1_SY97 ) @ ( SV62 @ sK2_SY307 @ sK1_SY97 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV61 @ SX0 @ SX1 ) @ ( SV62 @ SX0 @ SX1 ) )
@ sK1_SY97 )
= $false ) ),
inference(sim,[status(thm)],[254]) ).
thf(307,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive
@ ^ [SY375: mu,SY376: $i] :
~ ( SV18 @ SY375 @ SY376 )
@ SV14 )
= $false )
| ( ( positive @ SV18 @ SV14 )
= $false ) ),
inference(sim,[status(thm)],[223]) ).
thf(308,plain,
! [SV14: $i,SV18: mu > $i > $o] :
( ( ( positive @ SV18 @ SV14 )
= $true )
| ( ( positive
@ ^ [SY377: mu,SY378: $i] :
~ ( SV18 @ SY377 @ SY378 )
@ SV14 )
= $true ) ),
inference(sim,[status(thm)],[212]) ).
thf(309,plain,
! [SV23: mu > $i > $o] :
( ( ( positive @ SV23 @ sK7_SY380 )
= $false )
| ( ( SV23 @ sK8_SY388 @ sK7_SY380 )
= $true ) ),
inference(sim,[status(thm)],[220]) ).
thf(310,plain,
! [SV137: mu > $i > $o] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( SV137 @ SX0 @ SX1 )
@ sK7_SY380 )
= $false )
| ( ( SV137 @ sK8_SY388 @ sK7_SY380 )
= $false ) ),
inference(sim,[status(thm)],[295]) ).
thf(311,plain,
! [SV143: mu > $i > $i,SV142: mu > $i > mu > $i > $o] :
( ( ( positive @ ( SV142 @ sK8_SY388 @ sK7_SY380 ) @ ( SV143 @ sK8_SY388 @ sK7_SY380 ) )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] :
~ ( positive @ ( SV142 @ SX0 @ SX1 ) @ ( SV143 @ SX0 @ SX1 ) )
@ sK7_SY380 )
= $false ) ),
inference(sim,[status(thm)],[266]) ).
thf(312,plain,
( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ sK1_SY97 )
= $false ),
inference(sim,[status(thm)],[157]) ).
thf(313,plain,
( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ sK7_SY380 )
= $false ),
inference(sim,[status(thm)],[160]) ).
thf(314,plain,
! [SV16: $i,SV20: mu > $i > $o] :
( ( ( positive @ SV20 @ SV16 )
= $false )
| ( ( positive
@ ^ [SX0: mu,SX1: $i] : $true
@ SV16 )
= $true ) ),
inference(sim,[status(thm)],[171]) ).
thf(315,plain,
! [SV21: mu > $i > $o,SV16: $i] :
( ( ( positive
@ ^ [SX0: mu,SX1: $i] : $false
@ SV16 )
= $false )
| ( ( positive @ SV21 @ SV16 )
= $true ) ),
inference(sim,[status(thm)],[175]) ).
thf(316,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[98,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,293,292,291,290,275,274,273,272,263,262,261,260,179,178,177,170,169,168,167,166,165,164,163,162,155,154,151,148,141,140,138,136,131,119,115,99]) ).
thf(317,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[316,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 13:48:00 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 154.63/26.14
% 154.63/26.14 No.of.Axioms: 5
% 154.63/26.14
% 154.63/26.14 Length.of.Defs: 4167
% 154.63/26.14
% 154.63/26.14 Contains.Choice.Funs: false
% 154.63/26.14 .........eprover: CPU time limit exceeded, terminating
% 154.63/26.14 ....
% 154.63/26.14
% 154.63/26.14 ********************************
% 154.63/26.14 * All subproblems solved! *
% 154.63/26.14 ********************************
% 154.63/26.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:316,loop_count:0,foatp_calls:2,translation:fof_full)
% 154.63/26.14
% 154.63/26.14 %**** Beginning of derivation protocol ****
% 154.63/26.14 % SZS output start CNFRefutation
% See solution above
% 154.63/26.15
% 154.63/26.15 %**** End of derivation protocol ****
% 154.63/26.15 %**** no. of clauses in derivation: 279 ****
% 154.63/26.15 %**** clause counter: 316 ****
% 154.63/26.15
% 154.63/26.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:316,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------