%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU481^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n016.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 10:44:34 AM UTC 2026
% Result : Theorem 90.69s 15.43s
% Output : CNFRefutation 90.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 30
% Syntax : Number of formulae : 163 ( 51 unt; 0 typ; 29 def)
% Number of atoms : 1042 ( 396 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2182 ( 497 ~; 337 |; 32 &;1270 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 199 ( 199 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 3 con; 0-4 aty)
% Number of variables : 627 ( 122 ^; 492 !; 13 ?; 627 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymm,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(tp_asymm,type,
asymm: ( $i > $i > $o ) > $o ).
thf(tp_confl,type,
confl: ( $i > $i > $o ) > $o ).
thf(tp_cr,type,
cr: ( $i > $i > $o ) > $o ).
thf(tp_idem,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_ind,type,
ind: ( $i > $i > $o ) > $o ).
thf(tp_infl,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_innf,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(tp_inv,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_irrefl,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(tp_join,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_lconfl,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(tp_mono,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(tp_nfof,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_norm,type,
norm: ( $i > $i > $o ) > $o ).
thf(tp_po,type,
po: ( $i > $i > $o ) > $o ).
thf(tp_rc,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_refl,type,
refl: ( $i > $i > $o ) > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SY58,type,
sK2_SY58: $i > $o ).
thf(tp_sK3_SY64,type,
sK3_SY64: $i > $i ).
thf(tp_sK4_SY62,type,
sK4_SY62: $i ).
thf(tp_sK5_SY49,type,
sK5_SY49: ( $i > $o ) > $i ).
thf(tp_sK6_SY66,type,
sK6_SY66: $i > ( $i > $o ) > $i > $i > $o ).
thf(tp_sc,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_sconfl,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(tp_so,type,
so: ( $i > $i > $o ) > $o ).
thf(tp_subrel,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(tp_symm,type,
symm: ( $i > $i > $o ) > $o ).
thf(tp_tc,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_term,type,
term: ( $i > $i > $o ) > $o ).
thf(tp_total,type,
total: ( $i > $i > $o ) > $o ).
thf(tp_trans,type,
trans: ( $i > $i > $o ) > $o ).
thf(tp_trc,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(tp_trsc,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(antisymm,definition,
( antisymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetric) ).
thf(asymm,definition,
( asymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ~ ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asymmetric) ).
thf(confl,definition,
( confl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( trc @ R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',confluent) ).
thf(cr,definition,
( cr
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( trsc @ R @ X @ Y )
=> ( join @ R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_rosser) ).
thf(idem,definition,
( idem
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] :
( ( F @ ( F @ R ) )
= ( F @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotent) ).
thf(ind,definition,
( ind
= ( ^ [R: $i > $i > $o] :
! [P: $i > $o] :
( ! [X: $i] :
( ! [Y: $i] :
( ( tc @ R @ X @ Y )
=> ( P @ Y ) )
=> ( P @ X ) )
=> ! [X: $i] : ( P @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satisfying_the_induction_principle) ).
thf(infl,definition,
( infl
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] : ( subrel @ R @ ( F @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inflationary) ).
thf(innf,definition,
( innf
= ( ^ [R: $i > $i > $o,X: $i] :
~ ? [Y: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_normal_form) ).
thf(inv,definition,
( inv
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(irrefl,definition,
( irrefl
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(join,definition,
( join
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
? [Z: $i] :
( ( trc @ R @ X @ Z )
& ( trc @ R @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',joinable) ).
thf(lconfl,definition,
( lconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',locally_confluent) ).
thf(mono,definition,
( mono
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o,S: $i > $i > $o] :
( ( subrel @ R @ S )
=> ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotonic) ).
thf(nfof,definition,
( nfof
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( trc @ R @ Y @ X )
& ( innf @ R @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normal_form_of) ).
thf(norm,definition,
( norm
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
? [Y: $i] : ( nfof @ R @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normalizing) ).
thf(po,definition,
( po
= ( ^ [R: $i > $i > $o] :
( ( refl @ R )
& ( antisymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order) ).
thf(rc,definition,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure) ).
thf(refl,definition,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive) ).
thf(sc,definition,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure) ).
thf(sconfl,definition,
( sconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',semi_confluent) ).
thf(so,definition,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order) ).
thf(subrel,definition,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel) ).
thf(symm,definition,
( symm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric) ).
thf(tc,definition,
( tc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
! [S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S ) )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure) ).
thf(term,definition,
( term
= ( ^ [R: $i > $i > $o] :
! [A: $i > $o] :
( ? [X: $i] : ( A @ X )
=> ? [X: $i] :
( ( A @ X )
& ! [Y: $i] :
( ( A @ Y )
=> ~ ( R @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',terminating) ).
thf(total,definition,
( total
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y )
| ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total) ).
thf(trans,definition,
( trans
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive) ).
thf(trc,definition,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_closure) ).
thf(trsc,definition,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure) ).
thf(1,conjecture,
! [R: $i > $i > $o] :
( ( ind @ R )
=> ( term @ R ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_implies_termination) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o] :
( ( ind @ R )
=> ( term @ R ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY1: $i > $o] :
( ! [SY2: $i] :
( ! [SY3: $i] :
( ! [SY22: $i > $i > $o] :
( ( ! [SY7: $i,SY8: $i,SY9: $i] :
( ( ( SY22 @ SY7 @ SY8 )
& ( SY22 @ SY8 @ SY9 ) )
=> ( SY22 @ SY7 @ SY9 ) )
& ! [SY13: $i,SY14: $i] :
( ( SY0 @ SY13 @ SY14 )
=> ( SY22 @ SY13 @ SY14 ) ) )
=> ( SY22 @ SY2 @ SY3 ) )
=> ( SY1 @ SY3 ) )
=> ( SY1 @ SY2 ) )
=> ! [X: $i] : ( SY1 @ X ) )
=> ! [SY29: $i > $o] :
( ? [X: $i] : ( SY29 @ X )
=> ? [SY31: $i] :
( ( SY29 @ SY31 )
& ! [SY32: $i] :
( ( SY29 @ SY32 )
=> ~ ( SY0 @ SY31 @ SY32 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,antisymm,asymm,confl,cr,idem,ind,infl,innf,inv,irrefl,join,lconfl,mono,nfof,norm,po,rc,refl,sc,sconfl,so,subrel,symm,tc,term,total,trans,trc,trsc]) ).
thf(4,plain,
( ( ! [SY48: $i > $o] :
( ! [SY49: $i] :
( ! [SY50: $i] :
( ! [SY51: $i > $i > $o] :
( ( ! [SY7: $i,SY8: $i,SY9: $i] :
( ( ( SY51 @ SY7 @ SY8 )
& ( SY51 @ SY8 @ SY9 ) )
=> ( SY51 @ SY7 @ SY9 ) )
& ! [SY55: $i,SY56: $i] :
( ( sK1_SY0 @ SY55 @ SY56 )
=> ( SY51 @ SY55 @ SY56 ) ) )
=> ( SY51 @ SY49 @ SY50 ) )
=> ( SY48 @ SY50 ) )
=> ( SY48 @ SY49 ) )
=> ! [X: $i] : ( SY48 @ X ) )
=> ! [SY58: $i > $o] :
( ? [X: $i] : ( SY58 @ X )
=> ? [SY60: $i] :
( ( SY58 @ SY60 )
& ! [SY61: $i] :
( ( SY58 @ SY61 )
=> ~ ( sK1_SY0 @ SY60 @ SY61 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY48: $i > $o] :
( ! [SY49: $i] :
( ! [SY50: $i] :
( ! [SY51: $i > $i > $o] :
( ( ! [SY7: $i,SY8: $i,SY9: $i] :
( ( ( SY51 @ SY7 @ SY8 )
& ( SY51 @ SY8 @ SY9 ) )
=> ( SY51 @ SY7 @ SY9 ) )
& ! [SY55: $i,SY56: $i] :
( ( sK1_SY0 @ SY55 @ SY56 )
=> ( SY51 @ SY55 @ SY56 ) ) )
=> ( SY51 @ SY49 @ SY50 ) )
=> ( SY48 @ SY50 ) )
=> ( SY48 @ SY49 ) )
=> ! [X: $i] : ( SY48 @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY58: $i > $o] :
( ? [X: $i] : ( SY58 @ X )
=> ? [SY60: $i] :
( ( SY58 @ SY60 )
& ! [SY61: $i] :
( ( SY58 @ SY61 )
=> ~ ( sK1_SY0 @ SY60 @ SY61 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY58: $i > $o] :
( ? [X: $i] : ( SY58 @ X )
=> ? [SY60: $i] :
( ( SY58 @ SY60 )
& ! [SY61: $i] :
( ( SY58 @ SY61 )
=> ~ ( sK1_SY0 @ SY60 @ SY61 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( sK2_SY58 @ sK4_SY62 )
& ! [SY63: $i] :
( ( ( sK2_SY58 @ ( sK3_SY64 @ SY63 ) )
& ( sK1_SY0 @ SY63 @ ( sK3_SY64 @ SY63 ) ) )
| ~ ( sK2_SY58 @ SY63 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY48: $i > $o] :
( ( ! [SY65: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( sK6_SY66 @ SY65 @ SY48 @ SY72 @ SY73 )
| ~ ( sK6_SY66 @ SY65 @ SY48 @ SY73 @ SY74 )
| ( sK6_SY66 @ SY65 @ SY48 @ SY72 @ SY74 ) )
& ! [SY75: $i,SY76: $i] :
( ~ ( sK1_SY0 @ SY75 @ SY76 )
| ( sK6_SY66 @ SY65 @ SY48 @ SY75 @ SY76 ) )
& ~ ( sK6_SY66 @ SY65 @ SY48 @ ( sK5_SY49 @ SY48 ) @ SY65 ) )
| ( SY48 @ SY65 ) )
& ~ ( SY48 @ ( sK5_SY49 @ SY48 ) ) )
| ! [X: $i] : ( SY48 @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [SY48: $i > $o] :
( ( ! [SY65: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( sK6_SY66 @ SY65 @ SY48 @ SY72 @ SY73 )
| ~ ( sK6_SY66 @ SY65 @ SY48 @ SY73 @ SY74 )
| ( sK6_SY66 @ SY65 @ SY48 @ SY72 @ SY74 ) )
& ! [SY75: $i,SY76: $i] :
( ~ ( sK1_SY0 @ SY75 @ SY76 )
| ( sK6_SY66 @ SY65 @ SY48 @ SY75 @ SY76 ) )
& ~ ( sK6_SY66 @ SY65 @ SY48 @ ( sK5_SY49 @ SY48 ) @ SY65 ) )
| ( SY48 @ SY65 ) )
& ~ ( SY48 @ ( sK5_SY49 @ SY48 ) ) )
| ! [X: $i] : ( SY48 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ( sK2_SY58 @ sK4_SY62 )
& ! [SY63: $i] :
( ( ( sK2_SY58 @ ( sK3_SY64 @ SY63 ) )
& ( sK1_SY0 @ SY63 @ ( sK3_SY64 @ SY63 ) ) )
| ~ ( sK2_SY58 @ SY63 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( ~ ( sK2_SY58 @ sK4_SY62 )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SX0 ) )
| ~ ( sK1_SY0 @ SX0 @ ( sK3_SY64 @ SX0 ) ) )
| ~ ( sK2_SY58 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,antisymm,asymm,confl,cr,idem,ind,infl,innf,inv,irrefl,join,lconfl,mono,nfof,norm,po,rc,refl,sc,sconfl,so,subrel,symm,tc,term,total,trans,trc,trsc]) ).
thf(13,plain,
( ( ! [SX0: $i > $o] :
( ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( sK6_SY66 @ SX1 @ SX0 @ SX2 @ SX3 )
| ~ ( sK6_SY66 @ SX1 @ SX0 @ SX3 @ SX4 )
| ( sK6_SY66 @ SX1 @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( sK6_SY66 @ SX1 @ SX0 @ SX2 @ SX3 ) ) )
| ~ ~ ( sK6_SY66 @ SX1 @ SX0 @ ( sK5_SY49 @ SX0 ) @ SX1 ) )
| ( SX0 @ SX1 ) )
| ~ ~ ( SX0 @ ( sK5_SY49 @ SX0 ) ) )
| ! [SX1: $i] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,antisymm,asymm,confl,cr,idem,ind,infl,innf,inv,irrefl,join,lconfl,mono,nfof,norm,po,rc,refl,sc,sconfl,so,subrel,symm,tc,term,total,trans,trc,trsc]) ).
thf(14,plain,
( ( ~ ( sK2_SY58 @ sK4_SY62 )
| ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SX0 ) )
| ~ ( sK1_SY0 @ SX0 @ ( sK3_SY64 @ SX0 ) ) )
| ~ ( sK2_SY58 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ! [SY77: $i] :
( ~ ( ~ ~ ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY79 )
| ~ ( sK6_SY66 @ SY77 @ SV1 @ SY79 @ SY80 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY80 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ( sK1_SY0 @ SY81 @ SY82 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY81 @ SY82 ) ) )
| ~ ~ ( sK6_SY66 @ SY77 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SY77 ) )
| ( SV1 @ SY77 ) )
| ~ ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
| ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( sK2_SY58 @ sK4_SY62 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SX0 ) )
| ~ ( sK1_SY0 @ SX0 @ ( sK3_SY64 @ SX0 ) ) )
| ~ ( sK2_SY58 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ! [SY77: $i] :
( ~ ( ~ ~ ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY79 )
| ~ ( sK6_SY66 @ SY77 @ SV1 @ SY79 @ SY80 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY80 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ( sK1_SY0 @ SY81 @ SY82 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY81 @ SY82 ) ) )
| ~ ~ ( sK6_SY66 @ SY77 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SY77 ) )
| ( SV1 @ SY77 ) )
| ~ ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( sK2_SY58 @ sK4_SY62 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SX0 ) )
| ~ ( sK1_SY0 @ SX0 @ ( sK3_SY64 @ SX0 ) ) )
| ~ ( sK2_SY58 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ( ~ ! [SY77: $i] :
( ~ ( ~ ~ ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY79 )
| ~ ( sK6_SY66 @ SY77 @ SV1 @ SY79 @ SY80 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY80 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ( sK1_SY0 @ SY81 @ SY82 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY81 @ SY82 ) ) )
| ~ ~ ( sK6_SY66 @ SY77 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SY77 ) )
| ( SV1 @ SY77 ) )
| ~ ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
= $false )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: $i] :
( ( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) )
| ~ ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) ) )
| ~ ( sK2_SY58 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV1: $i > $o] :
( ( ( ~ ! [SY77: $i] :
( ~ ( ~ ~ ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY79 )
| ~ ( sK6_SY66 @ SY77 @ SV1 @ SY79 @ SY80 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY80 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ( sK1_SY0 @ SY81 @ SY82 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY81 @ SY82 ) ) )
| ~ ~ ( sK6_SY66 @ SY77 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SY77 ) )
| ( SV1 @ SY77 ) ) )
= $false )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( ~ ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
= $false )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) )
| ~ ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i > $o] :
( ( ( ! [SY77: $i] :
( ~ ( ~ ~ ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY79 )
| ~ ( sK6_SY66 @ SY77 @ SV1 @ SY79 @ SY80 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY78 @ SY80 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ~ ( sK1_SY0 @ SY81 @ SY82 )
| ( sK6_SY66 @ SY77 @ SV1 @ SY81 @ SY82 ) ) )
| ~ ~ ( sK6_SY66 @ SY77 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SY77 ) )
| ( SV1 @ SY77 ) ) )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: $i] :
( ( ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) )
| ~ ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
| ~ ~ ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 ) )
| ( SV1 @ SV3 ) )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY49 @ SV1 ) )
= $false )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i] :
( ( ( ~ ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i] :
( ( ( ~ ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) ) )
= $false )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
| ~ ~ ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( SV1 @ ( sK5_SY49 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i] :
( ( ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) )
= $true )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) )
= $true )
| ( ( ~ ( sK2_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
| ~ ~ ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( sK2_SY58 @ SV2 )
= $false )
| ( ( sK2_SY58 @ ( sK3_SY64 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( sK2_SY58 @ SV2 )
= $false )
| ( ( sK1_SY0 @ SV2 @ ( sK3_SY64 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ~ ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ~ ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) )
| ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ~ ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
= $false )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV5: $i,SV1: $i > $o] :
( ( ( SV1 @ SV5 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ ( sK5_SY49 @ SV1 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY85 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY85 @ SY86 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY84 @ SY86 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: $i > $o,SV3: $i] :
( ( ( ! [SY87: $i,SY88: $i] :
( ~ ( sK1_SY0 @ SY87 @ SY88 )
| ( sK6_SY66 @ SV3 @ SV1 @ SY87 @ SY88 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( ! [SY89: $i,SY90: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SY89 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SY89 @ SY90 )
| ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SY90 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV1: $i > $o,SV3: $i,SV7: $i] :
( ( ( ! [SY91: $i] :
( ~ ( sK1_SY0 @ SV7 @ SY91 )
| ( sK6_SY66 @ SV3 @ SV1 @ SV7 @ SY91 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV8: $i,SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( ! [SY92: $i] :
( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SY92 )
| ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SY92 ) ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV1: $i > $o,SV3: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( sK1_SY0 @ SV7 @ SV9 )
| ( sK6_SY66 @ SV3 @ SV1 @ SV7 @ SV9 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(55,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 )
| ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 ) )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV1: $i > $o,SV3: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( sK1_SY0 @ SV7 @ SV9 ) )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV7 @ SV9 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
| ~ ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 ) )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV1: $i > $o,SV3: $i,SV9: $i,SV7: $i] :
( ( ( sK1_SY0 @ SV7 @ SV9 )
= $false )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV7 @ SV9 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 ) )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i,SV1: $i > $o] :
( ( ( SV1 @ SV11 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV7 @ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV10: $i,SV8: $i,SV6: $i,SV1: $i > $o,SV3: $i] :
( ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 ) )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV6: $i,SV10: $i,SV8: $i,SV1: $i > $o,SV3: $i] :
( ( ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 )
= $false )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( ! [SY83: $i] : ( SV1 @ SY83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i,SV12: $i,SV1: $i > $o] :
( ( ( SV1 @ SV12 )
= $true )
| ( ( SV1 @ SV3 )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV6 @ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3 @ SV1 @ SV8 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV4: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV4 ) )
= $true )
| ( ( ~ ( SV15
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[34:[bind(SV1,$thf( ^ [SV14: $i] : ~ ( SV15 @ SV14 ) ))]]) ).
thf(69,plain,
! [SV3: $i] :
( ( $false = $true )
| ( $false = $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ ( sK5_SY49
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV16: $i] : $false ))]]) ).
thf(70,plain,
! [SV3: $i,SV5: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV5 ) )
= $true )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV14: $i] : ~ ( SV15 @ SV14 ) ))]]) ).
thf(71,plain,
! [SV3: $i,SV5: $i] :
( ( ( SV5 = sK4_SY62 )
= $true )
| ( ( SV3 = sK4_SY62 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 )
@ ( sK5_SY49
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 ) )
@ SV3 )
= $false ) ),
inference(prim_subst,[status(thm)],[48:[bind(SV1,$thf( ^ [SV13: $i] : ( SV13 = sK4_SY62 ) ))]]) ).
thf(73,plain,
! [SV9: $i,SV7: $i,SV3: $i] :
( ( $false = $true )
| ( $false = $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(prim_subst,[status(thm)],[60:[bind(SV1,$thf( ^ [SV16: $i] : $false ))]]) ).
thf(74,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV11 ) )
= $true )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(prim_subst,[status(thm)],[60:[bind(SV1,$thf( ^ [SV14: $i] : ~ ( SV15 @ SV14 ) ))]]) ).
thf(75,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i] :
( ( ( SV11 = sK4_SY62 )
= $true )
| ( ( SV3 = sK4_SY62 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 )
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(prim_subst,[status(thm)],[60:[bind(SV1,$thf( ^ [SV13: $i] : ( SV13 = sK4_SY62 ) ))]]) ).
thf(77,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i] :
( ( $false = $true )
| ( $false = $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV8
@ SV10 )
= $false ) ),
inference(prim_subst,[status(thm)],[63:[bind(SV1,$thf( ^ [SV16: $i] : $false ))]]) ).
thf(78,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i,SV12: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV12 ) )
= $true )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV8
@ SV10 )
= $false ) ),
inference(prim_subst,[status(thm)],[63:[bind(SV1,$thf( ^ [SV14: $i] : ~ ( SV15 @ SV14 ) ))]]) ).
thf(79,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i,SV12: $i] :
( ( ( SV12 = sK4_SY62 )
= $true )
| ( ( SV3 = sK4_SY62 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 )
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 )
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : ( SX0 = sK4_SY62 )
@ SV8
@ SV10 )
= $false ) ),
inference(prim_subst,[status(thm)],[63:[bind(SV1,$thf( ^ [SV13: $i] : ( SV13 = sK4_SY62 ) ))]]) ).
thf(80,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( ( SV1 @ SV4 )
= ( ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[34]) ).
thf(81,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ SV4 )
| ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
| ~ ( ~ ( SV1 @ SV4 )
| ~ ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[80]) ).
thf(82,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( ( SV1 @ SV4 )
= ( ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[80]) ).
thf(83,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( ~ ( ( SV1 @ SV4 )
| ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( ( SV1 @ SV4 )
| ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( ~ ( SV1 @ ( sK5_SY49 @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(89,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY49 @ SV1 ) )
= $false )
| ( ( SV1 @ SV4 )
= $true )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ~ ~ ~ ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[82:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( ~ ( SV32 @ SX0 ) ) ) ) ) ))]]) ).
thf(96,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( ~ ~ ~ ~ ( SV29 @ SV4 ) )
= $true )
| ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[82:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( ~ ( SV29 @ SX0 ) ) ) ) ))]]) ).
thf(97,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( ~ ~ ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[82:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( ~ ( SV26 @ SX0 ) ) ) ))]]) ).
thf(100,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( ~ ~ ( SV23 @ SV4 ) )
= $true )
| ( ( ~ ( SV23 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[82:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( ~ ( SV23 @ SX0 ) ) ))]]) ).
thf(101,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( ~ ( SV20 @ SV4 ) )
= $true )
| ( ( ~ ( SV20 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[82:[bind(SV1,$thf( ^ [SX0: $i] : ~ ( SV20 @ SX0 ) ))]]) ).
thf(104,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( SV20 @ SV4 )
= $false )
| ( ( ~ ( SV20 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(105,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ SV4 ) )
= $false )
| ( ( ~ ( SV23 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( ~ ~ ( SV26 @ SV4 ) )
= $false )
| ( ( ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( ~ ~ ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ~ ~ ~ ( SV32 @ SV4 ) )
= $false )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( SV20 @ SV4 )
= $false )
| ( ( SV20 @ SV4 )
= $false )
| ( ( ~ ~ ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( SV23 @ SV4 )
= $true )
| ( ( ~ ( SV23 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(118,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( ~ ~ ( SV29 @ SV4 ) )
= $true )
| ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(122,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ~ ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(124,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( ~ ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) ) )
= $false )
| ( ( SV20 @ SV4 )
= $false )
| ( ( SV20 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( SV23 @ SV4 )
= $true )
| ( ( SV23 @ SV4 )
= $true )
| ( ( ~ ~ ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(128,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( SV26 @ SV4 )
= $false )
| ( ( ~ ( SV26 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ~ ( SV32 @ SV4 ) )
= $false )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) )
= $true )
| ( ( SV20 @ SV4 )
= $false )
| ( ( SV20 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( ~ ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) ) )
= $true )
| ( ( SV23 @ SV4 )
= $true )
| ( ( SV23 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(138,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( SV26 @ SV4 )
= $false )
| ( ( SV26 @ SV4 )
= $false )
| ( ( ~ ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( SV29 @ SV4 )
= $true )
| ( ( ~ ( SV29 @ SV4 ) )
= $false )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(143,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) )
= $false )
| ( ( SV23 @ SV4 )
= $true )
| ( ( SV23 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( ~ ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) ) )
= $false )
| ( ( SV26 @ SV4 )
= $false )
| ( ( SV26 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( SV29 @ SV4 )
= $true )
| ( ( SV29 @ SV4 )
= $true )
| ( ( ~ ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(150,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( SV32 @ SV4 )
= $false )
| ( ( ~ ( SV32 @ SV4 ) )
= $true )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) )
= $true )
| ( ( SV26 @ SV4 )
= $false )
| ( ( SV26 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(153,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( ~ ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) ) )
= $true )
| ( ( SV29 @ SV4 )
= $true )
| ( ( SV29 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( SV32 @ SV4 )
= $false )
| ( ( SV32 @ SV4 )
= $false )
| ( ( ~ ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) )
= $false )
| ( ( SV29 @ SV4 )
= $true )
| ( ( SV29 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( ~ ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) ) )
= $false )
| ( ( SV32 @ SV4 )
= $false )
| ( ( SV32 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) )
= $true )
| ( ( SV32 @ SV4 )
= $false )
| ( ( SV32 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(163,plain,
! [SV4: $i,SV15: $i > $o] :
( ( ( SV15 @ SV4 )
= $false )
| ( ( ~ ( SV15
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(164,plain,
! [SV3: $i,SV5: $i,SV15: $i > $o] :
( ( ( SV15 @ SV5 )
= $false )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(165,plain,
! [SV9: $i,SV7: $i,SV3: $i,SV11: $i,SV15: $i > $o] :
( ( ( SV15 @ SV11 )
= $false )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(166,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i,SV12: $i,SV15: $i > $o] :
( ( ( SV15 @ SV12 )
= $false )
| ( ( ~ ( SV15 @ SV3 ) )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV8
@ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(167,plain,
! [SV4: $i,SV15: $i > $o] :
( ( ( SV15
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(168,plain,
! [SV5: $i,SV3: $i,SV15: $i > $o] :
( ( ( SV15 @ SV3 )
= $false )
| ( ( SV15 @ SV5 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 ) )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV9: $i,SV7: $i,SV11: $i,SV3: $i,SV15: $i > $o] :
( ( ( SV15 @ SV3 )
= $false )
| ( ( SV15 @ SV11 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV12: $i,SV3: $i,SV15: $i > $o] :
( ( ( SV15 @ SV3 )
= $false )
| ( ( SV15 @ SV12 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] :
~ ( SV15 @ SX0 )
@ SV8
@ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ ( sK5_SY49 @ SV1 ) )
= $false )
| ( ( SV1 @ SV4 )
= $true ) ),
inference(sim,[status(thm)],[89]) ).
thf(172,plain,
! [SV4: $i,SV20: $i > $o] :
( ( ( SV20
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ( SV20 @ SX0 ) ) )
= $true )
| ( ( SV20 @ SV4 )
= $false ) ),
inference(sim,[status(thm)],[134]) ).
thf(173,plain,
! [SV4: $i,SV23: $i > $o] :
( ( ( SV23
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ( SV23 @ SX0 ) ) )
= $false )
| ( ( SV23 @ SV4 )
= $true ) ),
inference(sim,[status(thm)],[143]) ).
thf(174,plain,
! [SV4: $i,SV26: $i > $o] :
( ( ( SV26
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ( SV26 @ SX0 ) ) )
= $true )
| ( ( SV26 @ SV4 )
= $false ) ),
inference(sim,[status(thm)],[152]) ).
thf(175,plain,
! [SV4: $i,SV29: $i > $o] :
( ( ( SV29
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ( SV29 @ SX0 ) ) )
= $false )
| ( ( SV29 @ SV4 )
= $true ) ),
inference(sim,[status(thm)],[157]) ).
thf(176,plain,
! [SV4: $i,SV32: $i > $o] :
( ( ( SV32
@ ( sK5_SY49
@ ^ [SX0: $i] :
~ ~ ~ ~ ~ ( SV32 @ SX0 ) ) )
= $true )
| ( ( SV32 @ SV4 )
= $false ) ),
inference(sim,[status(thm)],[162]) ).
thf(177,plain,
! [SV3: $i] :
( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ ( sK5_SY49
@ ^ [SX0: $i] : $false )
@ SV3 )
= $false ),
inference(sim,[status(thm)],[69]) ).
thf(178,plain,
! [SV9: $i,SV7: $i,SV3: $i] :
( ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV7
@ SV9 )
= $true )
| ( ( sK1_SY0 @ SV7 @ SV9 )
= $false ) ),
inference(sim,[status(thm)],[73]) ).
thf(179,plain,
! [SV8: $i,SV10: $i,SV6: $i,SV3: $i] :
( ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV6
@ SV10 )
= $true )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV6
@ SV8 )
= $false )
| ( ( sK6_SY66 @ SV3
@ ^ [SX0: $i] : $false
@ SV8
@ SV10 )
= $false ) ),
inference(sim,[status(thm)],[77]) ).
thf(180,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,179,178,177,176,175,174,173,172,171,170,169,168,167,79,75,71,63,60,48,39,38,34]) ).
thf(181,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU481^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.19 % Computer : n016.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Oct 6 15:30:34 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 90.69/15.43
% 90.69/15.43 No.of.Axioms: 0
% 90.69/15.43
% 90.69/15.43 Length.of.Defs: 5125
% 90.69/15.43
% 90.69/15.43 Contains.Choice.Funs: false
% 90.69/15.43 ...eprover: CPU time limit exceeded, terminating
% 90.69/15.43 .
% 90.69/15.43
% 90.69/15.43 ********************************
% 90.69/15.43 * All subproblems solved! *
% 90.69/15.43 ********************************
% 90.69/15.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:180,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 90.69/15.43
% 90.69/15.43 %**** Beginning of derivation protocol ****
% 90.69/15.43 % SZS output start CNFRefutation
% See solution above
% 90.69/15.43
% 90.69/15.43 %**** End of derivation protocol ****
% 90.69/15.43 %**** no. of clauses in derivation: 134 ****
% 90.69/15.43 %**** clause counter: 180 ****
% 90.69/15.43
% 90.69/15.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:180,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------