%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU463^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:44:32 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 30
% Syntax : Number of formulae : 138 ( 61 unt; 0 typ; 29 def)
% Number of atoms : 741 ( 281 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2059 ( 262 ~; 273 |; 76 &;1360 @)
% ( 0 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 277 ( 277 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 5 con; 0-3 aty)
% Number of variables : 497 ( 43 ^; 449 !; 5 ?; 497 :)
% 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_sK10_SY196,type,
sK10_SY196: ( $i > $i > $o ) > $i ).
thf(tp_sK11_SY197,type,
sK11_SY197: ( $i > $i > $o ) > $i ).
thf(tp_sK12_SY181,type,
sK12_SY181: ( $i > $i > $o ) > $i ).
thf(tp_sK13_SY186,type,
sK13_SY186: ( $i > $i > $o ) > $i ).
thf(tp_sK14_SY198,type,
sK14_SY198: ( $i > $i > $o ) > $i ).
thf(tp_sK15_SY199,type,
sK15_SY199: ( $i > $i > $o ) > $i ).
thf(tp_sK16_SY181,type,
sK16_SY181: ( $i > $i > $o ) > $i ).
thf(tp_sK17_SY181,type,
sK17_SY181: ( $i > $i > $o ) > $i ).
thf(tp_sK18_SY186,type,
sK18_SY186: ( $i > $i > $o ) > $i ).
thf(tp_sK19_SY186,type,
sK19_SY186: ( $i > $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK20_SY200,type,
sK20_SY200: ( $i > $i > $o ) > $i ).
thf(tp_sK21_SY201,type,
sK21_SY201: ( $i > $i > $o ) > $i ).
thf(tp_sK22_SY202,type,
sK22_SY202: ( $i > $i > $o ) > $i ).
thf(tp_sK23_SY203,type,
sK23_SY203: ( $i > $i > $o ) > $i ).
thf(tp_sK2_SY83,type,
sK2_SY83: $i ).
thf(tp_sK3_SY104,type,
sK3_SY104: $i ).
thf(tp_sK4_SY124,type,
sK4_SY124: $i ).
thf(tp_sK5_SY143,type,
sK5_SY143: $i > $i > $o ).
thf(tp_sK6_SY178,type,
sK6_SY178: ( $i > $i > $o ) > $i ).
thf(tp_sK7_SY183,type,
sK7_SY183: ( $i > $i > $o ) > $i ).
thf(tp_sK8_SY192,type,
sK8_SY192: ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY194,type,
sK9_SY194: ( $i > $i > $o ) > $i ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',inflationary) ).
thf(innf,definition,
( innf
= ( ^ [R: $i > $i > $o,X: $i] :
~ ? [Y: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_normal_form) ).
thf(inv,definition,
( inv
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
thf(irrefl,definition,
( irrefl
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',normalizing) ).
thf(po,definition,
( po
= ( ^ [R: $i > $i > $o] :
( ( refl @ R )
& ( antisymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',reflexive_closure) ).
thf(refl,definition,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',semi_confluent) ).
thf(so,definition,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',transitive) ).
thf(trc,definition,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_closure) ).
thf(trsc,definition,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure) ).
thf(1,conjecture,
! [R: $i > $i > $o,X: $i,Y: $i,Z: $i,S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S )
& ( tc @ R @ X @ Y )
& ( tc @ R @ Y @ Z ) )
=> ( S @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive3) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o,X: $i,Y: $i,Z: $i,S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S )
& ( tc @ R @ X @ Y )
& ( tc @ R @ Y @ Z ) )
=> ( S @ X @ Z ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o,SY1: $i,SY2: $i,SY3: $i,SY4: $i > $i > $o] :
( ( ! [SY5: $i,SY6: $i,SY7: $i] :
( ( ( SY4 @ SY5 @ SY6 )
& ( SY4 @ SY6 @ SY7 ) )
=> ( SY4 @ SY5 @ SY7 ) )
& ! [SY11: $i,SY12: $i] :
( ( SY0 @ SY11 @ SY12 )
=> ( SY4 @ SY11 @ SY12 ) )
& ! [SY31: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY31 @ SY16 @ SY17 )
& ( SY31 @ SY17 @ SY18 ) )
=> ( SY31 @ SY16 @ SY18 ) )
& ! [SY22: $i,SY23: $i] :
( ( SY0 @ SY22 @ SY23 )
=> ( SY31 @ SY22 @ SY23 ) ) )
=> ( SY31 @ SY1 @ SY2 ) )
& ! [SY55: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY55 @ SY40 @ SY41 )
& ( SY55 @ SY41 @ SY42 ) )
=> ( SY55 @ SY40 @ SY42 ) )
& ! [SY46: $i,SY47: $i] :
( ( SY0 @ SY46 @ SY47 )
=> ( SY55 @ SY46 @ SY47 ) ) )
=> ( SY55 @ SY2 @ SY3 ) ) )
=> ( SY4 @ SY1 @ SY3 ) ) )
= $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,
( ( ! [SY83: $i,SY84: $i,SY85: $i,SY86: $i > $i > $o] :
( ( ! [SY5: $i,SY6: $i,SY7: $i] :
( ( ( SY86 @ SY5 @ SY6 )
& ( SY86 @ SY6 @ SY7 ) )
=> ( SY86 @ SY5 @ SY7 ) )
& ! [SY90: $i,SY91: $i] :
( ( sK1_SY0 @ SY90 @ SY91 )
=> ( SY86 @ SY90 @ SY91 ) )
& ! [SY92: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY92 @ SY16 @ SY17 )
& ( SY92 @ SY17 @ SY18 ) )
=> ( SY92 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY92 @ SY96 @ SY97 ) ) )
=> ( SY92 @ SY83 @ SY84 ) )
& ! [SY98: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY98 @ SY40 @ SY41 )
& ( SY98 @ SY41 @ SY42 ) )
=> ( SY98 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY98 @ SY102 @ SY103 ) ) )
=> ( SY98 @ SY84 @ SY85 ) ) )
=> ( SY86 @ SY83 @ SY85 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY104: $i,SY105: $i,SY106: $i > $i > $o] :
( ( ! [SY5: $i,SY6: $i,SY7: $i] :
( ( ( SY106 @ SY5 @ SY6 )
& ( SY106 @ SY6 @ SY7 ) )
=> ( SY106 @ SY5 @ SY7 ) )
& ! [SY90: $i,SY91: $i] :
( ( sK1_SY0 @ SY90 @ SY91 )
=> ( SY106 @ SY90 @ SY91 ) )
& ! [SY112: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY112 @ SY16 @ SY17 )
& ( SY112 @ SY17 @ SY18 ) )
=> ( SY112 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY112 @ SY96 @ SY97 ) ) )
=> ( SY112 @ sK2_SY83 @ SY104 ) )
& ! [SY98: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY98 @ SY40 @ SY41 )
& ( SY98 @ SY41 @ SY42 ) )
=> ( SY98 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY98 @ SY102 @ SY103 ) ) )
=> ( SY98 @ SY104 @ SY105 ) ) )
=> ( SY106 @ sK2_SY83 @ SY105 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY124: $i,SY125: $i > $i > $o] :
( ( ! [SY5: $i,SY6: $i,SY7: $i] :
( ( ( SY125 @ SY5 @ SY6 )
& ( SY125 @ SY6 @ SY7 ) )
=> ( SY125 @ SY5 @ SY7 ) )
& ! [SY90: $i,SY91: $i] :
( ( sK1_SY0 @ SY90 @ SY91 )
=> ( SY125 @ SY90 @ SY91 ) )
& ! [SY131: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY131 @ SY16 @ SY17 )
& ( SY131 @ SY17 @ SY18 ) )
=> ( SY131 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY131 @ SY96 @ SY97 ) ) )
=> ( SY131 @ sK2_SY83 @ sK3_SY104 ) )
& ! [SY137: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY137 @ SY40 @ SY41 )
& ( SY137 @ SY41 @ SY42 ) )
=> ( SY137 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY137 @ SY102 @ SY103 ) ) )
=> ( SY137 @ sK3_SY104 @ SY124 ) ) )
=> ( SY125 @ sK2_SY83 @ SY124 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY143: $i > $i > $o] :
( ( ! [SY5: $i,SY6: $i,SY7: $i] :
( ( ( SY143 @ SY5 @ SY6 )
& ( SY143 @ SY6 @ SY7 ) )
=> ( SY143 @ SY5 @ SY7 ) )
& ! [SY90: $i,SY91: $i] :
( ( sK1_SY0 @ SY90 @ SY91 )
=> ( SY143 @ SY90 @ SY91 ) )
& ! [SY131: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY131 @ SY16 @ SY17 )
& ( SY131 @ SY17 @ SY18 ) )
=> ( SY131 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY131 @ SY96 @ SY97 ) ) )
=> ( SY131 @ sK2_SY83 @ sK3_SY104 ) )
& ! [SY155: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY155 @ SY40 @ SY41 )
& ( SY155 @ SY41 @ SY42 ) )
=> ( SY155 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY155 @ SY102 @ SY103 ) ) )
=> ( SY155 @ sK3_SY104 @ sK4_SY124 ) ) )
=> ( SY143 @ sK2_SY83 @ sK4_SY124 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ( ( sK5_SY143 @ SY161 @ SY162 )
& ( sK5_SY143 @ SY162 @ SY163 ) )
=> ( sK5_SY143 @ SY161 @ SY163 ) )
& ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( sK5_SY143 @ SY164 @ SY165 ) )
& ! [SY131: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY131 @ SY16 @ SY17 )
& ( SY131 @ SY17 @ SY18 ) )
=> ( SY131 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY131 @ SY96 @ SY97 ) ) )
=> ( SY131 @ sK2_SY83 @ sK3_SY104 ) )
& ! [SY155: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY155 @ SY40 @ SY41 )
& ( SY155 @ SY41 @ SY42 ) )
=> ( SY155 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY155 @ SY102 @ SY103 ) ) )
=> ( SY155 @ sK3_SY104 @ sK4_SY124 ) ) )
=> ( sK5_SY143 @ sK2_SY83 @ sK4_SY124 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ( ( sK5_SY143 @ SY161 @ SY162 )
& ( sK5_SY143 @ SY162 @ SY163 ) )
=> ( sK5_SY143 @ SY161 @ SY163 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( sK5_SY143 @ SY164 @ SY165 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SY131: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY131 @ SY16 @ SY17 )
& ( SY131 @ SY17 @ SY18 ) )
=> ( SY131 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY131 @ SY96 @ SY97 ) ) )
=> ( SY131 @ sK2_SY83 @ sK3_SY104 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [SY155: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY155 @ SY40 @ SY41 )
& ( SY155 @ SY41 @ SY42 ) )
=> ( SY155 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY155 @ SY102 @ SY103 ) ) )
=> ( SY155 @ sK3_SY104 @ sK4_SY124 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(13,plain,
( ( sK5_SY143 @ sK2_SY83 @ sK4_SY124 )
= $false ),
inference(standard_cnf,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( sK5_SY143 @ sK2_SY83 @ sK4_SY124 ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SY155: $i > $i > $o] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ( ( SY155 @ SY40 @ SY41 )
& ( SY155 @ SY41 @ SY42 ) )
=> ( SY155 @ SY40 @ SY42 ) )
& ! [SY102: $i,SY103: $i] :
( ( sK1_SY0 @ SY102 @ SY103 )
=> ( SY155 @ SY102 @ SY103 ) ) )
=> ( SY155 @ sK3_SY104 @ sK4_SY124 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SY131: $i > $i > $o] :
( ( ! [SY16: $i,SY17: $i,SY18: $i] :
( ( ( SY131 @ SY16 @ SY17 )
& ( SY131 @ SY17 @ SY18 ) )
=> ( SY131 @ SY16 @ SY18 ) )
& ! [SY96: $i,SY97: $i] :
( ( sK1_SY0 @ SY96 @ SY97 )
=> ( SY131 @ SY96 @ SY97 ) ) )
=> ( SY131 @ sK2_SY83 @ sK3_SY104 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( sK5_SY143 @ SY164 @ SY165 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(18,plain,
( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ( ( sK5_SY143 @ SY161 @ SY162 )
& ( sK5_SY143 @ SY162 @ SY163 ) )
=> ( sK5_SY143 @ SY161 @ SY163 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ~ ( sK5_SY143 @ sK2_SY83 @ sK4_SY124 ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX1 @ SX2 ) ) )
| ( SX0 @ sK3_SY104 @ sK4_SY124 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,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(21,plain,
( ( ! [SX0: $i > $i > $o] :
( ~ ~ ( ~ ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( SX0 @ SX1 @ SX2 )
| ~ ( SX0 @ SX2 @ SX3 ) )
| ( SX0 @ SX1 @ SX3 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( sK1_SY0 @ SX1 @ SX2 )
| ( SX0 @ SX1 @ SX2 ) ) )
| ( SX0 @ sK2_SY83 @ sK3_SY104 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,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(22,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ( sK5_SY143 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,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(23,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( sK5_SY143 @ SX0 @ SX1 )
| ~ ( sK5_SY143 @ SX1 @ SX2 ) )
| ( sK5_SY143 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,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(24,plain,
( ( sK5_SY143 @ sK2_SY83 @ sK4_SY124 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV1: $i > $i > $o] :
( ( ~ ~ ( ~ ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
| ( SV1 @ sK3_SY104 @ sK4_SY124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV2: $i > $i > $o] :
( ( ~ ~ ( ~ ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
| ( SV2 @ sK2_SY83 @ sK3_SY104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY188: $i] :
( ~ ( sK1_SY0 @ SV3 @ SY188 )
| ( sK5_SY143 @ SV3 @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ~ ~ ( ~ ( sK5_SY143 @ SV4 @ SY189 )
| ~ ( sK5_SY143 @ SY189 @ SY190 ) )
| ( sK5_SY143 @ SV4 @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ( sK1_SY0 @ SV3 @ SV5 )
| ( sK5_SY143 @ SV3 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV6: $i,SV4: $i] :
( ( ! [SY191: $i] :
( ~ ~ ( ~ ( sK5_SY143 @ SV4 @ SV6 )
| ~ ( sK5_SY143 @ SV6 @ SY191 ) )
| ( sK5_SY143 @ SV4 @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( sK1_SY0 @ SV3 @ SV5 ) )
= $true )
| ( ( sK5_SY143 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ~ ~ ( ~ ( sK5_SY143 @ SV4 @ SV6 )
| ~ ( sK5_SY143 @ SV6 @ SV7 ) )
| ( sK5_SY143 @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) )
| ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: $i,SV3: $i] :
( ( ( sK1_SY0 @ SV3 @ SV5 )
= $false )
| ( ( sK5_SY143 @ SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( sK5_SY143 @ SV4 @ SV6 )
| ~ ( sK5_SY143 @ SV6 @ SV7 ) ) )
= $true )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) ) )
= $true )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) ) )
= $true )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( ~ ( sK5_SY143 @ SV4 @ SV6 )
| ~ ( sK5_SY143 @ SV6 @ SV7 ) ) )
= $false )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ( SV1 @ SY178 @ SY179 )
| ~ ( SV1 @ SY179 @ SY180 ) )
| ( SV1 @ SY178 @ SY180 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ( SV2 @ SY183 @ SY184 )
| ~ ( SV2 @ SY184 @ SY185 ) )
| ( SV2 @ SY183 @ SY185 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( sK5_SY143 @ SV4 @ SV6 )
| ~ ( sK5_SY143 @ SV6 @ SV7 ) )
= $true )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY192: $i,SY193: $i] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ SY192 )
| ~ ( SV1 @ SY192 @ SY193 ) )
| ( SV1 @ ( sK6_SY178 @ SV1 ) @ SY193 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(48,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY194: $i,SY195: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ SY194 )
| ~ ( SV2 @ SY194 @ SY195 ) )
| ( SV2 @ ( sK7_SY183 @ SV2 ) @ SY195 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(49,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( sK5_SY143 @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( sK5_SY143 @ SV6 @ SV7 ) )
= $true )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY196: $i] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ SY196 ) )
| ( SV1 @ ( sK6_SY178 @ SV1 ) @ SY196 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(51,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY197: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ SY197 ) )
| ( SV2 @ ( sK7_SY183 @ SV2 ) @ SY197 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(52,plain,
! [SV7: $i,SV6: $i,SV4: $i] :
( ( ( sK5_SY143 @ SV4 @ SV6 )
= $false )
| ( ( ~ ( sK5_SY143 @ SV6 @ SV7 ) )
= $true )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) )
| ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(54,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) )
| ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(55,plain,
! [SV4: $i,SV7: $i,SV6: $i] :
( ( ( sK5_SY143 @ SV6 @ SV7 )
= $false )
| ( ( sK5_SY143 @ SV4 @ SV6 )
= $false )
| ( ( sK5_SY143 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) ) )
= $true )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) ) )
= $true )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY198: $i] :
( ~ ( sK1_SY0 @ ( sK12_SY181 @ SV1 ) @ SY198 )
| ( SV1 @ ( sK12_SY181 @ SV1 ) @ SY198 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(66,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY199: $i] :
( ~ ( sK1_SY0 @ ( sK13_SY186 @ SV2 ) @ SY199 )
| ( SV2 @ ( sK13_SY186 @ SV2 ) @ SY199 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(68,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK12_SY181 @ SV1 ) @ ( sK14_SY198 @ SV1 ) )
| ( SV1 @ ( sK12_SY181 @ SV1 ) @ ( sK14_SY198 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(71,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK13_SY186 @ SV2 ) @ ( sK15_SY199 @ SV2 ) )
| ( SV2 @ ( sK13_SY186 @ SV2 ) @ ( sK15_SY199 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(74,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(75,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( ~ ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(76,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK12_SY181 @ SV1 ) @ ( sK14_SY198 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK12_SY181 @ SV1 ) @ ( sK14_SY198 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( ~ ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(80,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK13_SY186 @ SV2 ) @ ( sK15_SY199 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(81,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK13_SY186 @ SV2 ) @ ( sK15_SY199 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY181: $i,SY182: $i] :
( ~ ( sK1_SY0 @ SY181 @ SY182 )
| ( SV1 @ SY181 @ SY182 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK12_SY181 @ SV1 ) @ ( sK14_SY198 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $false )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY186: $i,SY187: $i] :
( ~ ( sK1_SY0 @ SY186 @ SY187 )
| ( SV2 @ SY186 @ SY187 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK13_SY186 @ SV2 ) @ ( sK15_SY199 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY200: $i] :
( ~ ( sK1_SY0 @ ( sK16_SY181 @ SV1 ) @ SY200 )
| ( SV1 @ ( sK16_SY181 @ SV1 ) @ SY200 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[82]) ).
thf(89,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY201: $i] :
( ~ ( sK1_SY0 @ ( sK17_SY181 @ SV1 ) @ SY201 )
| ( SV1 @ ( sK17_SY181 @ SV1 ) @ SY201 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(90,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY202: $i] :
( ~ ( sK1_SY0 @ ( sK18_SY186 @ SV2 ) @ SY202 )
| ( SV2 @ ( sK18_SY186 @ SV2 ) @ SY202 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(91,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY203: $i] :
( ~ ( sK1_SY0 @ ( sK19_SY186 @ SV2 ) @ SY203 )
| ( SV2 @ ( sK19_SY186 @ SV2 ) @ SY203 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(92,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK16_SY181 @ SV1 ) @ ( sK20_SY200 @ SV1 ) )
| ( SV1 @ ( sK16_SY181 @ SV1 ) @ ( sK20_SY200 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(93,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK17_SY181 @ SV1 ) @ ( sK21_SY201 @ SV1 ) )
| ( SV1 @ ( sK17_SY181 @ SV1 ) @ ( sK21_SY201 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(94,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK18_SY186 @ SV2 ) @ ( sK22_SY202 @ SV2 ) )
| ( SV2 @ ( sK18_SY186 @ SV2 ) @ ( sK22_SY202 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(95,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK19_SY186 @ SV2 ) @ ( sK23_SY203 @ SV2 ) )
| ( SV2 @ ( sK19_SY186 @ SV2 ) @ ( sK23_SY203 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(96,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK16_SY181 @ SV1 ) @ ( sK20_SY200 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK16_SY181 @ SV1 ) @ ( sK20_SY200 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK17_SY181 @ SV1 ) @ ( sK21_SY201 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(99,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK17_SY181 @ SV1 ) @ ( sK21_SY201 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK18_SY186 @ SV2 ) @ ( sK22_SY202 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK18_SY186 @ SV2 ) @ ( sK22_SY202 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(102,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK19_SY186 @ SV2 ) @ ( sK23_SY203 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK19_SY186 @ SV2 ) @ ( sK23_SY203 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(104,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK16_SY181 @ SV1 ) @ ( sK20_SY200 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK6_SY178 @ SV1 ) @ ( sK8_SY192 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK17_SY181 @ SV1 ) @ ( sK21_SY201 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK8_SY192 @ SV1 ) @ ( sK10_SY196 @ SV1 ) )
= $true )
| ( ( SV1 @ sK3_SY104 @ sK4_SY124 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK18_SY186 @ SV2 ) @ ( sK22_SY202 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK7_SY183 @ SV2 ) @ ( sK9_SY194 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(107,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK19_SY186 @ SV2 ) @ ( sK23_SY203 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK9_SY194 @ SV2 ) @ ( sK11_SY197 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY83 @ sK3_SY104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(108,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,107,106,105,104,103,101,99,97,87,84,81,77,55,39]) ).
thf(109,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU463^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n005.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:25:19 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.24
% 0.10/0.24 No.of.Axioms: 0
% 0.10/0.24
% 0.10/0.24 Length.of.Defs: 5096
% 0.10/0.24
% 0.10/0.24 Contains.Choice.Funs: false
% 0.10/0.24 ....
% 0.10/0.24
% 0.10/0.24 ********************************
% 0.10/0.24 * All subproblems solved! *
% 0.10/0.24 ********************************
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.24
% 0.10/0.24 %**** Beginning of derivation protocol ****
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24
% 0.10/0.24 %**** End of derivation protocol ****
% 0.10/0.24 %**** no. of clauses in derivation: 109 ****
% 0.10/0.24 %**** clause counter: 108 ****
% 0.10/0.24
% 0.10/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------