%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU469^1 : 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 : 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 10:44:33 AM UTC 2026
% Result : Theorem 0.48s 0.34s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 30
% Syntax : Number of formulae : 178 ( 89 unt; 0 typ; 29 def)
% Number of atoms : 1214 ( 527 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 3311 ( 688 ~; 627 |; 61 &;1854 @)
% ( 0 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 333 ( 333 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 6 con; 0-3 aty)
% Number of variables : 766 ( 43 ^; 718 !; 5 ?; 766 :)
% 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_SY246,type,
sK10_SY246: ( $i > $i > $o ) > $i ).
thf(tp_sK11_SY247,type,
sK11_SY247: ( $i > $i > $o ) > $i ).
thf(tp_sK12_SY231,type,
sK12_SY231: ( $i > $i > $o ) > $i ).
thf(tp_sK13_SY236,type,
sK13_SY236: ( $i > $i > $o ) > $i ).
thf(tp_sK14_SY248,type,
sK14_SY248: ( $i > $i > $o ) > $i ).
thf(tp_sK15_SY249,type,
sK15_SY249: ( $i > $i > $o ) > $i ).
thf(tp_sK16_SY231,type,
sK16_SY231: ( $i > $i > $o ) > $i ).
thf(tp_sK17_SY231,type,
sK17_SY231: ( $i > $i > $o ) > $i ).
thf(tp_sK18_SY236,type,
sK18_SY236: ( $i > $i > $o ) > $i ).
thf(tp_sK19_SY236,type,
sK19_SY236: ( $i > $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK20_SY250,type,
sK20_SY250: ( $i > $i > $o ) > $i ).
thf(tp_sK21_SY251,type,
sK21_SY251: ( $i > $i > $o ) > $i ).
thf(tp_sK22_SY252,type,
sK22_SY252: ( $i > $i > $o ) > $i ).
thf(tp_sK23_SY253,type,
sK23_SY253: ( $i > $i > $o ) > $i ).
thf(tp_sK24_SX0,type,
sK24_SX0: $i ).
thf(tp_sK25_SY254,type,
sK25_SY254: $i > $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY166,type,
sK3_SY166: $i ).
thf(tp_sK4_SY186,type,
sK4_SY186: $i ).
thf(tp_sK5_SY217,type,
sK5_SY217: $i > $i > $o ).
thf(tp_sK6_SY228,type,
sK6_SY228: ( $i > $i > $o ) > $i ).
thf(tp_sK7_SY233,type,
sK7_SY233: ( $i > $i > $o ) > $i ).
thf(tp_sK8_SY242,type,
sK8_SY242: ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY244,type,
sK9_SY244: ( $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] :
( ( trans @ ( trc @ R ) )
& ( refl @ ( trc @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_closure_is_transitive_reflexive) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o] :
( ( trans @ ( trc @ R ) )
& ( refl @ ( trc @ R ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY27: $i,SY28: $i,SY29: $i] :
( ( ( ( SY27 = SY28 )
| ! [SY37: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY37 @ SY4 @ SY5 )
& ( SY37 @ SY5 @ SY6 ) )
=> ( SY37 @ SY4 @ SY6 ) )
& ! [SY10: $i,SY11: $i] :
( ( SY0 @ SY10 @ SY11 )
=> ( SY37 @ SY10 @ SY11 ) ) )
=> ( SY37 @ SY27 @ SY28 ) ) )
& ( ( SY28 = SY29 )
| ! [SY50: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY50 @ SY4 @ SY5 )
& ( SY50 @ SY5 @ SY6 ) )
=> ( SY50 @ SY4 @ SY6 ) )
& ! [SY10: $i,SY11: $i] :
( ( SY0 @ SY10 @ SY11 )
=> ( SY50 @ SY10 @ SY11 ) ) )
=> ( SY50 @ SY28 @ SY29 ) ) ) )
=> ( ( SY27 = SY29 )
| ! [SY63: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY63 @ SY4 @ SY5 )
& ( SY63 @ SY5 @ SY6 ) )
=> ( SY63 @ SY4 @ SY6 ) )
& ! [SY10: $i,SY11: $i] :
( ( SY0 @ SY10 @ SY11 )
=> ( SY63 @ SY10 @ SY11 ) ) )
=> ( SY63 @ SY27 @ SY29 ) ) ) )
& ! [SY95: $i] :
( ( SY95 = SY95 )
| ! [SY103: $i > $i > $o] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ( ( SY103 @ SY72 @ SY73 )
& ( SY103 @ SY73 @ SY74 ) )
=> ( SY103 @ SY72 @ SY74 ) )
& ! [SY78: $i,SY79: $i] :
( ( SY0 @ SY78 @ SY79 )
=> ( SY103 @ SY78 @ SY79 ) ) )
=> ( SY103 @ SY95 @ SY95 ) ) ) ) )
= $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,
( ( ! [SY138: $i,SY139: $i,SY140: $i] :
( ( ( ( SY138 = SY139 )
| ! [SY141: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY141 @ SY4 @ SY5 )
& ( SY141 @ SY5 @ SY6 ) )
=> ( SY141 @ SY4 @ SY6 ) )
& ! [SY145: $i,SY146: $i] :
( ( sK1_SY0 @ SY145 @ SY146 )
=> ( SY141 @ SY145 @ SY146 ) ) )
=> ( SY141 @ SY138 @ SY139 ) ) )
& ( ( SY139 = SY140 )
| ! [SY147: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY147 @ SY4 @ SY5 )
& ( SY147 @ SY5 @ SY6 ) )
=> ( SY147 @ SY4 @ SY6 ) )
& ! [SY151: $i,SY152: $i] :
( ( sK1_SY0 @ SY151 @ SY152 )
=> ( SY147 @ SY151 @ SY152 ) ) )
=> ( SY147 @ SY139 @ SY140 ) ) ) )
=> ( ( SY138 = SY140 )
| ! [SY153: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY153 @ SY4 @ SY5 )
& ( SY153 @ SY5 @ SY6 ) )
=> ( SY153 @ SY4 @ SY6 ) )
& ! [SY157: $i,SY158: $i] :
( ( sK1_SY0 @ SY157 @ SY158 )
=> ( SY153 @ SY157 @ SY158 ) ) )
=> ( SY153 @ SY138 @ SY140 ) ) ) )
& ! [SY159: $i] :
( ( SY159 = SY159 )
| ! [SY160: $i > $i > $o] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ( ( SY160 @ SY72 @ SY73 )
& ( SY160 @ SY73 @ SY74 ) )
=> ( SY160 @ SY72 @ SY74 ) )
& ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( SY160 @ SY164 @ SY165 ) ) )
=> ( SY160 @ SY159 @ SY159 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY138: $i,SY139: $i,SY140: $i] :
( ( ( ( SY138 = SY139 )
| ! [SY141: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY141 @ SY4 @ SY5 )
& ( SY141 @ SY5 @ SY6 ) )
=> ( SY141 @ SY4 @ SY6 ) )
& ! [SY145: $i,SY146: $i] :
( ( sK1_SY0 @ SY145 @ SY146 )
=> ( SY141 @ SY145 @ SY146 ) ) )
=> ( SY141 @ SY138 @ SY139 ) ) )
& ( ( SY139 = SY140 )
| ! [SY147: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY147 @ SY4 @ SY5 )
& ( SY147 @ SY5 @ SY6 ) )
=> ( SY147 @ SY4 @ SY6 ) )
& ! [SY151: $i,SY152: $i] :
( ( sK1_SY0 @ SY151 @ SY152 )
=> ( SY147 @ SY151 @ SY152 ) ) )
=> ( SY147 @ SY139 @ SY140 ) ) ) )
=> ( ( SY138 = SY140 )
| ! [SY153: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY153 @ SY4 @ SY5 )
& ( SY153 @ SY5 @ SY6 ) )
=> ( SY153 @ SY4 @ SY6 ) )
& ! [SY157: $i,SY158: $i] :
( ( sK1_SY0 @ SY157 @ SY158 )
=> ( SY153 @ SY157 @ SY158 ) ) )
=> ( SY153 @ SY138 @ SY140 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ! [SY159: $i] :
( ( SY159 = SY159 )
| ! [SY160: $i > $i > $o] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ( ( SY160 @ SY72 @ SY73 )
& ( SY160 @ SY73 @ SY74 ) )
=> ( SY160 @ SY72 @ SY74 ) )
& ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( SY160 @ SY164 @ SY165 ) ) )
=> ( SY160 @ SY159 @ SY159 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ! [SY138: $i,SY139: $i,SY140: $i] :
( ( ( ( SY138 = SY139 )
| ! [SY141: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY141 @ SY4 @ SY5 )
& ( SY141 @ SY5 @ SY6 ) )
=> ( SY141 @ SY4 @ SY6 ) )
& ! [SY145: $i,SY146: $i] :
( ( sK1_SY0 @ SY145 @ SY146 )
=> ( SY141 @ SY145 @ SY146 ) ) )
=> ( SY141 @ SY138 @ SY139 ) ) )
& ( ( SY139 = SY140 )
| ! [SY147: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY147 @ SY4 @ SY5 )
& ( SY147 @ SY5 @ SY6 ) )
=> ( SY147 @ SY4 @ SY6 ) )
& ! [SY151: $i,SY152: $i] :
( ( sK1_SY0 @ SY151 @ SY152 )
=> ( SY147 @ SY151 @ SY152 ) ) )
=> ( SY147 @ SY139 @ SY140 ) ) ) )
=> ( ( SY138 = SY140 )
| ! [SY153: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY153 @ SY4 @ SY5 )
& ( SY153 @ SY5 @ SY6 ) )
=> ( SY153 @ SY4 @ SY6 ) )
& ! [SY157: $i,SY158: $i] :
( ( sK1_SY0 @ SY157 @ SY158 )
=> ( SY153 @ SY157 @ SY158 ) ) )
=> ( SY153 @ SY138 @ SY140 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ! [SY159: $i] :
( ( SY159 = SY159 )
| ! [SY160: $i > $i > $o] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ( ( SY160 @ SY72 @ SY73 )
& ( SY160 @ SY73 @ SY74 ) )
=> ( SY160 @ SY72 @ SY74 ) )
& ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( SY160 @ SY164 @ SY165 ) ) )
=> ( SY160 @ SY159 @ SY159 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SY138: $i,SY139: $i,SY140: $i] :
( ( ( ( SY138 = SY139 )
| ! [SY141: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY141 @ SY4 @ SY5 )
& ( SY141 @ SY5 @ SY6 ) )
=> ( SY141 @ SY4 @ SY6 ) )
& ! [SY145: $i,SY146: $i] :
( ( sK1_SY0 @ SY145 @ SY146 )
=> ( SY141 @ SY145 @ SY146 ) ) )
=> ( SY141 @ SY138 @ SY139 ) ) )
& ( ( SY139 = SY140 )
| ! [SY147: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY147 @ SY4 @ SY5 )
& ( SY147 @ SY5 @ SY6 ) )
=> ( SY147 @ SY4 @ SY6 ) )
& ! [SY151: $i,SY152: $i] :
( ( sK1_SY0 @ SY151 @ SY152 )
=> ( SY147 @ SY151 @ SY152 ) ) )
=> ( SY147 @ SY139 @ SY140 ) ) ) )
=> ( ( SY138 = SY140 )
| ! [SY153: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY153 @ SY4 @ SY5 )
& ( SY153 @ SY5 @ SY6 ) )
=> ( SY153 @ SY4 @ SY6 ) )
& ! [SY157: $i,SY158: $i] :
( ( sK1_SY0 @ SY157 @ SY158 )
=> ( SY153 @ SY157 @ SY158 ) ) )
=> ( SY153 @ SY138 @ SY140 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ( SX0 = SX1 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX0 @ SX1 ) ) )
| ~ ( ( SX1 = SX2 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX1 @ SX2 ) ) ) )
| ( SX0 = SX2 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,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(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ( SX0 = SX1 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX0 @ SX1 ) ) )
| ~ ( ( SX1 = SX2 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX1 @ SX2 ) ) ) )
| ( SX0 = SX2 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY166: $i,SY167: $i] :
( ~ ~ ( ~ ( ( sK2_SX0 = SY166 )
| ! [SY168: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY168 @ SX4 @ SX5 )
| ~ ( SY168 @ SX5 @ SX6 ) )
| ( SY168 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY168 @ SX4 @ SX5 ) ) )
| ( SY168 @ sK2_SX0 @ SY166 ) ) )
| ~ ( ( SY166 = SY167 )
| ! [SX3: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SX3 @ SX4 @ SX5 )
| ~ ( SX3 @ SX5 @ SX6 ) )
| ( SX3 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SX3 @ SX4 @ SX5 ) ) )
| ( SX3 @ SY166 @ SY167 ) ) ) )
| ( sK2_SX0 = SY167 )
| ! [SY180: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY180 @ SX4 @ SX5 )
| ~ ( SY180 @ SX5 @ SX6 ) )
| ( SY180 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY180 @ SX4 @ SX5 ) ) )
| ( SY180 @ sK2_SX0 @ SY167 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(13,plain,
( ( ! [SY186: $i] :
( ~ ~ ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
| ~ ( ( sK3_SY166 = SY186 )
| ! [SY193: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY193 @ SX4 @ SX5 )
| ~ ( SY193 @ SX5 @ SX6 ) )
| ( SY193 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY193 @ SX4 @ SX5 ) ) )
| ( SY193 @ sK3_SY166 @ SY186 ) ) ) )
| ( sK2_SX0 = SY186 )
| ! [SY180: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY180 @ SX4 @ SX5 )
| ~ ( SY180 @ SX5 @ SX6 ) )
| ( SY180 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY180 @ SX4 @ SX5 ) ) )
| ( SY180 @ sK2_SX0 @ SY186 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
| ~ ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) ) )
| ( sK2_SX0 = sK4_SY186 )
| ! [SY217: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY217 @ SX4 @ SX5 )
| ~ ( SY217 @ SX5 @ SX6 ) )
| ( SY217 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY217 @ SX4 @ SX5 ) ) )
| ( SY217 @ sK2_SX0 @ sK4_SY186 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( ~ ~ ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
| ~ ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(16,plain,
( ( ( sK2_SX0 = sK4_SY186 )
| ! [SY217: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY217 @ SX4 @ SX5 )
| ~ ( SY217 @ SX5 @ SX6 ) )
| ( SY217 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY217 @ SX4 @ SX5 ) ) )
| ( SY217 @ sK2_SX0 @ sK4_SY186 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
| ~ ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(18,plain,
( ( sK2_SX0 = sK4_SY186 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [SY217: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY217 @ SX4 @ SX5 )
| ~ ( SY217 @ SX5 @ SX6 ) )
| ( SY217 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY217 @ SX4 @ SX5 ) ) )
| ( SY217 @ sK2_SX0 @ sK4_SY186 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
| ~ ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) )
| ~ ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) )
| ( sK5_SY217 @ sK2_SX0 @ sK4_SY186 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(22,plain,
( ( ~ ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ~ ( ~ ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) )
| ~ ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( sK5_SY217 @ sK2_SX0 @ sK4_SY186 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ( sK2_SX0 = sK3_SY166 )
| ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ( sK3_SY166 = sK4_SY186 )
| ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( ~ ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) )
| ~ ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ( sK2_SX0 = sK3_SY166 )
= $true )
| ( ( ! [SY187: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY187 @ SX4 @ SX5 )
| ~ ( SY187 @ SX5 @ SX6 ) )
| ( SY187 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY187 @ SX4 @ SX5 ) ) )
| ( SY187 @ sK2_SX0 @ sK3_SY166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( sK3_SY166 = sK4_SY186 )
= $true )
| ( ( ! [SY211: $i > $i > $o] :
( ~ ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( SY211 @ SX4 @ SX5 )
| ~ ( SY211 @ SX5 @ SX6 ) )
| ( SY211 @ SX4 @ SX6 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( sK1_SY0 @ SX4 @ SX5 )
| ( SY211 @ SX4 @ SX5 ) ) )
| ( SY211 @ sK3_SY166 @ sK4_SY186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) )
| ~ ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) )
| ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
| ( SV1 @ sK2_SX0 @ sK3_SY166 ) )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) )
| ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
| ( SV2 @ sK3_SY166 @ sK4_SY186 ) )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) )
| ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) )
| ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SY223 @ SY224 )
| ~ ( sK5_SY217 @ SY224 @ SY225 ) )
| ( sK5_SY217 @ SY223 @ SY225 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SY226: $i,SY227: $i] :
( ~ ( sK1_SY0 @ SY226 @ SY227 )
| ( sK5_SY217 @ SY226 @ SY227 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) )
| ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) )
| ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SV3 @ SY238 )
| ~ ( sK5_SY217 @ SY238 @ SY239 ) )
| ( sK5_SY217 @ SV3 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i] :
( ( ! [SY240: $i] :
( ~ ( sK1_SY0 @ SV4 @ SY240 )
| ( sK5_SY217 @ SV4 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) )
| ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) )
| ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY241: $i] :
( ~ ~ ( ~ ( sK5_SY217 @ SV3 @ SV5 )
| ~ ( sK5_SY217 @ SV5 @ SY241 ) )
| ( sK5_SY217 @ SV3 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i,SV4: $i] :
( ( ~ ( sK1_SY0 @ SV4 @ SV6 )
| ( sK5_SY217 @ SV4 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) ) )
= $true )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) ) )
= $true )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ~ ~ ( ~ ( sK5_SY217 @ SV3 @ SV5 )
| ~ ( sK5_SY217 @ SV5 @ SV7 ) )
| ( sK5_SY217 @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV6: $i,SV4: $i] :
( ( ( ~ ( sK1_SY0 @ SV4 @ SV6 ) )
= $true )
| ( ( sK5_SY217 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ~ ( ~ ( SV1 @ SY228 @ SY229 )
| ~ ( SV1 @ SY229 @ SY230 ) )
| ( SV1 @ SY228 @ SY230 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ~ ( ~ ( SV2 @ SY233 @ SY234 )
| ~ ( SV2 @ SY234 @ SY235 ) )
| ( SV2 @ SY233 @ SY235 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( sK5_SY217 @ SV3 @ SV5 )
| ~ ( sK5_SY217 @ SV5 @ SV7 ) ) )
= $true )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: $i,SV4: $i] :
( ( ( sK1_SY0 @ SV4 @ SV6 )
= $false )
| ( ( sK5_SY217 @ SV4 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY242: $i,SY243: $i] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ SY242 )
| ~ ( SV1 @ SY242 @ SY243 ) )
| ( SV1 @ ( sK6_SY228 @ SV1 ) @ SY243 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(57,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY244: $i,SY245: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ SY244 )
| ~ ( SV2 @ SY244 @ SY245 ) )
| ( SV2 @ ( sK7_SY233 @ SV2 ) @ SY245 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(58,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( sK5_SY217 @ SV3 @ SV5 )
| ~ ( sK5_SY217 @ SV5 @ SV7 ) ) )
= $false )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY246: $i] :
( ~ ~ ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ SY246 ) )
| ( SV1 @ ( sK6_SY228 @ SV1 ) @ SY246 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY247: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ SY247 ) )
| ( SV2 @ ( sK7_SY233 @ SV2 ) @ SY247 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(61,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( sK5_SY217 @ SV3 @ SV5 )
| ~ ( sK5_SY217 @ SV5 @ SV7 ) )
= $true )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) )
| ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(63,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) )
| ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(64,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( sK5_SY217 @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( sK5_SY217 @ SV5 @ SV7 ) )
= $true )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( sK5_SY217 @ SV3 @ SV5 )
= $false )
| ( ( ~ ( sK5_SY217 @ SV5 @ SV7 ) )
= $true )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) ) )
= $true )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) ) )
= $true )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV3: $i,SV7: $i,SV5: $i] :
( ( ( sK5_SY217 @ SV5 @ SV7 )
= $false )
| ( ( sK5_SY217 @ SV3 @ SV5 )
= $false )
| ( ( sK5_SY217 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
| ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY248: $i] :
( ~ ( sK1_SY0 @ ( sK12_SY231 @ SV1 ) @ SY248 )
| ( SV1 @ ( sK12_SY231 @ SV1 ) @ SY248 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(77,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
| ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY249: $i] :
( ~ ( sK1_SY0 @ ( sK13_SY236 @ SV2 ) @ SY249 )
| ( SV2 @ ( sK13_SY236 @ SV2 ) @ SY249 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(79,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK12_SY231 @ SV1 ) @ ( sK14_SY248 @ SV1 ) )
| ( SV1 @ ( sK12_SY231 @ SV1 ) @ ( sK14_SY248 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(82,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(83,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK13_SY236 @ SV2 ) @ ( sK15_SY249 @ SV2 ) )
| ( SV2 @ ( sK13_SY236 @ SV2 ) @ ( sK15_SY249 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(85,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( ~ ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK12_SY231 @ SV1 ) @ ( sK14_SY248 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK12_SY231 @ SV1 ) @ ( sK14_SY248 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(91,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK13_SY236 @ SV2 ) @ ( sK15_SY249 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(92,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK13_SY236 @ SV2 ) @ ( sK15_SY249 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(93,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY231: $i,SY232: $i] :
( ~ ( sK1_SY0 @ SY231 @ SY232 )
| ( SV1 @ SY231 @ SY232 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK12_SY231 @ SV1 ) @ ( sK14_SY248 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $false )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY236: $i,SY237: $i] :
( ~ ( sK1_SY0 @ SY236 @ SY237 )
| ( SV2 @ SY236 @ SY237 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK13_SY236 @ SV2 ) @ ( sK15_SY249 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $false )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(99,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY250: $i] :
( ~ ( sK1_SY0 @ ( sK16_SY231 @ SV1 ) @ SY250 )
| ( SV1 @ ( sK16_SY231 @ SV1 ) @ SY250 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[93]) ).
thf(100,plain,
! [SV1: $i > $i > $o] :
( ( ( ! [SY251: $i] :
( ~ ( sK1_SY0 @ ( sK17_SY231 @ SV1 ) @ SY251 )
| ( SV1 @ ( sK17_SY231 @ SV1 ) @ SY251 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(101,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY252: $i] :
( ~ ( sK1_SY0 @ ( sK18_SY236 @ SV2 ) @ SY252 )
| ( SV2 @ ( sK18_SY236 @ SV2 ) @ SY252 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(102,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY253: $i] :
( ~ ( sK1_SY0 @ ( sK19_SY236 @ SV2 ) @ SY253 )
| ( SV2 @ ( sK19_SY236 @ SV2 ) @ SY253 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(103,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK16_SY231 @ SV1 ) @ ( sK20_SY250 @ SV1 ) )
| ( SV1 @ ( sK16_SY231 @ SV1 ) @ ( sK20_SY250 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(104,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK17_SY231 @ SV1 ) @ ( sK21_SY251 @ SV1 ) )
| ( SV1 @ ( sK17_SY231 @ SV1 ) @ ( sK21_SY251 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(105,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK18_SY236 @ SV2 ) @ ( sK22_SY252 @ SV2 ) )
| ( SV2 @ ( sK18_SY236 @ SV2 ) @ ( sK22_SY252 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(106,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK19_SY236 @ SV2 ) @ ( sK23_SY253 @ SV2 ) )
| ( SV2 @ ( sK19_SY236 @ SV2 ) @ ( sK23_SY253 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(107,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK16_SY231 @ SV1 ) @ ( sK20_SY250 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK16_SY231 @ SV1 ) @ ( sK20_SY250 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV1: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK17_SY231 @ SV1 ) @ ( sK21_SY251 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(110,plain,
! [SV1: $i > $i > $o] :
( ( ( SV1 @ ( sK17_SY231 @ SV1 ) @ ( sK21_SY251 @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK18_SY236 @ SV2 ) @ ( sK22_SY252 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK18_SY236 @ SV2 ) @ ( sK22_SY252 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(113,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK19_SY236 @ SV2 ) @ ( sK23_SY253 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(114,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK19_SY236 @ SV2 ) @ ( sK23_SY253 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(115,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK16_SY231 @ SV1 ) @ ( sK20_SY250 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK6_SY228 @ SV1 ) @ ( sK8_SY242 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV1: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK17_SY231 @ SV1 ) @ ( sK21_SY251 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK8_SY242 @ SV1 ) @ ( sK10_SY246 @ SV1 ) )
= $true )
| ( ( SV1 @ sK2_SX0 @ sK3_SY166 )
= $true )
| ( ( sK2_SX0 = sK3_SY166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(117,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK18_SY236 @ SV2 ) @ ( sK22_SY252 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK7_SY233 @ SV2 ) @ ( sK9_SY244 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(118,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK19_SY236 @ SV2 ) @ ( sK23_SY253 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK9_SY244 @ SV2 ) @ ( sK11_SY247 @ SV2 ) )
= $true )
| ( ( SV2 @ sK3_SY166 @ sK4_SY186 )
= $true )
| ( ( sK3_SY166 = sK4_SY186 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(119,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,118,117,116,115,114,112,110,108,98,95,92,88,74,55,25]) ).
thf(120,plain,
( ( ~ ! [SY159: $i] :
( ( SY159 = SY159 )
| ! [SY160: $i > $i > $o] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ( ( SY160 @ SY72 @ SY73 )
& ( SY160 @ SY73 @ SY74 ) )
=> ( SY160 @ SY72 @ SY74 ) )
& ! [SY164: $i,SY165: $i] :
( ( sK1_SY0 @ SY164 @ SY165 )
=> ( SY160 @ SY164 @ SY165 ) ) )
=> ( SY160 @ SY159 @ SY159 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = SX0 )
| ! [SX1: $i > $i > $o] :
( ~ ~ ( ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( SX1 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 @ SX4 ) )
| ( SX1 @ SX2 @ SX4 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX2 @ SX3 ) ) )
| ( SX1 @ SX0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120,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(122,plain,
( ( ! [SX0: $i] :
( ( SX0 = SX0 )
| ! [SX1: $i > $i > $o] :
( ~ ~ ( ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( SX1 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 @ SX4 ) )
| ( SX1 @ SX2 @ SX4 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX2 @ SX3 ) ) )
| ( SX1 @ SX0 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(123,plain,
( ( ( sK24_SX0 = sK24_SX0 )
| ! [SY254: $i > $i > $o] :
( ~ ~ ( ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( SY254 @ SX2 @ SX3 )
| ~ ( SY254 @ SX3 @ SX4 ) )
| ( SY254 @ SX2 @ SX4 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SY254 @ SX2 @ SX3 ) ) )
| ( SY254 @ sK24_SX0 @ sK24_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[122]) ).
thf(124,plain,
( ( sK24_SX0 = sK24_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(125,plain,
( ( ! [SY254: $i > $i > $o] :
( ~ ~ ( ~ ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( SY254 @ SX2 @ SX3 )
| ~ ( SY254 @ SX3 @ SX4 ) )
| ( SY254 @ SX2 @ SX4 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SY254 @ SX2 @ SX3 ) ) )
| ( SY254 @ sK24_SX0 @ sK24_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(126,plain,
( ( ~ ~ ( ~ ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) )
| ( sK25_SY254 @ sK24_SX0 @ sK24_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(127,plain,
( ( ~ ~ ( ~ ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(128,plain,
( ( sK25_SY254 @ sK24_SX0 @ sK24_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(129,plain,
( ( ~ ( ~ ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(130,plain,
( ( ~ ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(131,plain,
( ( ~ ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(132,plain,
( ( ~ ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(133,plain,
( ( ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SY260 @ SY261 )
| ~ ( sK25_SY254 @ SY261 @ SY262 ) )
| ( sK25_SY254 @ SY260 @ SY262 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(134,plain,
( ( ! [SY263: $i,SY264: $i] :
( ~ ( sK1_SY0 @ SY263 @ SY264 )
| ( sK25_SY254 @ SY263 @ SY264 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(135,plain,
! [SV8: $i] :
( ( ! [SY265: $i,SY266: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SV8 @ SY265 )
| ~ ( sK25_SY254 @ SY265 @ SY266 ) )
| ( sK25_SY254 @ SV8 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(136,plain,
! [SV9: $i] :
( ( ! [SY267: $i] :
( ~ ( sK1_SY0 @ SV9 @ SY267 )
| ( sK25_SY254 @ SV9 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(137,plain,
! [SV10: $i,SV8: $i] :
( ( ! [SY268: $i] :
( ~ ~ ( ~ ( sK25_SY254 @ SV8 @ SV10 )
| ~ ( sK25_SY254 @ SV10 @ SY268 ) )
| ( sK25_SY254 @ SV8 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(138,plain,
! [SV11: $i,SV9: $i] :
( ( ~ ( sK1_SY0 @ SV9 @ SV11 )
| ( sK25_SY254 @ SV9 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(139,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ~ ~ ( ~ ( sK25_SY254 @ SV8 @ SV10 )
| ~ ( sK25_SY254 @ SV10 @ SV12 ) )
| ( sK25_SY254 @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(140,plain,
! [SV11: $i,SV9: $i] :
( ( ( ~ ( sK1_SY0 @ SV9 @ SV11 ) )
= $true )
| ( ( sK25_SY254 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(141,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( sK25_SY254 @ SV8 @ SV10 )
| ~ ( sK25_SY254 @ SV10 @ SV12 ) ) )
= $true )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(142,plain,
! [SV11: $i,SV9: $i] :
( ( ( sK1_SY0 @ SV9 @ SV11 )
= $false )
| ( ( sK25_SY254 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( ~ ( sK25_SY254 @ SV8 @ SV10 )
| ~ ( sK25_SY254 @ SV10 @ SV12 ) ) )
= $false )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(144,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( sK25_SY254 @ SV8 @ SV10 )
| ~ ( sK25_SY254 @ SV10 @ SV12 ) )
= $true )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(145,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( sK25_SY254 @ SV8 @ SV10 ) )
= $true )
| ( ( ~ ( sK25_SY254 @ SV10 @ SV12 ) )
= $true )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(146,plain,
! [SV12: $i,SV10: $i,SV8: $i] :
( ( ( sK25_SY254 @ SV8 @ SV10 )
= $false )
| ( ( ~ ( sK25_SY254 @ SV10 @ SV12 ) )
= $true )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(147,plain,
! [SV8: $i,SV12: $i,SV10: $i] :
( ( ( sK25_SY254 @ SV10 @ SV12 )
= $false )
| ( ( sK25_SY254 @ SV8 @ SV10 )
= $false )
| ( ( sK25_SY254 @ SV8 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(148,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[124,147,142,128]) ).
thf(149,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[148,119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU469^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n016.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:30:14 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.34
% 0.48/0.34 No.of.Axioms: 0
% 0.48/0.34
% 0.48/0.34 Length.of.Defs: 5096
% 0.48/0.34
% 0.48/0.34 Contains.Choice.Funs: false
% 0.48/0.34 .......
% 0.48/0.34
% 0.48/0.34 ********************************
% 0.48/0.34 * All subproblems solved! *
% 0.48/0.34 ********************************
% 0.48/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,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:148,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.48/0.34
% 0.48/0.34 %**** Beginning of derivation protocol ****
% 0.48/0.34 % SZS output start CNFRefutation
% See solution above
% 0.48/0.34
% 0.48/0.34 %**** End of derivation protocol ****
% 0.48/0.34 %**** no. of clauses in derivation: 149 ****
% 0.48/0.34 %**** clause counter: 148 ****
% 0.48/0.34
% 0.48/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,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:148,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------