%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU462^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 99 ( 56 unt; 0 typ; 29 def)
% Number of atoms : 489 ( 177 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1218 ( 150 ~; 151 |; 47 &; 812 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 4 con; 0-3 aty)
% Number of variables : 326 ( 43 ^; 278 !; 5 ?; 326 :)
% 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_SY105,type,
sK10_SY105: ( $i > $i > $o ) > $i ).
thf(tp_sK11_SY105,type,
sK11_SY105: ( $i > $i > $o ) > $i ).
thf(tp_sK12_SY114,type,
sK12_SY114: ( $i > $i > $o ) > $i ).
thf(tp_sK13_SY115,type,
sK13_SY115: ( $i > $i > $o ) > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SY51,type,
sK2_SY51: $i ).
thf(tp_sK3_SY65,type,
sK3_SY65: $i ).
thf(tp_sK4_SY78,type,
sK4_SY78: $i > $i > $o ).
thf(tp_sK5_SY102,type,
sK5_SY102: ( $i > $i > $o ) > $i ).
thf(tp_sK6_SY110,type,
sK6_SY110: ( $i > $i > $o ) > $i ).
thf(tp_sK7_SY112,type,
sK7_SY112: ( $i > $i > $o ) > $i ).
thf(tp_sK8_SY105,type,
sK8_SY105: ( $i > $i > $o ) > $i ).
thf(tp_sK9_SY113,type,
sK9_SY113: ( $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/sandbox2/benchmark/theBenchmark.p',antisymmetric) ).
thf(asymm,definition,
( asymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ~ ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asymmetric) ).
thf(confl,definition,
( confl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( trc @ R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',confluent) ).
thf(cr,definition,
( cr
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( trsc @ R @ X @ Y )
=> ( join @ R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_rosser) ).
thf(idem,definition,
( idem
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] :
( ( F @ ( F @ R ) )
= ( F @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotent) ).
thf(ind,definition,
( ind
= ( ^ [R: $i > $i > $o] :
! [P: $i > $o] :
( ! [X: $i] :
( ! [Y: $i] :
( ( tc @ R @ X @ Y )
=> ( P @ Y ) )
=> ( P @ X ) )
=> ! [X: $i] : ( P @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satisfying_the_induction_principle) ).
thf(infl,definition,
( infl
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o] : ( subrel @ R @ ( F @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inflationary) ).
thf(innf,definition,
( innf
= ( ^ [R: $i > $i > $o,X: $i] :
~ ? [Y: $i] : ( R @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_normal_form) ).
thf(inv,definition,
( inv
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
thf(irrefl,definition,
( irrefl
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
~ ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexive) ).
thf(join,definition,
( join
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
? [Z: $i] :
( ( trc @ R @ X @ Z )
& ( trc @ R @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',joinable) ).
thf(lconfl,definition,
( lconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',locally_confluent) ).
thf(mono,definition,
( mono
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o,S: $i > $i > $o] :
( ( subrel @ R @ S )
=> ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotonic) ).
thf(nfof,definition,
( nfof
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( trc @ R @ Y @ X )
& ( innf @ R @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normal_form_of) ).
thf(norm,definition,
( norm
= ( ^ [R: $i > $i > $o] :
! [X: $i] :
? [Y: $i] : ( nfof @ R @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normalizing) ).
thf(po,definition,
( po
= ( ^ [R: $i > $i > $o] :
( ( refl @ R )
& ( antisymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order) ).
thf(rc,definition,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure) ).
thf(refl,definition,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive) ).
thf(sc,definition,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure) ).
thf(sconfl,definition,
( sconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',semi_confluent) ).
thf(so,definition,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order) ).
thf(subrel,definition,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel) ).
thf(symm,definition,
( symm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric) ).
thf(tc,definition,
( tc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
! [S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S ) )
=> ( S @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure) ).
thf(term,definition,
( term
= ( ^ [R: $i > $i > $o] :
! [A: $i > $o] :
( ? [X: $i] : ( A @ X )
=> ? [X: $i] :
( ( A @ X )
& ! [Y: $i] :
( ( A @ Y )
=> ~ ( R @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',terminating) ).
thf(total,definition,
( total
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y )
| ( R @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total) ).
thf(trans,definition,
( trans
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive) ).
thf(trc,definition,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_closure) ).
thf(trsc,definition,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure) ).
thf(1,conjecture,
! [R: $i > $i > $o,X: $i,Y: $i,S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S )
& ( tc @ R @ X @ Y ) )
=> ( S @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive2) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o,X: $i,Y: $i,S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S )
& ( tc @ R @ X @ Y ) )
=> ( S @ X @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o,SY1: $i,SY2: $i,SY3: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY3 @ SY4 @ SY5 )
& ( SY3 @ SY5 @ SY6 ) )
=> ( SY3 @ SY4 @ SY6 ) )
& ! [SY10: $i,SY11: $i] :
( ( SY0 @ SY10 @ SY11 )
=> ( SY3 @ SY10 @ SY11 ) )
& ! [SY30: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY30 @ SY15 @ SY16 )
& ( SY30 @ SY16 @ SY17 ) )
=> ( SY30 @ SY15 @ SY17 ) )
& ! [SY21: $i,SY22: $i] :
( ( SY0 @ SY21 @ SY22 )
=> ( SY30 @ SY21 @ SY22 ) ) )
=> ( SY30 @ SY1 @ SY2 ) ) )
=> ( SY3 @ SY1 @ SY2 ) ) )
= $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,
( ( ! [SY51: $i,SY52: $i,SY53: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY53 @ SY4 @ SY5 )
& ( SY53 @ SY5 @ SY6 ) )
=> ( SY53 @ SY4 @ SY6 ) )
& ! [SY57: $i,SY58: $i] :
( ( sK1_SY0 @ SY57 @ SY58 )
=> ( SY53 @ SY57 @ SY58 ) )
& ! [SY59: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY59 @ SY15 @ SY16 )
& ( SY59 @ SY16 @ SY17 ) )
=> ( SY59 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY59 @ SY63 @ SY64 ) ) )
=> ( SY59 @ SY51 @ SY52 ) ) )
=> ( SY53 @ SY51 @ SY52 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY65: $i,SY66: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY66 @ SY4 @ SY5 )
& ( SY66 @ SY5 @ SY6 ) )
=> ( SY66 @ SY4 @ SY6 ) )
& ! [SY57: $i,SY58: $i] :
( ( sK1_SY0 @ SY57 @ SY58 )
=> ( SY66 @ SY57 @ SY58 ) )
& ! [SY72: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY72 @ SY15 @ SY16 )
& ( SY72 @ SY16 @ SY17 ) )
=> ( SY72 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY72 @ SY63 @ SY64 ) ) )
=> ( SY72 @ sK2_SY51 @ SY65 ) ) )
=> ( SY66 @ sK2_SY51 @ SY65 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY78: $i > $i > $o] :
( ( ! [SY4: $i,SY5: $i,SY6: $i] :
( ( ( SY78 @ SY4 @ SY5 )
& ( SY78 @ SY5 @ SY6 ) )
=> ( SY78 @ SY4 @ SY6 ) )
& ! [SY57: $i,SY58: $i] :
( ( sK1_SY0 @ SY57 @ SY58 )
=> ( SY78 @ SY57 @ SY58 ) )
& ! [SY84: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY84 @ SY15 @ SY16 )
& ( SY84 @ SY16 @ SY17 ) )
=> ( SY84 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY84 @ SY63 @ SY64 ) ) )
=> ( SY84 @ sK2_SY51 @ sK3_SY65 ) ) )
=> ( SY78 @ sK2_SY51 @ sK3_SY65 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( ( sK4_SY78 @ SY90 @ SY91 )
& ( sK4_SY78 @ SY91 @ SY92 ) )
=> ( sK4_SY78 @ SY90 @ SY92 ) )
& ! [SY93: $i,SY94: $i] :
( ( sK1_SY0 @ SY93 @ SY94 )
=> ( sK4_SY78 @ SY93 @ SY94 ) )
& ! [SY84: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY84 @ SY15 @ SY16 )
& ( SY84 @ SY16 @ SY17 ) )
=> ( SY84 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY84 @ SY63 @ SY64 ) ) )
=> ( SY84 @ sK2_SY51 @ sK3_SY65 ) ) )
=> ( sK4_SY78 @ sK2_SY51 @ sK3_SY65 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( ( sK4_SY78 @ SY90 @ SY91 )
& ( sK4_SY78 @ SY91 @ SY92 ) )
=> ( sK4_SY78 @ SY90 @ SY92 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY93: $i,SY94: $i] :
( ( sK1_SY0 @ SY93 @ SY94 )
=> ( sK4_SY78 @ SY93 @ SY94 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [SY84: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY84 @ SY15 @ SY16 )
& ( SY84 @ SY16 @ SY17 ) )
=> ( SY84 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY84 @ SY63 @ SY64 ) ) )
=> ( SY84 @ sK2_SY51 @ sK3_SY65 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(11,plain,
( ( sK4_SY78 @ sK2_SY51 @ sK3_SY65 )
= $false ),
inference(standard_cnf,[status(thm)],[7]) ).
thf(12,plain,
( ( ~ ( sK4_SY78 @ sK2_SY51 @ sK3_SY65 ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY84: $i > $i > $o] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ( ( SY84 @ SY15 @ SY16 )
& ( SY84 @ SY16 @ SY17 ) )
=> ( SY84 @ SY15 @ SY17 ) )
& ! [SY63: $i,SY64: $i] :
( ( sK1_SY0 @ SY63 @ SY64 )
=> ( SY84 @ SY63 @ SY64 ) ) )
=> ( SY84 @ sK2_SY51 @ sK3_SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ! [SY93: $i,SY94: $i] :
( ( sK1_SY0 @ SY93 @ SY94 )
=> ( sK4_SY78 @ SY93 @ SY94 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( ( sK4_SY78 @ SY90 @ SY91 )
& ( sK4_SY78 @ SY91 @ SY92 ) )
=> ( sK4_SY78 @ SY90 @ SY92 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ ( sK4_SY78 @ sK2_SY51 @ sK3_SY65 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX1 )
| ( sK4_SY78 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,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(18,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_SY51 @ sK3_SY65 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(19,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( sK4_SY78 @ SX0 @ SX1 )
| ~ ( sK4_SY78 @ SX1 @ SX2 ) )
| ( sK4_SY78 @ SX0 @ SX2 ) ) )
= $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(20,plain,
( ( sK4_SY78 @ sK2_SY51 @ sK3_SY65 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: $i] :
( ( ! [SY101: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY101 )
| ( sK4_SY78 @ SV1 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i > $i > $o] :
( ( ~ ~ ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
| ( SV2 @ sK2_SY51 @ sK3_SY65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ~ ( ~ ( sK4_SY78 @ SV3 @ SY107 )
| ~ ( sK4_SY78 @ SY107 @ SY108 ) )
| ( sK4_SY78 @ SV3 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( sK1_SY0 @ SV1 @ SV4 )
| ( sK4_SY78 @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY109: $i] :
( ~ ~ ( ~ ( sK4_SY78 @ SV3 @ SV5 )
| ~ ( sK4_SY78 @ SV5 @ SY109 ) )
| ( sK4_SY78 @ SV3 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV4 ) )
= $true )
| ( ( sK4_SY78 @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ~ ~ ( ~ ( sK4_SY78 @ SV3 @ SV5 )
| ~ ( sK4_SY78 @ SV5 @ SV6 ) )
| ( sK4_SY78 @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i,SV1: $i] :
( ( ( sK1_SY0 @ SV1 @ SV4 )
= $false )
| ( ( sK4_SY78 @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) )
| ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( sK4_SY78 @ SV3 @ SV5 )
| ~ ( sK4_SY78 @ SV5 @ SV6 ) ) )
= $true )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) ) )
= $true )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( ~ ( sK4_SY78 @ SV3 @ SV5 )
| ~ ( sK4_SY78 @ SV5 @ SV6 ) ) )
= $false )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( SV2 @ SY102 @ SY103 )
| ~ ( SV2 @ SY103 @ SY104 ) )
| ( SV2 @ SY102 @ SY104 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( sK4_SY78 @ SV3 @ SV5 )
| ~ ( sK4_SY78 @ SV5 @ SV6 ) )
= $true )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY110: $i,SY111: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ SY110 )
| ~ ( SV2 @ SY110 @ SY111 ) )
| ( SV2 @ ( sK5_SY102 @ SV2 ) @ SY111 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(38,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( sK4_SY78 @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( sK4_SY78 @ SV5 @ SV6 ) )
= $true )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY112: $i] :
( ~ ~ ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
| ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ SY112 ) )
| ( SV2 @ ( sK5_SY102 @ SV2 ) @ SY112 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(40,plain,
! [SV6: $i,SV5: $i,SV3: $i] :
( ( ( sK4_SY78 @ SV3 @ SV5 )
= $false )
| ( ( ~ ( sK4_SY78 @ SV5 @ SV6 ) )
= $true )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
| ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) )
| ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(42,plain,
! [SV3: $i,SV6: $i,SV5: $i] :
( ( ( sK4_SY78 @ SV5 @ SV6 )
= $false )
| ( ( sK4_SY78 @ SV3 @ SV5 )
= $false )
| ( ( sK4_SY78 @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
| ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
| ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) ) )
= $true )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
| ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY113: $i] :
( ~ ( sK1_SY0 @ ( sK8_SY105 @ SV2 ) @ SY113 )
| ( SV2 @ ( sK8_SY105 @ SV2 ) @ SY113 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(49,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK8_SY105 @ SV2 ) @ ( sK9_SY113 @ SV2 ) )
| ( SV2 @ ( sK8_SY105 @ SV2 ) @ ( sK9_SY113 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(52,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK8_SY105 @ SV2 ) @ ( sK9_SY113 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK8_SY105 @ SV2 ) @ ( sK9_SY113 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY105: $i,SY106: $i] :
( ~ ( sK1_SY0 @ SY105 @ SY106 )
| ( SV2 @ SY105 @ SY106 ) ) )
= $false )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK8_SY105 @ SV2 ) @ ( sK9_SY113 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $false )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY114: $i] :
( ~ ( sK1_SY0 @ ( sK10_SY105 @ SV2 ) @ SY114 )
| ( SV2 @ ( sK10_SY105 @ SV2 ) @ SY114 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV2: $i > $i > $o] :
( ( ( ! [SY115: $i] :
( ~ ( sK1_SY0 @ ( sK11_SY105 @ SV2 ) @ SY115 )
| ( SV2 @ ( sK11_SY105 @ SV2 ) @ SY115 ) ) )
= $false )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(61,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK10_SY105 @ SV2 ) @ ( sK12_SY114 @ SV2 ) )
| ( SV2 @ ( sK10_SY105 @ SV2 ) @ ( sK12_SY114 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(62,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK11_SY105 @ SV2 ) @ ( sK13_SY115 @ SV2 ) )
| ( SV2 @ ( sK11_SY105 @ SV2 ) @ ( sK13_SY115 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(63,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK10_SY105 @ SV2 ) @ ( sK12_SY114 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(64,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK10_SY105 @ SV2 ) @ ( sK12_SY114 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
! [SV2: $i > $i > $o] :
( ( ( ~ ( sK1_SY0 @ ( sK11_SY105 @ SV2 ) @ ( sK13_SY115 @ SV2 ) ) )
= $false )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
! [SV2: $i > $i > $o] :
( ( ( SV2 @ ( sK11_SY105 @ SV2 ) @ ( sK13_SY115 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK10_SY105 @ SV2 ) @ ( sK12_SY114 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK5_SY102 @ SV2 ) @ ( sK6_SY110 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV2: $i > $i > $o] :
( ( ( sK1_SY0 @ ( sK11_SY105 @ SV2 ) @ ( sK13_SY115 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK6_SY110 @ SV2 ) @ ( sK7_SY112 @ SV2 ) )
= $true )
| ( ( SV2 @ sK2_SY51 @ sK3_SY65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,68,67,66,64,58,55,42,30]) ).
thf(70,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU462^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % 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 15:25:54 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 0
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 5125
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22 ..
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 70 ****
% 0.10/0.22 %**** clause counter: 69 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:69,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------