%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:25 AM UTC 2026
% Result : Theorem 0.40s 0.28s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 44
% Syntax : Number of formulae : 179 ( 94 unt; 0 typ; 40 def)
% Number of atoms : 1470 ( 381 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 3236 ( 576 ~; 538 |; 64 &;2025 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 56 usr; 9 con; 0-3 aty)
% Number of variables : 649 ( 72 ^; 550 !; 27 ?; 649 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_reg,type,
reg: $tType ).
thf(tp_a,type,
a: $i > $i > $o ).
thf(tp_c,type,
c: reg > reg > $o ).
thf(tp_catalunya,type,
catalunya: reg ).
thf(tp_dc,type,
dc: reg > reg > $o ).
thf(tp_ec,type,
ec: reg > reg > $o ).
thf(tp_eq,type,
eq: reg > reg > $o ).
thf(tp_fool,type,
fool: $i > $i > $o ).
thf(tp_france,type,
france: reg ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_ntpp,type,
ntpp: reg > reg > $o ).
thf(tp_o,type,
o: reg > reg > $o ).
thf(tp_p,type,
p: reg > reg > $o ).
thf(tp_paris,type,
paris: reg ).
thf(tp_po,type,
po: reg > reg > $o ).
thf(tp_pp,type,
pp: reg > reg > $o ).
thf(tp_sK1_SY69,type,
sK1_SY69: $i ).
thf(tp_sK2_SY207,type,
sK2_SY207: $i ).
thf(tp_sK3_SY4,type,
sK3_SY4: reg ).
thf(tp_sK4_SY53,type,
sK4_SY53: reg > reg > reg ).
thf(tp_sK5_SY236,type,
sK5_SY236: reg > reg > reg ).
thf(tp_sK6_SY233,type,
sK6_SY233: reg > reg ).
thf(tp_sK7_SY126,type,
sK7_SY126: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY172,type,
sK8_SY172: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY203,type,
sK9_SY203: ( $i > $o ) > $i > $i ).
thf(tp_spain,type,
spain: reg ).
thf(tp_tpp,type,
tpp: reg > reg > $o ).
thf(dc,definition,
( dc
= ( ^ [X: reg,Y: reg] :
~ ( c @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dc) ).
thf(ec,definition,
( ec
= ( ^ [X: reg,Y: reg] :
( ( c @ X @ Y )
& ~ ( o @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ec) ).
thf(eq,definition,
( eq
= ( ^ [X: reg,Y: reg] :
( ( p @ X @ Y )
& ( p @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq) ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reg_type) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(ntpp,definition,
( ntpp
= ( ^ [X: reg,Y: reg] :
( ( pp @ X @ Y )
& ~ ? [Z: reg] :
( ( ec @ Z @ X )
& ( ec @ Z @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ntpp) ).
thf(o,definition,
( o
= ( ^ [X: reg,Y: reg] :
? [Z: reg] :
( ( p @ Z @ X )
& ( p @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o) ).
thf(p,definition,
( p
= ( ^ [X: reg,Y: reg] :
! [Z: reg] :
( ( c @ Z @ X )
=> ( c @ Z @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p) ).
thf(po,definition,
( po
= ( ^ [X: reg,Y: reg] :
( ( o @ X @ Y )
& ~ ( p @ X @ Y )
& ~ ( p @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',po) ).
thf(pp,definition,
( pp
= ( ^ [X: reg,Y: reg] :
( ( p @ X @ Y )
& ~ ( p @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pp) ).
thf(tpp,definition,
( tpp
= ( ^ [X: reg,Y: reg] :
( ( pp @ X @ Y )
& ? [Z: reg] :
( ( ec @ Z @ X )
& ( ec @ Z @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tpp) ).
thf(4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool) ).
thf(6,axiom,
( mvalid
@ ( mforall_prop
@ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(9,conjecture,
( mvalid
@ ( mbox @ fool
@ ^ [X: $i] :
~ ? [Z: reg] :
! [Y: reg] : ( ntpp @ Z @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(10,negated_conjecture,
( ( mvalid
@ ( mbox @ fool
@ ^ [X: $i] :
~ ? [Z: reg] :
! [Y: reg] : ( ntpp @ Z @ Y ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [SY69: $i,SY70: $i] :
( ~ ( fool @ SY69 @ SY70 )
| ~ ? [SY4: reg] :
! [SY5: reg] :
( ! [SY47: reg] :
( ( c @ SY47 @ SY4 )
=> ( c @ SY47 @ SY5 ) )
& ~ ! [SY48: reg] :
( ( c @ SY48 @ SY5 )
=> ( c @ SY48 @ SY4 ) )
& ~ ? [SY49: reg] :
( ( c @ SY49 @ SY4 )
& ~ ? [SY29: reg] :
( ! [SY22: reg] :
( ( c @ SY22 @ SY29 )
=> ( c @ SY22 @ SY49 ) )
& ! [SY31: reg] :
( ( c @ SY31 @ SY29 )
=> ( c @ SY31 @ SY4 ) ) )
& ( c @ SY49 @ SY5 )
& ~ ? [SY53: reg] :
( ! [SY37: reg] :
( ( c @ SY37 @ SY53 )
=> ( c @ SY37 @ SY49 ) )
& ! [SY55: reg] :
( ( c @ SY55 @ SY53 )
=> ( c @ SY55 @ SY5 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(12,plain,
( ( ! [SY124: $i,SY125: $i > $o] :
( ~ ! [SY126: $i] :
( ~ ( fool @ SY124 @ SY126 )
| ( SY125 @ SY126 ) )
| ! [SY127: $i] :
( ~ ( a @ SY124 @ SY127 )
| ( SY125 @ SY127 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(13,plain,
( ( ! [SY170: $i,SY171: $i > $o] :
( ~ ! [SY172: $i] :
( ~ ( fool @ SY170 @ SY172 )
| ( SY171 @ SY172 ) )
| ! [SY173: $i] :
( ~ ( fool @ SY170 @ SY173 )
| ! [SY166: $i] :
( ~ ( fool @ SY173 @ SY166 )
| ( SY171 @ SY166 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(14,plain,
( ( ! [SY201: $i,SY202: $i > $o] :
( ~ ! [SY203: $i] :
( ~ ( fool @ SY201 @ SY203 )
| ( SY202 @ SY203 ) )
| ( SY202 @ SY201 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(15,plain,
( ( ! [SY207: $i] :
( ~ ( fool @ sK1_SY69 @ SY207 )
| ~ ? [SY4: reg] :
! [SY5: reg] :
( ! [SY47: reg] :
( ( c @ SY47 @ SY4 )
=> ( c @ SY47 @ SY5 ) )
& ~ ! [SY48: reg] :
( ( c @ SY48 @ SY5 )
=> ( c @ SY48 @ SY4 ) )
& ~ ? [SY49: reg] :
( ( c @ SY49 @ SY4 )
& ~ ? [SY29: reg] :
( ! [SY22: reg] :
( ( c @ SY22 @ SY29 )
=> ( c @ SY22 @ SY49 ) )
& ! [SY31: reg] :
( ( c @ SY31 @ SY29 )
=> ( c @ SY31 @ SY4 ) ) )
& ( c @ SY49 @ SY5 )
& ~ ? [SY53: reg] :
( ! [SY37: reg] :
( ( c @ SY37 @ SY53 )
=> ( c @ SY37 @ SY49 ) )
& ! [SY55: reg] :
( ( c @ SY55 @ SY53 )
=> ( c @ SY55 @ SY5 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(16,plain,
( ( ~ ( fool @ sK1_SY69 @ sK2_SY207 )
| ~ ? [SY4: reg] :
! [SY5: reg] :
( ! [SY47: reg] :
( ( c @ SY47 @ SY4 )
=> ( c @ SY47 @ SY5 ) )
& ~ ! [SY48: reg] :
( ( c @ SY48 @ SY5 )
=> ( c @ SY48 @ SY4 ) )
& ~ ? [SY49: reg] :
( ( c @ SY49 @ SY4 )
& ~ ? [SY29: reg] :
( ! [SY22: reg] :
( ( c @ SY22 @ SY29 )
=> ( c @ SY22 @ SY49 ) )
& ! [SY31: reg] :
( ( c @ SY31 @ SY29 )
=> ( c @ SY31 @ SY4 ) ) )
& ( c @ SY49 @ SY5 )
& ~ ? [SY53: reg] :
( ! [SY37: reg] :
( ( c @ SY37 @ SY53 )
=> ( c @ SY37 @ SY49 ) )
& ! [SY55: reg] :
( ( c @ SY55 @ SY53 )
=> ( c @ SY55 @ SY5 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ~ ( ~ ( fool @ sK1_SY69 @ sK2_SY207 )
| ~ ? [SY4: reg] :
! [SY5: reg] :
( ! [SY47: reg] :
( ( c @ SY47 @ SY4 )
=> ( c @ SY47 @ SY5 ) )
& ~ ! [SY48: reg] :
( ( c @ SY48 @ SY5 )
=> ( c @ SY48 @ SY4 ) )
& ~ ? [SY49: reg] :
( ( c @ SY49 @ SY4 )
& ~ ? [SY29: reg] :
( ! [SY22: reg] :
( ( c @ SY22 @ SY29 )
=> ( c @ SY22 @ SY49 ) )
& ! [SY31: reg] :
( ( c @ SY31 @ SY29 )
=> ( c @ SY31 @ SY4 ) ) )
& ( c @ SY49 @ SY5 )
& ~ ? [SY53: reg] :
( ! [SY37: reg] :
( ( c @ SY37 @ SY53 )
=> ( c @ SY37 @ SY49 ) )
& ! [SY55: reg] :
( ( c @ SY55 @ SY53 )
=> ( c @ SY55 @ SY5 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ( fool @ sK1_SY69 @ sK2_SY207 )
& ! [SY230: reg,SY231: reg] :
( ~ ( c @ SY231 @ sK3_SY4 )
| ( c @ SY231 @ SY230 ) )
& ! [SY232: reg] :
( ( c @ ( sK6_SY233 @ SY232 ) @ SY232 )
& ~ ( c @ ( sK6_SY233 @ SY232 ) @ sK3_SY4 ) )
& ! [SY234: reg,SY235: reg] :
( ~ ( c @ SY235 @ sK3_SY4 )
| ( ! [SY244: reg] :
( ~ ( c @ SY244 @ ( sK5_SY236 @ SY235 @ SY234 ) )
| ( c @ SY244 @ SY235 ) )
& ! [SY245: reg] :
( ~ ( c @ SY245 @ ( sK5_SY236 @ SY235 @ SY234 ) )
| ( c @ SY245 @ sK3_SY4 ) ) )
| ~ ( c @ SY235 @ SY234 )
| ( ! [SY242: reg] :
( ~ ( c @ SY242 @ ( sK4_SY53 @ SY235 @ SY234 ) )
| ( c @ SY242 @ SY235 ) )
& ! [SY243: reg] :
( ~ ( c @ SY243 @ ( sK4_SY53 @ SY235 @ SY234 ) )
| ( c @ SY243 @ SY234 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY124: $i,SY125: $i > $o] :
( ( ( fool @ SY124 @ ( sK7_SY126 @ SY125 @ SY124 ) )
& ~ ( SY125 @ ( sK7_SY126 @ SY125 @ SY124 ) ) )
| ! [SY127: $i] :
( ~ ( a @ SY124 @ SY127 )
| ( SY125 @ SY127 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(20,plain,
( ( ! [SY170: $i,SY171: $i > $o] :
( ( ( fool @ SY170 @ ( sK8_SY172 @ SY171 @ SY170 ) )
& ~ ( SY171 @ ( sK8_SY172 @ SY171 @ SY170 ) ) )
| ! [SY173: $i] :
( ~ ( fool @ SY170 @ SY173 )
| ! [SY166: $i] :
( ~ ( fool @ SY173 @ SY166 )
| ( SY171 @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(21,plain,
( ( ! [SY201: $i,SY202: $i > $o] :
( ( ( fool @ SY201 @ ( sK9_SY203 @ SY202 @ SY201 ) )
& ~ ( SY202 @ ( sK9_SY203 @ SY202 @ SY201 ) ) )
| ( SY202 @ SY201 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(22,plain,
( ( ! [SY201: $i,SY202: $i > $o] :
( ( ( fool @ SY201 @ ( sK9_SY203 @ SY202 @ SY201 ) )
& ~ ( SY202 @ ( sK9_SY203 @ SY202 @ SY201 ) ) )
| ( SY202 @ SY201 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [SY170: $i,SY171: $i > $o] :
( ( ( fool @ SY170 @ ( sK8_SY172 @ SY171 @ SY170 ) )
& ~ ( SY171 @ ( sK8_SY172 @ SY171 @ SY170 ) ) )
| ! [SY173: $i] :
( ~ ( fool @ SY170 @ SY173 )
| ! [SY166: $i] :
( ~ ( fool @ SY173 @ SY166 )
| ( SY171 @ SY166 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(24,plain,
( ( ! [SY124: $i,SY125: $i > $o] :
( ( ( fool @ SY124 @ ( sK7_SY126 @ SY125 @ SY124 ) )
& ~ ( SY125 @ ( sK7_SY126 @ SY125 @ SY124 ) ) )
| ! [SY127: $i] :
( ~ ( a @ SY124 @ SY127 )
| ( SY125 @ SY127 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(25,plain,
( ( ( fool @ sK1_SY69 @ sK2_SY207 )
& ! [SY230: reg,SY231: reg] :
( ~ ( c @ SY231 @ sK3_SY4 )
| ( c @ SY231 @ SY230 ) )
& ! [SY232: reg] :
( ( c @ ( sK6_SY233 @ SY232 ) @ SY232 )
& ~ ( c @ ( sK6_SY233 @ SY232 ) @ sK3_SY4 ) )
& ! [SY234: reg,SY235: reg] :
( ~ ( c @ SY235 @ sK3_SY4 )
| ( ! [SY244: reg] :
( ~ ( c @ SY244 @ ( sK5_SY236 @ SY235 @ SY234 ) )
| ( c @ SY244 @ SY235 ) )
& ! [SY245: reg] :
( ~ ( c @ SY245 @ ( sK5_SY236 @ SY235 @ SY234 ) )
| ( c @ SY245 @ sK3_SY4 ) ) )
| ~ ( c @ SY235 @ SY234 )
| ( ! [SY242: reg] :
( ~ ( c @ SY242 @ ( sK4_SY53 @ SY235 @ SY234 ) )
| ( c @ SY242 @ SY235 ) )
& ! [SY243: reg] :
( ~ ( c @ SY243 @ ( sK4_SY53 @ SY235 @ SY234 ) )
| ( c @ SY243 @ SY234 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( fool @ SX0 @ ( sK7_SY126 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK7_SY126 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a @ SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(27,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( fool @ SX0 @ ( sK8_SY172 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK8_SY172 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( fool @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( fool @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(28,plain,
( ( ~ ( ~ ( fool @ sK1_SY69 @ sK2_SY207 )
| ~ ~ ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
| ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( fool @ SX0 @ ( sK9_SY203 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK9_SY203 @ SX1 @ SX0 ) ) )
| ( SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,dc,ec,eq,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor,ntpp,o,p,po,pp,tpp]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY246: $i > $o] :
( ~ ( ~ ( fool @ SV1 @ ( sK7_SY126 @ SY246 @ SV1 ) )
| ~ ~ ( SY246 @ ( sK7_SY126 @ SY246 @ SV1 ) ) )
| ! [SY247: $i] :
( ~ ( a @ SV1 @ SY247 )
| ( SY246 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV2: $i] :
( ( ! [SY248: $i > $o] :
( ~ ( ~ ( fool @ SV2 @ ( sK8_SY172 @ SY248 @ SV2 ) )
| ~ ~ ( SY248 @ ( sK8_SY172 @ SY248 @ SV2 ) ) )
| ! [SY249: $i] :
( ~ ( fool @ SV2 @ SY249 )
| ! [SX3: $i] :
( ~ ( fool @ SY249 @ SX3 )
| ( SY248 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( fool @ sK1_SY69 @ sK2_SY207 )
| ~ ~ ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
| ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY251: $i > $o] :
( ~ ( ~ ( fool @ SV3 @ ( sK9_SY203 @ SY251 @ SV3 ) )
| ~ ~ ( SY251 @ ( sK9_SY203 @ SY251 @ SV3 ) ) )
| ( SY251 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: $i > $o,SV1: $i] :
( ( ~ ( ~ ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
| ~ ~ ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) ) )
| ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ~ ( ~ ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) ) )
| ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( fool @ sK1_SY69 @ sK2_SY207 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
| ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV6: $i > $o,SV3: $i] :
( ( ~ ( ~ ( fool @ SV3 @ ( sK9_SY203 @ SV6 @ SV3 ) )
| ~ ~ ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) ) )
| ( SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV4: $i > $o,SV1: $i] :
( ( ( ~ ( ~ ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
| ~ ~ ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ( ~ ( ~ ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( fool @ sK1_SY69 @ sK2_SY207 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
| ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(43,plain,
! [SV6: $i > $o,SV3: $i] :
( ( ( ~ ( ~ ( fool @ SV3 @ ( sK9_SY203 @ SV6 @ SV3 ) )
| ~ ~ ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) ) ) )
= $true )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV4: $i > $o,SV1: $i] :
( ( ( ~ ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
| ~ ~ ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
| ~ ~ ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(46,plain,
( ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
| ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i > $o,SV3: $i] :
( ( ( ~ ( fool @ SV3 @ ( sK9_SY203 @ SV6 @ SV3 ) )
| ~ ~ ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) ) )
= $false )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV4: $i > $o,SV1: $i] :
( ( ( ~ ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV1: $i,SV4: $i > $o] :
( ( ( ~ ~ ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV2: $i,SV5: $i > $o] :
( ( ( ~ ~ ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) ) )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
( ( ~ ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
( ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(54,plain,
! [SV6: $i > $o,SV3: $i] :
( ( ( ~ ( fool @ SV3 @ ( sK9_SY203 @ SV6 @ SV3 ) ) )
= $false )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(55,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( ~ ~ ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) ) )
= $false )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(56,plain,
! [SV4: $i > $o,SV1: $i] :
( ( ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(57,plain,
! [SV1: $i,SV4: $i > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(58,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(59,plain,
! [SV2: $i,SV5: $i > $o] :
( ( ( ~ ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(60,plain,
( ( ~ ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(61,plain,
( ( ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK5_SY236 @ SX1 @ SX0 ) )
| ( c @ SX2 @ sK3_SY4 ) ) )
| ~ ( c @ SX1 @ SX0 )
| ~ ( ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX1 ) )
| ~ ! [SX2: reg] :
( ~ ( c @ SX2 @ ( sK4_SY53 @ SX1 @ SX0 ) )
| ( c @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(62,plain,
! [SV6: $i > $o,SV3: $i] :
( ( ( fool @ SV3 @ ( sK9_SY203 @ SV6 @ SV3 ) )
= $true )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(63,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( ~ ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) ) )
= $true )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(64,plain,
! [SV4: $i > $o,SV7: $i,SV1: $i] :
( ( ( ~ ( a @ SV1 @ SV7 )
| ( SV4 @ SV7 ) )
= $true )
| ( ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV1: $i,SV4: $i > $o] :
( ( ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( a @ SV1 @ SY252 )
| ( SV4 @ SY252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV5: $i > $o,SV8: $i,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ SV8 )
| ! [SY255: $i] :
( ~ ( fool @ SV8 @ SY255 )
| ( SV5 @ SY255 ) ) )
= $true )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV2: $i,SV5: $i > $o] :
( ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( fool @ SV2 @ SY253 )
| ! [SY254: $i] :
( ~ ( fool @ SY253 @ SY254 )
| ( SV5 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
( ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) )
| ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV9: reg] :
( ( ! [SY256: reg] :
( ~ ( c @ SY256 @ sK3_SY4 )
| ~ ( ~ ! [SY257: reg] :
( ~ ( c @ SY257 @ ( sK5_SY236 @ SY256 @ SV9 ) )
| ( c @ SY257 @ SY256 ) )
| ~ ! [SY258: reg] :
( ~ ( c @ SY258 @ ( sK5_SY236 @ SY256 @ SV9 ) )
| ( c @ SY258 @ sK3_SY4 ) ) )
| ~ ( c @ SY256 @ SV9 )
| ~ ( ~ ! [SY259: reg] :
( ~ ( c @ SY259 @ ( sK4_SY53 @ SY256 @ SV9 ) )
| ( c @ SY259 @ SY256 ) )
| ~ ! [SY260: reg] :
( ~ ( c @ SY260 @ ( sK4_SY53 @ SY256 @ SV9 ) )
| ( c @ SY260 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV3: $i,SV6: $i > $o] :
( ( ( SV6 @ ( sK9_SY203 @ SV6 @ SV3 ) )
= $false )
| ( ( SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV4: $i > $o,SV7: $i,SV1: $i] :
( ( ( ~ ( a @ SV1 @ SV7 ) )
= $true )
| ( ( SV4 @ SV7 )
= $true )
| ( ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV4: $i > $o,SV10: $i,SV1: $i] :
( ( ( ~ ( a @ SV1 @ SV10 )
| ( SV4 @ SV10 ) )
= $true )
| ( ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV5: $i > $o,SV8: $i,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY255: $i] :
( ~ ( fool @ SV8 @ SY255 )
| ( SV5 @ SY255 ) ) )
= $true )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV5: $i > $o,SV11: $i,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ SV11 )
| ! [SY261: $i] :
( ~ ( fool @ SV11 @ SY261 )
| ( SV5 @ SY261 ) ) )
= $true )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(75,plain,
( ( ~ ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV9: reg,SV12: reg] :
( ( ~ ( c @ SV12 @ sK3_SY4 )
| ~ ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) )
| ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) )
| ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV4: $i > $o,SV7: $i,SV1: $i] :
( ( ( a @ SV1 @ SV7 )
= $false )
| ( ( SV4 @ SV7 )
= $true )
| ( ( fool @ SV1 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(79,plain,
! [SV4: $i > $o,SV10: $i,SV1: $i] :
( ( ( ~ ( a @ SV1 @ SV10 ) )
= $true )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV5: $i > $o,SV8: $i,SV2: $i] :
( ( ( fool @ SV2 @ SV8 )
= $false )
| ( ( ! [SY255: $i] :
( ~ ( fool @ SV8 @ SY255 )
| ( SV5 @ SY255 ) ) )
= $true )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV5: $i > $o,SV11: $i,SV2: $i] :
( ( ( ~ ( fool @ SV2 @ SV11 ) )
= $true )
| ( ( ! [SY261: $i] :
( ~ ( fool @ SV11 @ SY261 )
| ( SV5 @ SY261 ) ) )
= $true )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
( ( ! [SX0: reg,SX1: reg] :
( ~ ( c @ SX1 @ sK3_SY4 )
| ( c @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(83,plain,
( ( ! [SX0: reg] :
~ ( ~ ( c @ ( sK6_SY233 @ SX0 ) @ SX0 )
| ~ ~ ( c @ ( sK6_SY233 @ SX0 ) @ sK3_SY4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV9: reg,SV12: reg] :
( ( ( ~ ( c @ SV12 @ sK3_SY4 )
| ~ ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) )
| ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) ) )
= $true )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV4: $i > $o,SV10: $i,SV1: $i] :
( ( ( a @ SV1 @ SV10 )
= $false )
| ( ( SV4 @ SV10 )
= $true )
| ( ( SV4 @ ( sK7_SY126 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV2: $i,SV5: $i > $o,SV13: $i,SV8: $i] :
( ( ( ~ ( fool @ SV8 @ SV13 )
| ( SV5 @ SV13 ) )
= $true )
| ( ( fool @ SV2 @ SV8 )
= $false )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV5: $i > $o,SV11: $i,SV2: $i] :
( ( ( fool @ SV2 @ SV11 )
= $false )
| ( ( ! [SY261: $i] :
( ~ ( fool @ SV11 @ SY261 )
| ( SV5 @ SY261 ) ) )
= $true )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV14: reg] :
( ( ! [SY266: reg] :
( ~ ( c @ SY266 @ sK3_SY4 )
| ( c @ SY266 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV15: reg] :
( ( ~ ( ~ ( c @ ( sK6_SY233 @ SV15 ) @ SV15 )
| ~ ~ ( c @ ( sK6_SY233 @ SV15 ) @ sK3_SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV9: reg,SV12: reg] :
( ( ( ~ ( c @ SV12 @ sK3_SY4 ) )
= $true )
| ( ( ~ ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) )
| ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) ) )
= $true )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV2: $i,SV5: $i > $o,SV13: $i,SV8: $i] :
( ( ( ~ ( fool @ SV8 @ SV13 ) )
= $true )
| ( ( SV5 @ SV13 )
= $true )
| ( ( fool @ SV2 @ SV8 )
= $false )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV2: $i,SV5: $i > $o,SV16: $i,SV11: $i] :
( ( ( ~ ( fool @ SV11 @ SV16 )
| ( SV5 @ SV16 ) )
= $true )
| ( ( fool @ SV2 @ SV11 )
= $false )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV14: reg,SV17: reg] :
( ( ~ ( c @ SV17 @ sK3_SY4 )
| ( c @ SV17 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV15: reg] :
( ( ~ ( c @ ( sK6_SY233 @ SV15 ) @ SV15 )
| ~ ~ ( c @ ( sK6_SY233 @ SV15 ) @ sK3_SY4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV9: reg,SV12: reg] :
( ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) )
| ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) ) )
= $true )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV2: $i,SV5: $i > $o,SV13: $i,SV8: $i] :
( ( ( fool @ SV8 @ SV13 )
= $false )
| ( ( SV5 @ SV13 )
= $true )
| ( ( fool @ SV2 @ SV8 )
= $false )
| ( ( fool @ SV2 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV2: $i,SV5: $i > $o,SV16: $i,SV11: $i] :
( ( ( ~ ( fool @ SV11 @ SV16 ) )
= $true )
| ( ( SV5 @ SV16 )
= $true )
| ( ( fool @ SV2 @ SV11 )
= $false )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV14: reg,SV17: reg] :
( ( ( ~ ( c @ SV17 @ sK3_SY4 ) )
= $true )
| ( ( c @ SV17 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV15: reg] :
( ( ~ ( c @ ( sK6_SY233 @ SV15 ) @ SV15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV15: reg] :
( ( ~ ~ ( c @ ( sK6_SY233 @ SV15 ) @ sK3_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV9: reg,SV12: reg] :
( ( ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) )
| ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV2: $i,SV5: $i > $o,SV16: $i,SV11: $i] :
( ( ( fool @ SV11 @ SV16 )
= $false )
| ( ( SV5 @ SV16 )
= $true )
| ( ( fool @ SV2 @ SV11 )
= $false )
| ( ( SV5 @ ( sK8_SY172 @ SV5 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV14: reg,SV17: reg] :
( ( ( c @ SV17 @ sK3_SY4 )
= $false )
| ( ( c @ SV17 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV15: reg] :
( ( c @ ( sK6_SY233 @ SV15 ) @ SV15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(105,plain,
! [SV15: reg] :
( ( ~ ( c @ ( sK6_SY233 @ SV15 ) @ sK3_SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV9: reg,SV12: reg] :
( ( ( ~ ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) ) )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(107,plain,
! [SV9: reg,SV12: reg] :
( ( ( ~ ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV15: reg] :
( ( c @ ( sK6_SY233 @ SV15 ) @ sK3_SY4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(109,plain,
! [SV9: reg,SV12: reg] :
( ( ( ! [SY262: reg] :
( ~ ( c @ SY262 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY262 @ SV12 ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(110,plain,
! [SV9: reg,SV12: reg] :
( ( ( ! [SY263: reg] :
( ~ ( c @ SY263 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SY263 @ sK3_SY4 ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
! [SV9: reg,SV12: reg,SV18: reg] :
( ( ( ~ ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SV18 @ SV12 ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(112,plain,
! [SV9: reg,SV12: reg,SV19: reg] :
( ( ( ~ ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
| ( c @ SV19 @ sK3_SY4 ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(113,plain,
! [SV9: reg,SV12: reg,SV18: reg] :
( ( ( ~ ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(114,plain,
! [SV9: reg,SV12: reg,SV19: reg] :
( ( ( ~ ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV9: reg,SV12: reg,SV18: reg] :
( ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV9: reg,SV12: reg,SV19: reg] :
( ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( ~ ( c @ SV12 @ SV9 )
| ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ~ ( c @ SV12 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ~ ( c @ SV12 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( c @ SV12 @ SV9 )
= $false )
| ( ( ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(120,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( c @ SV12 @ SV9 )
= $false )
| ( ( ~ ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) ) )
= $true )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(121,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) )
| ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(123,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(124,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(125,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(126,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ~ ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $false )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
! [SV18: reg,SV9: reg,SV12: reg] :
( ( ( ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(129,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ! [SY264: reg] :
( ~ ( c @ SY264 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY264 @ SV12 ) ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(130,plain,
! [SV19: reg,SV9: reg,SV12: reg] :
( ( ( ! [SY265: reg] :
( ~ ( c @ SY265 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SY265 @ SV9 ) ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(131,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV20: reg] :
( ( ( ~ ( c @ SV20 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SV20 @ SV12 ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(132,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV21: reg] :
( ( ( ~ ( c @ SV21 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SV21 @ SV9 ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(133,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV22: reg] :
( ( ( ~ ( c @ SV22 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SV22 @ SV12 ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV23: reg] :
( ( ( ~ ( c @ SV23 @ ( sK4_SY53 @ SV12 @ SV9 ) )
| ( c @ SV23 @ SV9 ) )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV20: reg] :
( ( ( ~ ( c @ SV20 @ ( sK4_SY53 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV20 @ SV12 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV21: reg] :
( ( ( ~ ( c @ SV21 @ ( sK4_SY53 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV21 @ SV9 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV22: reg] :
( ( ( ~ ( c @ SV22 @ ( sK4_SY53 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV22 @ SV12 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV23: reg] :
( ( ( ~ ( c @ SV23 @ ( sK4_SY53 @ SV12 @ SV9 ) ) )
= $true )
| ( ( c @ SV23 @ SV9 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV20: reg] :
( ( ( c @ SV20 @ ( sK4_SY53 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV20 @ SV12 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV18: reg,SV9: reg,SV12: reg,SV21: reg] :
( ( ( c @ SV21 @ ( sK4_SY53 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV21 @ SV9 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV18 @ SV12 )
= $true )
| ( ( c @ SV18 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV22: reg] :
( ( ( c @ SV22 @ ( sK4_SY53 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV22 @ SV12 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(142,plain,
! [SV19: reg,SV9: reg,SV12: reg,SV23: reg] :
( ( ( c @ SV23 @ ( sK4_SY53 @ SV12 @ SV9 ) )
= $false )
| ( ( c @ SV23 @ SV9 )
= $true )
| ( ( c @ SV12 @ SV9 )
= $false )
| ( ( c @ SV12 @ sK3_SY4 )
= $false )
| ( ( c @ SV19 @ sK3_SY4 )
= $true )
| ( ( c @ SV19 @ ( sK5_SY236 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,142,141,140,139,108,104,103,102,96,85,78,70,62]) ).
thf(144,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n005.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 10:01:59 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
% 0.40/0.28
% 0.40/0.28 No.of.Axioms: 8
% 0.40/0.28
% 0.40/0.28 Length.of.Defs: 6571
% 0.40/0.28
% 0.40/0.28 Contains.Choice.Funs: false
% 0.40/0.28 ........
% 0.40/0.28
% 0.40/0.28 ********************************
% 0.40/0.28 * All subproblems solved! *
% 0.40/0.28 ********************************
% 0.40/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:143,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.40/0.28
% 0.40/0.28 %**** Beginning of derivation protocol ****
% 0.40/0.28 % SZS output start CNFRefutation
% See solution above
% 0.40/0.28
% 0.40/0.28 %**** End of derivation protocol ****
% 0.40/0.28 %**** no. of clauses in derivation: 139 ****
% 0.40/0.28 %**** clause counter: 143 ****
% 0.40/0.28
% 0.40/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:143,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------