%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL877^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : 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 10:31:01 AM UTC 2026
% Result : Theorem 0.92s 0.47s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 32
% Syntax : Number of formulae : 157 ( 90 unt; 0 typ; 31 def)
% Number of atoms : 1064 ( 360 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 1955 ( 439 ~; 380 |; 8 &;1110 @)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 8 con; 0-4 aty)
% Number of variables : 556 ( 84 ^; 466 !; 6 ?; 556 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
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_sK10_SY148,type,
sK10_SY148: $i ).
thf(tp_sK11_SY155,type,
sK11_SY155: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i > $i > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY124,type,
sK3_SY124: $i > $o ).
thf(tp_sK4_SY133,type,
sK4_SY133: $i ).
thf(tp_sK5_SY132,type,
sK5_SY132: $i ).
thf(tp_sK6_SY139,type,
sK6_SY139: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SY140,type,
sK8_SY140: $i > $o ).
thf(tp_sK9_SY149,type,
sK9_SY149: $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,conjecture,
! [R: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ R @ Phi ) ) @ ( mbox @ R @ ( mnot @ ( mbox @ R @ Phi ) ) ) ) ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mdia @ R @ Phi ) @ ( mbox @ R @ ( mdia @ R @ Phi ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ! [R: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ R @ Phi ) ) @ ( mbox @ R @ ( mnot @ ( mbox @ R @ Phi ) ) ) ) ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mdia @ R @ Phi ) @ ( mbox @ R @ ( mdia @ R @ Phi ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i > $i > $o] :
( ! [SY43: $i,SY44: $i > $o] :
( ~ ~ ! [SY45: $i] :
( ~ ( SY0 @ SY43 @ SY45 )
| ( SY44 @ SY45 ) )
| ! [SY46: $i] :
( ~ ( SY0 @ SY43 @ SY46 )
| ~ ! [SY39: $i] :
( ~ ( SY0 @ SY46 @ SY39 )
| ( SY44 @ SY39 ) ) ) )
<=> ! [SY98: $i,SY99: $i > $o] :
( ~ ~ ! [SY100: $i] :
( ~ ( SY0 @ SY98 @ SY100 )
| ~ ( SY99 @ SY100 ) )
| ! [SY101: $i] :
( ~ ( SY0 @ SY98 @ SY101 )
| ~ ! [SY94: $i] :
( ~ ( SY0 @ SY101 @ SY94 )
| ~ ( SY99 @ SY94 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,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]) ).
thf(4,plain,
( ( ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) )
<=> ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) )
=> ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(6,plain,
( ( ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) )
=> ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[4]) ).
thf(7,plain,
( ( ~ ( ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) )
=> ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) )
=> ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) )
=> ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) )
| ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,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]) ).
thf(11,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) )
| ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY124: $i > $o] :
( ~ ~ ! [SY125: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY125 )
| ~ ( SY124 @ SY125 ) )
| ! [SY126: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY126 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SY126 @ SX3 )
| ~ ( SY124 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV1: $i] :
( ( ! [SY128: $i > $o] :
( ~ ~ ! [SY129: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY129 )
| ( SY128 @ SY129 ) )
| ! [SY130: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY130 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SY130 @ SX3 )
| ( SY128 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ! [SY132: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY132 )
| ~ ( sK3_SY124 @ SY132 ) )
| ! [SY133: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY133 )
| ~ ! [SY134: $i] :
( ~ ( sK1_SY0 @ SY133 @ SY134 )
| ~ ( sK3_SY124 @ SY134 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ~ ~ ! [SY135: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY135 )
| ( SV2 @ SY135 ) )
| ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ! [SY132: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY132 )
| ~ ( sK3_SY124 @ SY132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [SY133: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY133 )
| ~ ! [SY134: $i] :
( ~ ( sK1_SY0 @ SY133 @ SY134 )
| ~ ( sK3_SY124 @ SY134 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ( ~ ~ ! [SY135: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY135 )
| ( SV2 @ SY135 ) ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SY132: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY132 )
| ~ ( sK3_SY124 @ SY132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK4_SY133 )
| ~ ! [SY138: $i] :
( ~ ( sK1_SY0 @ sK4_SY133 @ SY138 )
| ~ ( sK3_SY124 @ SY138 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(24,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ( ~ ! [SY135: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY135 )
| ( SV2 @ SY135 ) ) )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY132: $i] :
( ~ ( sK1_SY0 @ sK2_SX0 @ SY132 )
| ~ ( sK3_SY124 @ SY132 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK4_SY133 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ! [SY138: $i] :
( ~ ( sK1_SY0 @ sK4_SY133 @ SY138 )
| ~ ( sK3_SY124 @ SY138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV2: $i > $o,SV1: $i] :
( ( ( ! [SY135: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY135 )
| ( SV2 @ SY135 ) ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK5_SY132 )
| ~ ( sK3_SY124 @ sK5_SY132 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
( ( sK1_SY0 @ sK2_SX0 @ sK4_SY133 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [SY138: $i] :
( ~ ( sK1_SY0 @ sK4_SY133 @ SY138 )
| ~ ( sK3_SY124 @ SY138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV3 )
| ( SV2 @ SV3 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( sK1_SY0 @ sK2_SX0 @ sK5_SY132 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ( sK3_SY124 @ sK5_SY132 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV4: $i] :
( ( ~ ( sK1_SY0 @ sK4_SY133 @ SV4 )
| ~ ( sK3_SY124 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV3 ) )
= $true )
| ( ( SV2 @ SV3 )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( sK1_SY0 @ sK2_SX0 @ sK5_SY132 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( sK3_SY124 @ sK5_SY132 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV4: $i] :
( ( ( ~ ( sK1_SY0 @ sK4_SY133 @ SV4 ) )
= $true )
| ( ( ~ ( sK3_SY124 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i > $o,SV3: $i,SV1: $i] :
( ( ( sK1_SY0 @ SV1 @ SV3 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( sK1_SY0 @ SV1 @ SY136 )
| ~ ! [SY137: $i] :
( ~ ( sK1_SY0 @ SY136 @ SY137 )
| ( SV2 @ SY137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: $i] :
( ( ( sK1_SY0 @ sK4_SY133 @ SV4 )
= $false )
| ( ( ~ ( sK3_SY124 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: $i,SV2: $i > $o,SV5: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV5 )
| ~ ! [SY139: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY139 )
| ( SV2 @ SY139 ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV4: $i] :
( ( ( sK3_SY124 @ SV4 )
= $false )
| ( ( sK1_SY0 @ sK4_SY133 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: $i,SV2: $i > $o,SV5: $i,SV1: $i] :
( ( ( ~ ( sK1_SY0 @ SV1 @ SV5 ) )
= $true )
| ( ( ~ ! [SY139: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY139 )
| ( SV2 @ SY139 ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV3: $i,SV2: $i > $o,SV5: $i,SV1: $i] :
( ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( ~ ! [SY139: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY139 )
| ( SV2 @ SY139 ) ) )
= $true )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
! [SV3: $i,SV1: $i,SV2: $i > $o,SV5: $i] :
( ( ( ! [SY139: $i] :
( ~ ( sK1_SY0 @ SV5 @ SY139 )
| ( SV2 @ SY139 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i,SV5: $i] :
( ( ( ~ ( sK1_SY0 @ SV5 @ ( sK6_SY139 @ SV3 @ SV1 @ SV2 @ SV5 ) )
| ( SV2 @ ( sK6_SY139 @ SV3 @ SV1 @ SV2 @ SV5 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(48,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i,SV5: $i] :
( ( ( ~ ( sK1_SY0 @ SV5 @ ( sK6_SY139 @ SV3 @ SV1 @ SV2 @ SV5 ) ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(49,plain,
! [SV5: $i,SV1: $i,SV3: $i,SV2: $i > $o] :
( ( ( SV2 @ ( sK6_SY139 @ SV3 @ SV1 @ SV2 @ SV5 ) )
= $false )
| ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
! [SV2: $i > $o,SV1: $i,SV3: $i,SV5: $i] :
( ( ( sK1_SY0 @ SV5 @ ( sK6_SY139 @ SV3 @ SV1 @ SV2 @ SV5 ) )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV5 )
= $false )
| ( ( SV2 @ SV3 )
= $true )
| ( ( sK1_SY0 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,50,49,43,38,37]) ).
thf(52,plain,
( ( ~ ( ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY121 )
| ~ ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( sK1_SY0 @ SY119 @ SY122 )
| ~ ! [SY123: $i] :
( ~ ( sK1_SY0 @ SY122 @ SY123 )
| ~ ( SY120 @ SY123 ) ) ) )
=> ! [SY114: $i,SY115: $i > $o] :
( ~ ~ ! [SY116: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY116 )
| ( SY115 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( sK1_SY0 @ SY114 @ SY117 )
| ~ ! [SY118: $i] :
( ~ ( sK1_SY0 @ SY117 @ SY118 )
| ( SY115 @ SY118 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(53,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) )
| ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,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]) ).
thf(54,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) )
| ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(55,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( sK1_SY0 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SX2 @ SX3 )
| ~ ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [SY140: $i > $o] :
( ~ ~ ! [SY141: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY141 )
| ( SY140 @ SY141 ) )
| ! [SY142: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY142 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SY142 @ SX3 )
| ( SY140 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(59,plain,
! [SV6: $i] :
( ( ! [SY144: $i > $o] :
( ~ ~ ! [SY145: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY145 )
| ~ ( SY144 @ SY145 ) )
| ! [SY146: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY146 )
| ~ ! [SX3: $i] :
( ~ ( sK1_SY0 @ SY146 @ SX3 )
| ~ ( SY144 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ~ ! [SY148: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY148 )
| ( sK8_SY140 @ SY148 ) )
| ! [SY149: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( sK1_SY0 @ SY149 @ SY150 )
| ( sK8_SY140 @ SY150 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(61,plain,
! [SV7: $i > $o,SV6: $i] :
( ( ~ ~ ! [SY151: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY151 )
| ~ ( SV7 @ SY151 ) )
| ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ~ ! [SY148: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY148 )
| ( sK8_SY140 @ SY148 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(63,plain,
( ( ! [SY149: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( sK1_SY0 @ SY149 @ SY150 )
| ( sK8_SY140 @ SY150 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV7: $i > $o,SV6: $i] :
( ( ( ~ ~ ! [SY151: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY151 )
| ~ ( SV7 @ SY151 ) ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ ! [SY148: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY148 )
| ( sK8_SY140 @ SY148 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(66,plain,
( ( ~ ( sK1_SY0 @ sK7_SX0 @ sK9_SY149 )
| ~ ! [SY154: $i] :
( ~ ( sK1_SY0 @ sK9_SY149 @ SY154 )
| ( sK8_SY140 @ SY154 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(67,plain,
! [SV7: $i > $o,SV6: $i] :
( ( ( ~ ! [SY151: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY151 )
| ~ ( SV7 @ SY151 ) ) )
= $false )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
( ( ! [SY148: $i] :
( ~ ( sK1_SY0 @ sK7_SX0 @ SY148 )
| ( sK8_SY140 @ SY148 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ( sK1_SY0 @ sK7_SX0 @ sK9_SY149 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(70,plain,
( ( ~ ! [SY154: $i] :
( ~ ( sK1_SY0 @ sK9_SY149 @ SY154 )
| ( sK8_SY140 @ SY154 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV7: $i > $o,SV6: $i] :
( ( ( ! [SY151: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY151 )
| ~ ( SV7 @ SY151 ) ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
( ( ~ ( sK1_SY0 @ sK7_SX0 @ sK10_SY148 )
| ( sK8_SY140 @ sK10_SY148 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(73,plain,
( ( sK1_SY0 @ sK7_SX0 @ sK9_SY149 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ! [SY154: $i] :
( ~ ( sK1_SY0 @ sK9_SY149 @ SY154 )
| ( sK8_SY140 @ SY154 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV7: $i > $o,SV8: $i,SV6: $i] :
( ( ( ~ ( sK1_SY0 @ SV6 @ SV8 )
| ~ ( SV7 @ SV8 ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
( ( ~ ( sK1_SY0 @ sK7_SX0 @ sK10_SY148 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(77,plain,
( ( sK8_SY140 @ sK10_SY148 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(78,plain,
! [SV9: $i] :
( ( ~ ( sK1_SY0 @ sK9_SY149 @ SV9 )
| ( sK8_SY140 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV7: $i > $o,SV8: $i,SV6: $i] :
( ( ( ~ ( sK1_SY0 @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( SV7 @ SV8 ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
( ( sK1_SY0 @ sK7_SX0 @ sK10_SY148 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV9: $i] :
( ( ( ~ ( sK1_SY0 @ sK9_SY149 @ SV9 ) )
= $true )
| ( ( sK8_SY140 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV7: $i > $o,SV8: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( SV7 @ SV8 ) )
= $true )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV9: $i] :
( ( ( sK1_SY0 @ sK9_SY149 @ SV9 )
= $false )
| ( ( sK8_SY140 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV6: $i,SV8: $i,SV7: $i > $o] :
( ( ( SV7 @ SV8 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( ! [SY152: $i] :
( ~ ( sK1_SY0 @ SV6 @ SY152 )
| ~ ! [SY153: $i] :
( ~ ( sK1_SY0 @ SY152 @ SY153 )
| ~ ( SV7 @ SY153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(85,plain,
! [SV8: $i,SV7: $i > $o,SV10: $i,SV6: $i] :
( ( ( ~ ( sK1_SY0 @ SV6 @ SV10 )
| ~ ! [SY155: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY155 )
| ~ ( SV7 @ SY155 ) ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(86,plain,
! [SV8: $i,SV7: $i > $o,SV10: $i,SV6: $i] :
( ( ( ~ ( sK1_SY0 @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ! [SY155: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY155 )
| ~ ( SV7 @ SY155 ) ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(87,plain,
! [SV8: $i,SV7: $i > $o,SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ~ ! [SY155: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY155 )
| ~ ( SV7 @ SY155 ) ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(88,plain,
! [SV8: $i,SV6: $i,SV7: $i > $o,SV10: $i] :
( ( ( ! [SY155: $i] :
( ~ ( sK1_SY0 @ SV10 @ SY155 )
| ~ ( SV7 @ SY155 ) ) )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(89,plain,
! [SV7: $i > $o,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( sK1_SY0 @ SV10 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) )
| ~ ( SV7 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) ) )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
! [SV7: $i > $o,SV6: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( sK1_SY0 @ SV10 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) ) )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(91,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV7: $i > $o] :
( ( ( ~ ( SV7 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) ) )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(92,plain,
! [SV7: $i > $o,SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(93,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV7: $i > $o] :
( ( ( SV7 @ ( sK11_SY155 @ SV8 @ SV6 @ SV7 @ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV7 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(94,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : $true
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV20: $i] : $true ))]]) ).
thf(96,plain,
! [SV18: $i > $o,SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( SV18 @ SV8 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(97,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK7_SX0 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK7_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV11: $i] : ( SV11 = sK7_SX0 ) ))]]) ).
thf(98,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK4_SY133 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK4_SY133 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV12: $i] : ( SV12 = sK4_SY133 ) ))]]) ).
thf(99,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK2_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV13: $i] : ( SV13 = sK2_SX0 ) ))]]) ).
thf(100,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK5_SY132 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK5_SY132 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV14: $i] : ( SV14 = sK5_SY132 ) ))]]) ).
thf(101,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK9_SY149 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK9_SY149 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV15: $i] : ( SV15 = sK9_SY149 ) ))]]) ).
thf(102,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK10_SY148 )
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK10_SY148 )
= $false ) ),
inference(prim_subst,[status(thm)],[92:[bind(SV7,$thf( ^ [SV16: $i] : ( SV16 = sK10_SY148 ) ))]]) ).
thf(105,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV18: $i > $o] :
( ( ( ~ ( SV18
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 )
@ SV10 ) ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( SV18 @ SV8 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(106,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK7_SX0 )
@ SV10 )
= sK7_SX0 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK7_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV11: $i] : ( SV11 = sK7_SX0 ) ))]]) ).
thf(107,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK4_SY133 )
@ SV10 )
= sK4_SY133 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK4_SY133 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV12: $i] : ( SV12 = sK4_SY133 ) ))]]) ).
thf(108,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV10 )
= sK2_SX0 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK2_SX0 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV13: $i] : ( SV13 = sK2_SX0 ) ))]]) ).
thf(109,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK5_SY132 )
@ SV10 )
= sK5_SY132 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK5_SY132 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV14: $i] : ( SV14 = sK5_SY132 ) ))]]) ).
thf(110,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK9_SY149 )
@ SV10 )
= sK9_SY149 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK9_SY149 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV15: $i] : ( SV15 = sK9_SY149 ) ))]]) ).
thf(111,plain,
! [SV10: $i,SV6: $i,SV8: $i] :
( ( ( ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK10_SY148 )
@ SV10 )
= sK10_SY148 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( SV8 = sK10_SY148 )
= $false ) ),
inference(prim_subst,[status(thm)],[93:[bind(SV7,$thf( ^ [SV16: $i] : ( SV16 = sK10_SY148 ) ))]]) ).
thf(112,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV18: $i > $o] :
( ( ( SV18 @ SV8 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 )
@ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(113,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV18: $i > $o] :
( ( ( SV18
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 )
@ SV10 ) )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( ~ ( SV18 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV10: $i,SV6: $i,SV8: $i,SV18: $i > $o] :
( ( ( SV18 @ SV8 )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( SV18
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] :
~ ( SV18 @ SX0 )
@ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(115,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK7_SX0 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK7_SX0 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK7_SX0 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[97:[bind(SV8,$thf( sK7_SX0 ))]]) ).
thf(116,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK4_SY133 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK4_SY133 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK4_SY133 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[98:[bind(SV8,$thf( sK4_SY133 ))]]) ).
thf(117,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK2_SX0 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK2_SX0 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV8,$thf( sK2_SX0 ))]]) ).
thf(118,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK5_SY132 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK5_SY132 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK5_SY132 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[100:[bind(SV8,$thf( sK5_SY132 ))]]) ).
thf(119,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK9_SY149 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK9_SY149 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK9_SY149 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV8,$thf( sK9_SY149 ))]]) ).
thf(120,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK10_SY148 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ sK10_SY148 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK10_SY148 )
@ SV10 ) )
= $true ) ),
inference(extuni,[status(esa)],[102:[bind(SV8,$thf( sK10_SY148 ))]]) ).
thf(121,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK7_SX0 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK7_SX0 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK7_SX0 )
@ SV10 )
= sK7_SX0 )
= $true ) ),
inference(extuni,[status(esa)],[106:[bind(SV8,$thf( sK7_SX0 ))]]) ).
thf(122,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK4_SY133 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK4_SY133 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK4_SY133 )
@ SV10 )
= sK4_SY133 )
= $true ) ),
inference(extuni,[status(esa)],[107:[bind(SV8,$thf( sK4_SY133 ))]]) ).
thf(123,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK2_SX0 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK2_SX0 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK2_SX0 )
@ SV10 )
= sK2_SX0 )
= $true ) ),
inference(extuni,[status(esa)],[108:[bind(SV8,$thf( sK2_SX0 ))]]) ).
thf(124,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK5_SY132 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK5_SY132 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK5_SY132 )
@ SV10 )
= sK5_SY132 )
= $true ) ),
inference(extuni,[status(esa)],[109:[bind(SV8,$thf( sK5_SY132 ))]]) ).
thf(125,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK9_SY149 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK9_SY149 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK9_SY149 )
@ SV10 )
= sK9_SY149 )
= $true ) ),
inference(extuni,[status(esa)],[110:[bind(SV8,$thf( sK9_SY149 ))]]) ).
thf(126,plain,
! [SV10: $i,SV6: $i] :
( ( ( sK1_SY0 @ SV6 @ sK10_SY148 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( ( sK11_SY155 @ sK10_SY148 @ SV6
@ ^ [SX0: $i] : ( SX0 = sK10_SY148 )
@ SV10 )
= sK10_SY148 )
= $true ) ),
inference(extuni,[status(esa)],[111:[bind(SV8,$thf( sK10_SY148 ))]]) ).
thf(127,plain,
! [SV6: $i,SV8: $i,SV10: $i] :
( ( ( sK1_SY0 @ SV10
@ ( sK11_SY155 @ SV8 @ SV6
@ ^ [SX0: $i] : $true
@ SV10 ) )
= $true )
| ( ( sK1_SY0 @ SV6 @ SV10 )
= $false )
| ( ( sK1_SY0 @ SV6 @ SV8 )
= $false ) ),
inference(sim,[status(thm)],[94]) ).
thf(128,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[73,127,126,125,124,123,122,121,120,119,118,117,116,115,114,112,93,92,83,80,77]) ).
thf(129,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[128,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL877^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.06/0.19 % Computer : n005.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 12:35:44 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.92/0.47
% 0.92/0.47 No.of.Axioms: 0
% 0.92/0.47
% 0.92/0.47 Length.of.Defs: 5324
% 0.92/0.47
% 0.92/0.47 Contains.Choice.Funs: false
% 0.92/0.47 .....
% 0.92/0.47
% 0.92/0.47 ********************************
% 0.92/0.47 * All subproblems solved! *
% 0.92/0.47 ********************************
% 0.92/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:128,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.92/0.47
% 0.92/0.47 %**** Beginning of derivation protocol ****
% 0.92/0.47 % SZS output start CNFRefutation
% See solution above
% 0.92/0.48
% 0.92/0.48 %**** End of derivation protocol ****
% 0.92/0.48 %**** no. of clauses in derivation: 126 ****
% 0.92/0.48 %**** clause counter: 128 ****
% 0.92/0.48
% 0.92/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,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:128,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------