%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : AGT027^1 : 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 : n017.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 10:07:08 AM UTC 2026
% Result : Theorem 1.42s 0.46s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 311 ( 128 unt; 0 typ; 31 def)
% Number of atoms : 1983 ( 590 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 4148 ( 725 ~; 715 |; 34 &;2666 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 269 ( 269 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 5 con; 0-3 aty)
% Number of variables : 974 ( 63 ^; 905 !; 6 ?; 974 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_a,type,
a: mu ).
thf(tp_a1,type,
a1: $i > $i > $o ).
thf(tp_a2,type,
a2: $i > $i > $o ).
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_p,type,
p: mu > $i > $o ).
thf(tp_q,type,
q: mu > $i > $o ).
thf(tp_r,type,
r: mu > $i > $o ).
thf(tp_s,type,
s: mu > $i > $o ).
thf(tp_sK10_SY393,type,
sK10_SY393: ( $i > $o ) > $i > $i ).
thf(tp_sK11_SY392,type,
sK11_SY392: ( $i > $o ) > $i > $i ).
thf(tp_sK12_SY433,type,
sK12_SY433: ( $i > $o ) > $i > $i ).
thf(tp_sK13_SY432,type,
sK13_SY432: ( $i > $o ) > $i > $i ).
thf(tp_sK14_SY450,type,
sK14_SY450: $i > $i ).
thf(tp_sK1_SY19,type,
sK1_SY19: $i ).
thf(tp_sK2_SY562,type,
sK2_SY562: mu > $i ).
thf(tp_sK3_SY63,type,
sK3_SY63: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK4_SY115,type,
sK4_SY115: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY169,type,
sK5_SY169: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY217,type,
sK6_SY217: ( $i > $o ) > $i > $i ).
thf(tp_sK7_SY265,type,
sK7_SY265: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY313,type,
sK8_SY313: ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY352,type,
sK9_SY352: ( $i > $o ) > $i > $i ).
thf(tp_tom,type,
tom: mu ).
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,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a2 @ Phi ) ) @ ( mbox @ a2 @ ( mnot @ ( mbox @ a2 @ Phi ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_a2) ).
thf(2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a1 @ Phi ) ) @ ( mbox @ a1 @ ( mnot @ ( mbox @ a1 @ Phi ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5_for_a1) ).
thf(3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a2 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_a2_a2) ).
thf(4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a2 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_a2_a1) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a1 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_a1_a2) ).
thf(6,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a1 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4s_for_a1_a1) ).
thf(7,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_I_for_a2_a1) ).
thf(8,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mnot @ ( mbox @ a2 @ ( mnot @ Phi ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_a2) ).
thf(9,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mnot @ ( mbox @ a1 @ ( mnot @ Phi ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_D_for_a1) ).
thf(10,axiom,
mvalid @ ( mdia @ a1 @ ( s @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a4) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X ) @ ( mbox @ a1 @ ( r @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X ) @ ( s @ X ) ) @ ( q @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a2) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X ) ) @ ( p @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1) ).
thf(14,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(15,negated_conjecture,
( ( mvalid
@ ( mexists_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [SY19: $i] :
~ ! [SY20: mu] :
~ ! [SY21: $i] :
( ~ ( a1 @ SY19 @ SY21 )
| ( p @ SY20 @ SY21 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15,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(17,plain,
( ( ! [SY67: $i,SY68: $i > $o] :
( ~ ~ ! [SY69: $i] :
( ~ ( a2 @ SY67 @ SY69 )
| ( SY68 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( a2 @ SY67 @ SY70 )
| ~ ! [SY63: $i] :
( ~ ( a2 @ SY70 @ SY63 )
| ( SY68 @ SY63 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,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(18,plain,
( ( ! [SY119: $i,SY120: $i > $o] :
( ~ ~ ! [SY121: $i] :
( ~ ( a1 @ SY119 @ SY121 )
| ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( a1 @ SY119 @ SY122 )
| ~ ! [SY115: $i] :
( ~ ( a1 @ SY122 @ SY115 )
| ( SY120 @ SY115 ) ) ) ) )
= $true ),
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(19,plain,
( ( ! [SY167: $i,SY168: $i > $o] :
( ~ ! [SY169: $i] :
( ~ ( a2 @ SY167 @ SY169 )
| ( SY168 @ SY169 ) )
| ! [SY170: $i] :
( ~ ( a2 @ SY167 @ SY170 )
| ! [SY163: $i] :
( ~ ( a2 @ SY170 @ SY163 )
| ( SY168 @ SY163 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,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(20,plain,
( ( ! [SY215: $i,SY216: $i > $o] :
( ~ ! [SY217: $i] :
( ~ ( a2 @ SY215 @ SY217 )
| ( SY216 @ SY217 ) )
| ! [SY218: $i] :
( ~ ( a1 @ SY215 @ SY218 )
| ! [SY211: $i] :
( ~ ( a2 @ SY218 @ SY211 )
| ( SY216 @ SY211 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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(21,plain,
( ( ! [SY263: $i,SY264: $i > $o] :
( ~ ! [SY265: $i] :
( ~ ( a1 @ SY263 @ SY265 )
| ( SY264 @ SY265 ) )
| ! [SY266: $i] :
( ~ ( a2 @ SY263 @ SY266 )
| ! [SY259: $i] :
( ~ ( a1 @ SY266 @ SY259 )
| ( SY264 @ SY259 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,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(22,plain,
( ( ! [SY311: $i,SY312: $i > $o] :
( ~ ! [SY313: $i] :
( ~ ( a1 @ SY311 @ SY313 )
| ( SY312 @ SY313 ) )
| ! [SY314: $i] :
( ~ ( a1 @ SY311 @ SY314 )
| ! [SY307: $i] :
( ~ ( a1 @ SY314 @ SY307 )
| ( SY312 @ SY307 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,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(23,plain,
( ( ! [SY350: $i,SY351: $i > $o] :
( ~ ! [SY352: $i] :
( ~ ( a2 @ SY350 @ SY352 )
| ( SY351 @ SY352 ) )
| ! [SY353: $i] :
( ~ ( a1 @ SY350 @ SY353 )
| ( SY351 @ SY353 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,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(24,plain,
( ( ! [SY390: $i,SY391: $i > $o] :
( ~ ! [SY392: $i] :
( ~ ( a2 @ SY390 @ SY392 )
| ( SY391 @ SY392 ) )
| ~ ! [SY393: $i] :
( ~ ( a2 @ SY390 @ SY393 )
| ~ ( SY391 @ SY393 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,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(25,plain,
( ( ! [SY430: $i,SY431: $i > $o] :
( ~ ! [SY432: $i] :
( ~ ( a1 @ SY430 @ SY432 )
| ( SY431 @ SY432 ) )
| ~ ! [SY433: $i] :
( ~ ( a1 @ SY430 @ SY433 )
| ~ ( SY431 @ SY433 ) ) ) )
= $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(26,plain,
( ( ! [SY449: $i] :
~ ! [SY450: $i] :
( ~ ( a1 @ SY449 @ SY450 )
| ~ ( s @ a @ SY450 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,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(27,plain,
( ( ! [SY479: $i,SY480: mu,SY481: $i] :
( ~ ( a1 @ SY479 @ SY481 )
| ~ ( s @ SY480 @ SY481 )
| ! [SY476: $i] :
( ~ ( a1 @ SY481 @ SY476 )
| ( r @ SY480 @ SY476 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,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(28,plain,
( ( ! [SY512: $i,SY513: mu,SY514: $i] :
( ~ ( a1 @ SY512 @ SY514 )
| ~ ~ ( ~ ( r @ SY513 @ SY514 )
| ~ ( s @ SY513 @ SY514 ) )
| ( q @ SY513 @ SY514 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,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(29,plain,
( ( ! [SY553: $i,SY554: mu,SY555: $i] :
( ~ ( a2 @ SY553 @ SY555 )
| ~ ~ ! [SY550: $i] :
( ~ ( a2 @ SY555 @ SY550 )
| ~ ( q @ SY554 @ SY550 ) )
| ( p @ SY554 @ SY555 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(30,plain,
( ( ~ ! [SY561: mu] :
~ ! [SY562: $i] :
( ~ ( a1 @ sK1_SY19 @ SY562 )
| ( p @ SY561 @ SY562 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(31,plain,
( ( ! [SY561: mu] :
~ ! [SY562: $i] :
( ~ ( a1 @ sK1_SY19 @ SY562 )
| ( p @ SY561 @ SY562 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [SY561: mu] :
( ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SY561 ) )
& ~ ( p @ SY561 @ ( sK2_SY562 @ SY561 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(33,plain,
( ( ! [SY67: $i,SY68: $i > $o] :
( ! [SY69: $i] :
( ~ ( a2 @ SY67 @ SY69 )
| ( SY68 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( a2 @ SY67 @ SY70 )
| ( ( a2 @ SY70 @ ( sK3_SY63 @ SY70 @ SY68 @ SY67 ) )
& ~ ( SY68 @ ( sK3_SY63 @ SY70 @ SY68 @ SY67 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(34,plain,
( ( ! [SY119: $i,SY120: $i > $o] :
( ! [SY121: $i] :
( ~ ( a1 @ SY119 @ SY121 )
| ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( a1 @ SY119 @ SY122 )
| ( ( a1 @ SY122 @ ( sK4_SY115 @ SY122 @ SY120 @ SY119 ) )
& ~ ( SY120 @ ( sK4_SY115 @ SY122 @ SY120 @ SY119 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(35,plain,
( ( ! [SY167: $i,SY168: $i > $o] :
( ( ( a2 @ SY167 @ ( sK5_SY169 @ SY168 @ SY167 ) )
& ~ ( SY168 @ ( sK5_SY169 @ SY168 @ SY167 ) ) )
| ! [SY170: $i] :
( ~ ( a2 @ SY167 @ SY170 )
| ! [SY163: $i] :
( ~ ( a2 @ SY170 @ SY163 )
| ( SY168 @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [SY215: $i,SY216: $i > $o] :
( ( ( a2 @ SY215 @ ( sK6_SY217 @ SY216 @ SY215 ) )
& ~ ( SY216 @ ( sK6_SY217 @ SY216 @ SY215 ) ) )
| ! [SY218: $i] :
( ~ ( a1 @ SY215 @ SY218 )
| ! [SY211: $i] :
( ~ ( a2 @ SY218 @ SY211 )
| ( SY216 @ SY211 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(37,plain,
( ( ! [SY263: $i,SY264: $i > $o] :
( ( ( a1 @ SY263 @ ( sK7_SY265 @ SY264 @ SY263 ) )
& ~ ( SY264 @ ( sK7_SY265 @ SY264 @ SY263 ) ) )
| ! [SY266: $i] :
( ~ ( a2 @ SY263 @ SY266 )
| ! [SY259: $i] :
( ~ ( a1 @ SY266 @ SY259 )
| ( SY264 @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(38,plain,
( ( ! [SY311: $i,SY312: $i > $o] :
( ( ( a1 @ SY311 @ ( sK8_SY313 @ SY312 @ SY311 ) )
& ~ ( SY312 @ ( sK8_SY313 @ SY312 @ SY311 ) ) )
| ! [SY314: $i] :
( ~ ( a1 @ SY311 @ SY314 )
| ! [SY307: $i] :
( ~ ( a1 @ SY314 @ SY307 )
| ( SY312 @ SY307 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(39,plain,
( ( ! [SY350: $i,SY351: $i > $o] :
( ( ( a2 @ SY350 @ ( sK9_SY352 @ SY351 @ SY350 ) )
& ~ ( SY351 @ ( sK9_SY352 @ SY351 @ SY350 ) ) )
| ! [SY353: $i] :
( ~ ( a1 @ SY350 @ SY353 )
| ( SY351 @ SY353 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(40,plain,
( ( ! [SY390: $i,SY391: $i > $o] :
( ( ( a2 @ SY390 @ ( sK11_SY392 @ SY391 @ SY390 ) )
& ~ ( SY391 @ ( sK11_SY392 @ SY391 @ SY390 ) ) )
| ( ( a2 @ SY390 @ ( sK10_SY393 @ SY391 @ SY390 ) )
& ( SY391 @ ( sK10_SY393 @ SY391 @ SY390 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(41,plain,
( ( ! [SY430: $i,SY431: $i > $o] :
( ( ( a1 @ SY430 @ ( sK13_SY432 @ SY431 @ SY430 ) )
& ~ ( SY431 @ ( sK13_SY432 @ SY431 @ SY430 ) ) )
| ( ( a1 @ SY430 @ ( sK12_SY433 @ SY431 @ SY430 ) )
& ( SY431 @ ( sK12_SY433 @ SY431 @ SY430 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(42,plain,
( ( ! [SY449: $i] :
( ( a1 @ SY449 @ ( sK14_SY450 @ SY449 ) )
& ( s @ a @ ( sK14_SY450 @ SY449 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(43,plain,
( ( ! [SY512: $i,SY513: mu,SY514: $i] :
( ~ ( a1 @ SY512 @ SY514 )
| ~ ( r @ SY513 @ SY514 )
| ~ ( s @ SY513 @ SY514 )
| ( q @ SY513 @ SY514 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(44,plain,
( ( ! [SY553: $i,SY554: mu,SY555: $i] :
( ~ ( a2 @ SY553 @ SY555 )
| ! [SY550: $i] :
( ~ ( a2 @ SY555 @ SY550 )
| ~ ( q @ SY554 @ SY550 ) )
| ( p @ SY554 @ SY555 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(45,plain,
( ( ! [SY553: $i,SY554: mu,SY555: $i] :
( ~ ( a2 @ SY553 @ SY555 )
| ! [SY550: $i] :
( ~ ( a2 @ SY555 @ SY550 )
| ~ ( q @ SY554 @ SY550 ) )
| ( p @ SY554 @ SY555 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [SY512: $i,SY513: mu,SY514: $i] :
( ~ ( a1 @ SY512 @ SY514 )
| ~ ( r @ SY513 @ SY514 )
| ~ ( s @ SY513 @ SY514 )
| ( q @ SY513 @ SY514 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(47,plain,
( ( ! [SY479: $i,SY480: mu,SY481: $i] :
( ~ ( a1 @ SY479 @ SY481 )
| ~ ( s @ SY480 @ SY481 )
| ! [SY476: $i] :
( ~ ( a1 @ SY481 @ SY476 )
| ( r @ SY480 @ SY476 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(48,plain,
( ( ! [SY449: $i] :
( ( a1 @ SY449 @ ( sK14_SY450 @ SY449 ) )
& ( s @ a @ ( sK14_SY450 @ SY449 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(49,plain,
( ( ! [SY430: $i,SY431: $i > $o] :
( ( ( a1 @ SY430 @ ( sK13_SY432 @ SY431 @ SY430 ) )
& ~ ( SY431 @ ( sK13_SY432 @ SY431 @ SY430 ) ) )
| ( ( a1 @ SY430 @ ( sK12_SY433 @ SY431 @ SY430 ) )
& ( SY431 @ ( sK12_SY433 @ SY431 @ SY430 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(50,plain,
( ( ! [SY390: $i,SY391: $i > $o] :
( ( ( a2 @ SY390 @ ( sK11_SY392 @ SY391 @ SY390 ) )
& ~ ( SY391 @ ( sK11_SY392 @ SY391 @ SY390 ) ) )
| ( ( a2 @ SY390 @ ( sK10_SY393 @ SY391 @ SY390 ) )
& ( SY391 @ ( sK10_SY393 @ SY391 @ SY390 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(51,plain,
( ( ! [SY350: $i,SY351: $i > $o] :
( ( ( a2 @ SY350 @ ( sK9_SY352 @ SY351 @ SY350 ) )
& ~ ( SY351 @ ( sK9_SY352 @ SY351 @ SY350 ) ) )
| ! [SY353: $i] :
( ~ ( a1 @ SY350 @ SY353 )
| ( SY351 @ SY353 ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(52,plain,
( ( ! [SY311: $i,SY312: $i > $o] :
( ( ( a1 @ SY311 @ ( sK8_SY313 @ SY312 @ SY311 ) )
& ~ ( SY312 @ ( sK8_SY313 @ SY312 @ SY311 ) ) )
| ! [SY314: $i] :
( ~ ( a1 @ SY311 @ SY314 )
| ! [SY307: $i] :
( ~ ( a1 @ SY314 @ SY307 )
| ( SY312 @ SY307 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(53,plain,
( ( ! [SY263: $i,SY264: $i > $o] :
( ( ( a1 @ SY263 @ ( sK7_SY265 @ SY264 @ SY263 ) )
& ~ ( SY264 @ ( sK7_SY265 @ SY264 @ SY263 ) ) )
| ! [SY266: $i] :
( ~ ( a2 @ SY263 @ SY266 )
| ! [SY259: $i] :
( ~ ( a1 @ SY266 @ SY259 )
| ( SY264 @ SY259 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(54,plain,
( ( ! [SY215: $i,SY216: $i > $o] :
( ( ( a2 @ SY215 @ ( sK6_SY217 @ SY216 @ SY215 ) )
& ~ ( SY216 @ ( sK6_SY217 @ SY216 @ SY215 ) ) )
| ! [SY218: $i] :
( ~ ( a1 @ SY215 @ SY218 )
| ! [SY211: $i] :
( ~ ( a2 @ SY218 @ SY211 )
| ( SY216 @ SY211 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(55,plain,
( ( ! [SY167: $i,SY168: $i > $o] :
( ( ( a2 @ SY167 @ ( sK5_SY169 @ SY168 @ SY167 ) )
& ~ ( SY168 @ ( sK5_SY169 @ SY168 @ SY167 ) ) )
| ! [SY170: $i] :
( ~ ( a2 @ SY167 @ SY170 )
| ! [SY163: $i] :
( ~ ( a2 @ SY170 @ SY163 )
| ( SY168 @ SY163 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(56,plain,
( ( ! [SY119: $i,SY120: $i > $o] :
( ! [SY121: $i] :
( ~ ( a1 @ SY119 @ SY121 )
| ( SY120 @ SY121 ) )
| ! [SY122: $i] :
( ~ ( a1 @ SY119 @ SY122 )
| ( ( a1 @ SY122 @ ( sK4_SY115 @ SY122 @ SY120 @ SY119 ) )
& ~ ( SY120 @ ( sK4_SY115 @ SY122 @ SY120 @ SY119 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(57,plain,
( ( ! [SY67: $i,SY68: $i > $o] :
( ! [SY69: $i] :
( ~ ( a2 @ SY67 @ SY69 )
| ( SY68 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( a2 @ SY67 @ SY70 )
| ( ( a2 @ SY70 @ ( sK3_SY63 @ SY70 @ SY68 @ SY67 ) )
& ~ ( SY68 @ ( sK3_SY63 @ SY70 @ SY68 @ SY67 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(58,plain,
( ( ! [SY561: mu] :
( ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SY561 ) )
& ~ ( p @ SY561 @ ( sK2_SY562 @ SY561 ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a2 @ SX0 @ ( sK9_SY352 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK9_SY352 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a1 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,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(60,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( a2 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( a2 @ SX0 @ SX2 )
| ~ ( ~ ( a2 @ SX2 @ ( sK3_SY63 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK3_SY63 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,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(61,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a1 @ SX0 @ ( sK7_SY265 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK7_SY265 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a2 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( a1 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,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(62,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a2 @ SX0 @ ( sK6_SY217 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK6_SY217 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( a2 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,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(63,plain,
( ( ! [SX0: $i] :
~ ( ~ ( a1 @ SX0 @ ( sK14_SY450 @ SX0 ) )
| ~ ( s @ a @ ( sK14_SY450 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,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(64,plain,
( ( ! [SX0: mu] :
~ ( ~ ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SX0 ) )
| ~ ~ ( p @ SX0 @ ( sK2_SY562 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58,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(65,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( a1 @ SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( a1 @ SX0 @ SX2 )
| ~ ( ~ ( a1 @ SX2 @ ( sK4_SY115 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK4_SY115 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,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(66,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a2 @ SX0 @ ( sK5_SY169 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK5_SY169 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a2 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( a2 @ SX2 @ SX3 )
| ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,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(67,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a1 @ SX0 @ ( sK8_SY313 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK8_SY313 @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( a1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( a1 @ 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(68,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a1 @ SX0 @ ( sK13_SY432 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK13_SY432 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( a1 @ SX0 @ ( sK12_SY433 @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK12_SY433 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,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(69,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( a2 @ SX0 @ ( sK11_SY392 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK11_SY392 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( a2 @ SX0 @ ( sK10_SY393 @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK10_SY393 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,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(70,plain,
! [SV1: $i] :
( ( ! [SY563: mu,SY564: $i] :
( ~ ( a2 @ SV1 @ SY564 )
| ! [SY550: $i] :
( ~ ( a2 @ SY564 @ SY550 )
| ~ ( q @ SY563 @ SY550 ) )
| ( p @ SY563 @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(71,plain,
! [SV2: $i] :
( ( ! [SY566: mu,SY567: $i] :
( ~ ( a1 @ SV2 @ SY567 )
| ~ ( r @ SY566 @ SY567 )
| ~ ( s @ SY566 @ SY567 )
| ( q @ SY566 @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(72,plain,
! [SV3: $i] :
( ( ! [SY568: mu,SY569: $i] :
( ~ ( a1 @ SV3 @ SY569 )
| ~ ( s @ SY568 @ SY569 )
| ! [SY476: $i] :
( ~ ( a1 @ SY569 @ SY476 )
| ( r @ SY568 @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(73,plain,
! [SV4: $i] :
( ( ! [SY571: $i > $o] :
( ~ ( ~ ( a2 @ SV4 @ ( sK9_SY352 @ SY571 @ SV4 ) )
| ~ ~ ( SY571 @ ( sK9_SY352 @ SY571 @ SV4 ) ) )
| ! [SY572: $i] :
( ~ ( a1 @ SV4 @ SY572 )
| ( SY571 @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(74,plain,
! [SV5: $i] :
( ( ! [SY573: $i > $o] :
( ! [SY574: $i] :
( ~ ( a2 @ SV5 @ SY574 )
| ( SY573 @ SY574 ) )
| ! [SY575: $i] :
( ~ ( a2 @ SV5 @ SY575 )
| ~ ( ~ ( a2 @ SY575 @ ( sK3_SY63 @ SY575 @ SY573 @ SV5 ) )
| ~ ~ ( SY573 @ ( sK3_SY63 @ SY575 @ SY573 @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY576: $i > $o] :
( ~ ( ~ ( a1 @ SV6 @ ( sK7_SY265 @ SY576 @ SV6 ) )
| ~ ~ ( SY576 @ ( sK7_SY265 @ SY576 @ SV6 ) ) )
| ! [SY577: $i] :
( ~ ( a2 @ SV6 @ SY577 )
| ! [SX3: $i] :
( ~ ( a1 @ SY577 @ SX3 )
| ( SY576 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(76,plain,
! [SV7: $i] :
( ( ! [SY579: $i > $o] :
( ~ ( ~ ( a2 @ SV7 @ ( sK6_SY217 @ SY579 @ SV7 ) )
| ~ ~ ( SY579 @ ( sK6_SY217 @ SY579 @ SV7 ) ) )
| ! [SY580: $i] :
( ~ ( a1 @ SV7 @ SY580 )
| ! [SX3: $i] :
( ~ ( a2 @ SY580 @ SX3 )
| ( SY579 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV8: $i] :
( ( ~ ( ~ ( a1 @ SV8 @ ( sK14_SY450 @ SV8 ) )
| ~ ( s @ a @ ( sK14_SY450 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV9: mu] :
( ( ~ ( ~ ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SV9 ) )
| ~ ~ ( p @ SV9 @ ( sK2_SY562 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV10: $i] :
( ( ! [SY582: $i > $o] :
( ! [SY583: $i] :
( ~ ( a1 @ SV10 @ SY583 )
| ( SY582 @ SY583 ) )
| ! [SY584: $i] :
( ~ ( a1 @ SV10 @ SY584 )
| ~ ( ~ ( a1 @ SY584 @ ( sK4_SY115 @ SY584 @ SY582 @ SV10 ) )
| ~ ~ ( SY582 @ ( sK4_SY115 @ SY584 @ SY582 @ SV10 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(80,plain,
! [SV11: $i] :
( ( ! [SY585: $i > $o] :
( ~ ( ~ ( a2 @ SV11 @ ( sK5_SY169 @ SY585 @ SV11 ) )
| ~ ~ ( SY585 @ ( sK5_SY169 @ SY585 @ SV11 ) ) )
| ! [SY586: $i] :
( ~ ( a2 @ SV11 @ SY586 )
| ! [SX3: $i] :
( ~ ( a2 @ SY586 @ SX3 )
| ( SY585 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(81,plain,
! [SV12: $i] :
( ( ! [SY588: $i > $o] :
( ~ ( ~ ( a1 @ SV12 @ ( sK8_SY313 @ SY588 @ SV12 ) )
| ~ ~ ( SY588 @ ( sK8_SY313 @ SY588 @ SV12 ) ) )
| ! [SY589: $i] :
( ~ ( a1 @ SV12 @ SY589 )
| ! [SX3: $i] :
( ~ ( a1 @ SY589 @ SX3 )
| ( SY588 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV13: $i] :
( ( ! [SY591: $i > $o] :
( ~ ( ~ ( a1 @ SV13 @ ( sK13_SY432 @ SY591 @ SV13 ) )
| ~ ~ ( SY591 @ ( sK13_SY432 @ SY591 @ SV13 ) ) )
| ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SY591 @ SV13 ) )
| ~ ( SY591 @ ( sK12_SY433 @ SY591 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV14: $i] :
( ( ! [SY592: $i > $o] :
( ~ ( ~ ( a2 @ SV14 @ ( sK11_SY392 @ SY592 @ SV14 ) )
| ~ ~ ( SY592 @ ( sK11_SY392 @ SY592 @ SV14 ) ) )
| ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SY592 @ SV14 ) )
| ~ ( SY592 @ ( sK10_SY393 @ SY592 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV15: mu,SV1: $i] :
( ( ! [SY593: $i] :
( ~ ( a2 @ SV1 @ SY593 )
| ! [SY594: $i] :
( ~ ( a2 @ SY593 @ SY594 )
| ~ ( q @ SV15 @ SY594 ) )
| ( p @ SV15 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(85,plain,
! [SV16: mu,SV2: $i] :
( ( ! [SY595: $i] :
( ~ ( a1 @ SV2 @ SY595 )
| ~ ( r @ SV16 @ SY595 )
| ~ ( s @ SV16 @ SY595 )
| ( q @ SV16 @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(86,plain,
! [SV17: mu,SV3: $i] :
( ( ! [SY596: $i] :
( ~ ( a1 @ SV3 @ SY596 )
| ~ ( s @ SV17 @ SY596 )
| ! [SY597: $i] :
( ~ ( a1 @ SY596 @ SY597 )
| ( r @ SV17 @ SY597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV18: $i > $o,SV4: $i] :
( ( ~ ( ~ ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
| ~ ~ ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) ) )
| ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV19: $i > $o,SV5: $i] :
( ( ! [SY599: $i] :
( ~ ( a2 @ SV5 @ SY599 )
| ( SV19 @ SY599 ) )
| ! [SY600: $i] :
( ~ ( a2 @ SV5 @ SY600 )
| ~ ( ~ ( a2 @ SY600 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV20: $i > $o,SV6: $i] :
( ( ~ ( ~ ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
| ~ ~ ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) ) )
| ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV21: $i > $o,SV7: $i] :
( ( ~ ( ~ ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
| ~ ~ ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) ) )
| ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV8: $i] :
( ( ~ ( a1 @ SV8 @ ( sK14_SY450 @ SV8 ) )
| ~ ( s @ a @ ( sK14_SY450 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV9: mu] :
( ( ~ ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SV9 ) )
| ~ ~ ( p @ SV9 @ ( sK2_SY562 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV22: $i > $o,SV10: $i] :
( ( ! [SY605: $i] :
( ~ ( a1 @ SV10 @ SY605 )
| ( SV22 @ SY605 ) )
| ! [SY606: $i] :
( ~ ( a1 @ SV10 @ SY606 )
| ~ ( ~ ( a1 @ SY606 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV23: $i > $o,SV11: $i] :
( ( ~ ( ~ ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
| ~ ~ ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) ) )
| ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV24: $i > $o,SV12: $i] :
( ( ~ ( ~ ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
| ~ ~ ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) ) )
| ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(96,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ~ ( ~ ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
| ~ ~ ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) ) )
| ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(97,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ~ ( ~ ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
| ~ ~ ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) ) )
| ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(98,plain,
! [SV15: mu,SV27: $i,SV1: $i] :
( ( ~ ( a2 @ SV1 @ SV27 )
| ! [SY611: $i] :
( ~ ( a2 @ SV27 @ SY611 )
| ~ ( q @ SV15 @ SY611 ) )
| ( p @ SV15 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV16: mu,SV28: $i,SV2: $i] :
( ( ~ ( a1 @ SV2 @ SV28 )
| ~ ( r @ SV16 @ SV28 )
| ~ ( s @ SV16 @ SV28 )
| ( q @ SV16 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV17: mu,SV29: $i,SV3: $i] :
( ( ~ ( a1 @ SV3 @ SV29 )
| ~ ( s @ SV17 @ SV29 )
| ! [SY612: $i] :
( ~ ( a1 @ SV29 @ SY612 )
| ( r @ SV17 @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV18: $i > $o,SV4: $i] :
( ( ( ~ ( ~ ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
| ~ ~ ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) ) ) )
= $true )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV19: $i > $o,SV5: $i] :
( ( ( ! [SY599: $i] :
( ~ ( a2 @ SV5 @ SY599 )
| ( SV19 @ SY599 ) ) )
= $true )
| ( ( ! [SY600: $i] :
( ~ ( a2 @ SV5 @ SY600 )
| ~ ( ~ ( a2 @ SY600 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV20: $i > $o,SV6: $i] :
( ( ( ~ ( ~ ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
| ~ ~ ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV21: $i > $o,SV7: $i] :
( ( ( ~ ( ~ ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
| ~ ~ ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV8: $i] :
( ( ~ ( a1 @ SV8 @ ( sK14_SY450 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(106,plain,
! [SV8: $i] :
( ( ~ ( s @ a @ ( sK14_SY450 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(107,plain,
! [SV9: mu] :
( ( ~ ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(108,plain,
! [SV9: mu] :
( ( ~ ~ ( p @ SV9 @ ( sK2_SY562 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(109,plain,
! [SV22: $i > $o,SV10: $i] :
( ( ( ! [SY605: $i] :
( ~ ( a1 @ SV10 @ SY605 )
| ( SV22 @ SY605 ) ) )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( a1 @ SV10 @ SY606 )
| ~ ( ~ ( a1 @ SY606 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV23: $i > $o,SV11: $i] :
( ( ( ~ ( ~ ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
| ~ ~ ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV24: $i > $o,SV12: $i] :
( ( ( ~ ( ~ ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
| ~ ~ ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) ) ) )
= $true )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( ~ ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
| ~ ~ ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( ~ ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
| ~ ~ ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV15: mu,SV27: $i,SV1: $i] :
( ( ( ~ ( a2 @ SV1 @ SV27 ) )
= $true )
| ( ( ! [SY611: $i] :
( ~ ( a2 @ SV27 @ SY611 )
| ~ ( q @ SV15 @ SY611 ) )
| ( p @ SV15 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV16: mu,SV28: $i,SV2: $i] :
( ( ( ~ ( a1 @ SV2 @ SV28 ) )
= $true )
| ( ( ~ ( r @ SV16 @ SV28 )
| ~ ( s @ SV16 @ SV28 )
| ( q @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV17: mu,SV29: $i,SV3: $i] :
( ( ( ~ ( a1 @ SV3 @ SV29 ) )
= $true )
| ( ( ~ ( s @ SV17 @ SV29 )
| ! [SY612: $i] :
( ~ ( a1 @ SV29 @ SY612 )
| ( r @ SV17 @ SY612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV18: $i > $o,SV4: $i] :
( ( ( ~ ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
| ~ ~ ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) ) )
= $false )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV19: $i > $o,SV30: $i,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ SV30 )
| ( SV19 @ SV30 ) )
= $true )
| ( ( ! [SY600: $i] :
( ~ ( a2 @ SV5 @ SY600 )
| ~ ( ~ ( a2 @ SY600 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV20: $i > $o,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
| ~ ~ ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV21: $i > $o,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
| ~ ~ ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV8: $i] :
( ( a1 @ SV8 @ ( sK14_SY450 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(122,plain,
! [SV8: $i] :
( ( s @ a @ ( sK14_SY450 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(123,plain,
! [SV9: mu] :
( ( a1 @ sK1_SY19 @ ( sK2_SY562 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(124,plain,
! [SV9: mu] :
( ( ~ ( p @ SV9 @ ( sK2_SY562 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(125,plain,
! [SV22: $i > $o,SV31: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV31 )
| ( SV22 @ SV31 ) )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( a1 @ SV10 @ SY606 )
| ~ ( ~ ( a1 @ SY606 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV23: $i > $o,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
| ~ ~ ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) ) )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV24: $i > $o,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
| ~ ~ ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) ) )
= $false )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
| ~ ~ ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
| ~ ~ ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV15: mu,SV27: $i,SV1: $i] :
( ( ( a2 @ SV1 @ SV27 )
= $false )
| ( ( ! [SY611: $i] :
( ~ ( a2 @ SV27 @ SY611 )
| ~ ( q @ SV15 @ SY611 ) )
| ( p @ SV15 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV16: mu,SV28: $i,SV2: $i] :
( ( ( a1 @ SV2 @ SV28 )
= $false )
| ( ( ~ ( r @ SV16 @ SV28 )
| ~ ( s @ SV16 @ SV28 )
| ( q @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV17: mu,SV29: $i,SV3: $i] :
( ( ( a1 @ SV3 @ SV29 )
= $false )
| ( ( ~ ( s @ SV17 @ SV29 )
| ! [SY612: $i] :
( ~ ( a1 @ SV29 @ SY612 )
| ( r @ SV17 @ SY612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV18: $i > $o,SV4: $i] :
( ( ( ~ ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) ) )
= $false )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(134,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( ~ ~ ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) ) )
= $false )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(135,plain,
! [SV19: $i > $o,SV30: $i,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ SV30 ) )
= $true )
| ( ( SV19 @ SV30 )
= $true )
| ( ( ! [SY600: $i] :
( ~ ( a2 @ SV5 @ SY600 )
| ~ ( ~ ( a2 @ SY600 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV20: $i > $o,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(137,plain,
! [SV6: $i,SV20: $i > $o] :
( ( ( ~ ~ ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(138,plain,
! [SV21: $i > $o,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(139,plain,
! [SV7: $i,SV21: $i > $o] :
( ( ( ~ ~ ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(140,plain,
! [SV9: mu] :
( ( p @ SV9 @ ( sK2_SY562 @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV22: $i > $o,SV31: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV31 ) )
= $true )
| ( ( SV22 @ SV31 )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( a1 @ SV10 @ SY606 )
| ~ ( ~ ( a1 @ SY606 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV23: $i > $o,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) ) )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(143,plain,
! [SV11: $i,SV23: $i > $o] :
( ( ( ~ ~ ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) ) )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(144,plain,
! [SV24: $i > $o,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) ) )
= $false )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(145,plain,
! [SV12: $i,SV24: $i > $o] :
( ( ( ~ ~ ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) ) )
= $false )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(146,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(147,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( ~ ~ ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(148,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(149,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( ~ ~ ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(150,plain,
! [SV1: $i,SV15: mu,SV27: $i] :
( ( ( ! [SY611: $i] :
( ~ ( a2 @ SV27 @ SY611 )
| ~ ( q @ SV15 @ SY611 ) ) )
= $true )
| ( ( p @ SV15 @ SV27 )
= $true )
| ( ( a2 @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(151,plain,
! [SV2: $i,SV28: $i,SV16: mu] :
( ( ( ~ ( r @ SV16 @ SV28 )
| ~ ( s @ SV16 @ SV28 ) )
= $true )
| ( ( q @ SV16 @ SV28 )
= $true )
| ( ( a1 @ SV2 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(152,plain,
! [SV3: $i,SV29: $i,SV17: mu] :
( ( ( ~ ( s @ SV17 @ SV29 ) )
= $true )
| ( ( ! [SY612: $i] :
( ~ ( a1 @ SV29 @ SY612 )
| ( r @ SV17 @ SY612 ) ) )
= $true )
| ( ( a1 @ SV3 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(153,plain,
! [SV18: $i > $o,SV4: $i] :
( ( ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $true )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(154,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) ) )
= $true )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(155,plain,
! [SV19: $i > $o,SV30: $i,SV5: $i] :
( ( ( a2 @ SV5 @ SV30 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( ! [SY600: $i] :
( ~ ( a2 @ SV5 @ SY600 )
| ~ ( ~ ( a2 @ SY600 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SY600 @ SV19 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(156,plain,
! [SV20: $i > $o,SV6: $i] :
( ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(157,plain,
! [SV6: $i,SV20: $i > $o] :
( ( ( ~ ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) ) )
= $true )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(158,plain,
! [SV21: $i > $o,SV7: $i] :
( ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(159,plain,
! [SV7: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) ) )
= $true )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(160,plain,
! [SV22: $i > $o,SV31: $i,SV10: $i] :
( ( ( a1 @ SV10 @ SV31 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( ! [SY606: $i] :
( ~ ( a1 @ SV10 @ SY606 )
| ~ ( ~ ( a1 @ SY606 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SY606 @ SV22 @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(161,plain,
! [SV23: $i > $o,SV11: $i] :
( ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(162,plain,
! [SV11: $i,SV23: $i > $o] :
( ( ( ~ ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) ) )
= $true )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(163,plain,
! [SV24: $i > $o,SV12: $i] :
( ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(164,plain,
! [SV12: $i,SV24: $i > $o] :
( ( ( ~ ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) ) )
= $true )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(165,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(166,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(167,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(168,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( ~ ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(169,plain,
! [SV1: $i,SV15: mu,SV32: $i,SV27: $i] :
( ( ( ~ ( a2 @ SV27 @ SV32 )
| ~ ( q @ SV15 @ SV32 ) )
= $true )
| ( ( p @ SV15 @ SV27 )
= $true )
| ( ( a2 @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV2: $i,SV28: $i,SV16: mu] :
( ( ( ~ ( r @ SV16 @ SV28 ) )
= $true )
| ( ( ~ ( s @ SV16 @ SV28 ) )
= $true )
| ( ( q @ SV16 @ SV28 )
= $true )
| ( ( a1 @ SV2 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV3: $i,SV29: $i,SV17: mu] :
( ( ( s @ SV17 @ SV29 )
= $false )
| ( ( ! [SY612: $i] :
( ~ ( a1 @ SV29 @ SY612 )
| ( r @ SV17 @ SY612 ) ) )
= $true )
| ( ( a1 @ SV3 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV18: $i > $o,SV33: $i,SV4: $i] :
( ( ( ~ ( a1 @ SV4 @ SV33 )
| ( SV18 @ SV33 ) )
= $true )
| ( ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $false )
| ( ( ! [SY598: $i] :
( ~ ( a1 @ SV4 @ SY598 )
| ( SV18 @ SY598 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV30: $i,SV19: $i > $o,SV34: $i,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ SV34 )
| ~ ( ~ ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) ) )
= $true )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV20: $i > $o,SV35: $i,SV6: $i] :
( ( ( ~ ( a2 @ SV6 @ SV35 )
| ! [SY613: $i] :
( ~ ( a1 @ SV35 @ SY613 )
| ( SV20 @ SY613 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV6: $i,SV20: $i > $o] :
( ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY601: $i] :
( ~ ( a2 @ SV6 @ SY601 )
| ! [SY602: $i] :
( ~ ( a1 @ SY601 @ SY602 )
| ( SV20 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV21: $i > $o,SV36: $i,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ SV36 )
| ! [SY614: $i] :
( ~ ( a2 @ SV36 @ SY614 )
| ( SV21 @ SY614 ) ) )
= $true )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV7: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY603: $i] :
( ~ ( a1 @ SV7 @ SY603 )
| ! [SY604: $i] :
( ~ ( a2 @ SY603 @ SY604 )
| ( SV21 @ SY604 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV31: $i,SV22: $i > $o,SV37: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV37 )
| ~ ( ~ ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) ) )
= $true )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(180,plain,
! [SV23: $i > $o,SV38: $i,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ SV38 )
| ! [SY615: $i] :
( ~ ( a2 @ SV38 @ SY615 )
| ( SV23 @ SY615 ) ) )
= $true )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(181,plain,
! [SV11: $i,SV23: $i > $o] :
( ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false )
| ( ( ! [SY607: $i] :
( ~ ( a2 @ SV11 @ SY607 )
| ! [SY608: $i] :
( ~ ( a2 @ SY607 @ SY608 )
| ( SV23 @ SY608 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(182,plain,
! [SV24: $i > $o,SV39: $i,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ SV39 )
| ! [SY616: $i] :
( ~ ( a1 @ SV39 @ SY616 )
| ( SV24 @ SY616 ) ) )
= $true )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(183,plain,
! [SV12: $i,SV24: $i > $o] :
( ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false )
| ( ( ! [SY609: $i] :
( ~ ( a1 @ SV12 @ SY609 )
| ! [SY610: $i] :
( ~ ( a1 @ SY609 @ SY610 )
| ( SV24 @ SY610 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(184,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(185,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(187,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(188,plain,
! [SV1: $i,SV15: mu,SV32: $i,SV27: $i] :
( ( ( ~ ( a2 @ SV27 @ SV32 ) )
= $true )
| ( ( ~ ( q @ SV15 @ SV32 ) )
= $true )
| ( ( p @ SV15 @ SV27 )
= $true )
| ( ( a2 @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(189,plain,
! [SV2: $i,SV28: $i,SV16: mu] :
( ( ( r @ SV16 @ SV28 )
= $false )
| ( ( ~ ( s @ SV16 @ SV28 ) )
= $true )
| ( ( q @ SV16 @ SV28 )
= $true )
| ( ( a1 @ SV2 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(190,plain,
! [SV3: $i,SV17: mu,SV40: $i,SV29: $i] :
( ( ( ~ ( a1 @ SV29 @ SV40 )
| ( r @ SV17 @ SV40 ) )
= $true )
| ( ( s @ SV17 @ SV29 )
= $false )
| ( ( a1 @ SV3 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(191,plain,
! [SV18: $i > $o,SV33: $i,SV4: $i] :
( ( ( ~ ( a1 @ SV4 @ SV33 ) )
= $true )
| ( ( SV18 @ SV33 )
= $true )
| ( ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(192,plain,
! [SV18: $i > $o,SV41: $i,SV4: $i] :
( ( ( ~ ( a1 @ SV4 @ SV41 )
| ( SV18 @ SV41 ) )
= $true )
| ( ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(193,plain,
! [SV30: $i,SV19: $i > $o,SV34: $i,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) ) )
= $true )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV20: $i > $o,SV35: $i,SV6: $i] :
( ( ( ~ ( a2 @ SV6 @ SV35 ) )
= $true )
| ( ( ! [SY613: $i] :
( ~ ( a1 @ SV35 @ SY613 )
| ( SV20 @ SY613 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(195,plain,
! [SV20: $i > $o,SV42: $i,SV6: $i] :
( ( ( ~ ( a2 @ SV6 @ SV42 )
| ! [SY617: $i] :
( ~ ( a1 @ SV42 @ SY617 )
| ( SV20 @ SY617 ) ) )
= $true )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV21: $i > $o,SV36: $i,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ SV36 ) )
= $true )
| ( ( ! [SY614: $i] :
( ~ ( a2 @ SV36 @ SY614 )
| ( SV21 @ SY614 ) ) )
= $true )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV21: $i > $o,SV43: $i,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ SV43 )
| ! [SY618: $i] :
( ~ ( a2 @ SV43 @ SY618 )
| ( SV21 @ SY618 ) ) )
= $true )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV31: $i,SV22: $i > $o,SV37: $i,SV10: $i] :
( ( ( ~ ( a1 @ SV10 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) ) )
= $true )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(199,plain,
! [SV23: $i > $o,SV38: $i,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ SV38 ) )
= $true )
| ( ( ! [SY615: $i] :
( ~ ( a2 @ SV38 @ SY615 )
| ( SV23 @ SY615 ) ) )
= $true )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV23: $i > $o,SV44: $i,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ SV44 )
| ! [SY619: $i] :
( ~ ( a2 @ SV44 @ SY619 )
| ( SV23 @ SY619 ) ) )
= $true )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV24: $i > $o,SV39: $i,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ SV39 ) )
= $true )
| ( ( ! [SY616: $i] :
( ~ ( a1 @ SV39 @ SY616 )
| ( SV24 @ SY616 ) ) )
= $true )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV24: $i > $o,SV45: $i,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ SV45 )
| ! [SY620: $i] :
( ~ ( a1 @ SV45 @ SY620 )
| ( SV24 @ SY620 ) ) )
= $true )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(204,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(205,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
| ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(207,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(208,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
| ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(209,plain,
! [SV1: $i,SV15: mu,SV32: $i,SV27: $i] :
( ( ( a2 @ SV27 @ SV32 )
= $false )
| ( ( ~ ( q @ SV15 @ SV32 ) )
= $true )
| ( ( p @ SV15 @ SV27 )
= $true )
| ( ( a2 @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(210,plain,
! [SV2: $i,SV28: $i,SV16: mu] :
( ( ( s @ SV16 @ SV28 )
= $false )
| ( ( r @ SV16 @ SV28 )
= $false )
| ( ( q @ SV16 @ SV28 )
= $true )
| ( ( a1 @ SV2 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(211,plain,
! [SV3: $i,SV17: mu,SV40: $i,SV29: $i] :
( ( ( ~ ( a1 @ SV29 @ SV40 ) )
= $true )
| ( ( r @ SV17 @ SV40 )
= $true )
| ( ( s @ SV17 @ SV29 )
= $false )
| ( ( a1 @ SV3 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(212,plain,
! [SV18: $i > $o,SV33: $i,SV4: $i] :
( ( ( a1 @ SV4 @ SV33 )
= $false )
| ( ( SV18 @ SV33 )
= $true )
| ( ( a2 @ SV4 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(213,plain,
! [SV18: $i > $o,SV41: $i,SV4: $i] :
( ( ( ~ ( a1 @ SV4 @ SV41 ) )
= $true )
| ( ( SV18 @ SV41 )
= $true )
| ( ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(214,plain,
! [SV30: $i,SV19: $i > $o,SV34: $i,SV5: $i] :
( ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( ~ ( ~ ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) ) )
= $true )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV20: $i > $o,SV35: $i,SV6: $i] :
( ( ( a2 @ SV6 @ SV35 )
= $false )
| ( ( ! [SY613: $i] :
( ~ ( a1 @ SV35 @ SY613 )
| ( SV20 @ SY613 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV20: $i > $o,SV42: $i,SV6: $i] :
( ( ( ~ ( a2 @ SV6 @ SV42 ) )
= $true )
| ( ( ! [SY617: $i] :
( ~ ( a1 @ SV42 @ SY617 )
| ( SV20 @ SY617 ) ) )
= $true )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV21: $i > $o,SV36: $i,SV7: $i] :
( ( ( a1 @ SV7 @ SV36 )
= $false )
| ( ( ! [SY614: $i] :
( ~ ( a2 @ SV36 @ SY614 )
| ( SV21 @ SY614 ) ) )
= $true )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV21: $i > $o,SV43: $i,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ SV43 ) )
= $true )
| ( ( ! [SY618: $i] :
( ~ ( a2 @ SV43 @ SY618 )
| ( SV21 @ SY618 ) ) )
= $true )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(219,plain,
! [SV31: $i,SV22: $i > $o,SV37: $i,SV10: $i] :
( ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( ~ ( ~ ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) ) )
= $true )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(220,plain,
! [SV23: $i > $o,SV38: $i,SV11: $i] :
( ( ( a2 @ SV11 @ SV38 )
= $false )
| ( ( ! [SY615: $i] :
( ~ ( a2 @ SV38 @ SY615 )
| ( SV23 @ SY615 ) ) )
= $true )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(221,plain,
! [SV23: $i > $o,SV44: $i,SV11: $i] :
( ( ( ~ ( a2 @ SV11 @ SV44 ) )
= $true )
| ( ( ! [SY619: $i] :
( ~ ( a2 @ SV44 @ SY619 )
| ( SV23 @ SY619 ) ) )
= $true )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(222,plain,
! [SV24: $i > $o,SV39: $i,SV12: $i] :
( ( ( a1 @ SV12 @ SV39 )
= $false )
| ( ( ! [SY616: $i] :
( ~ ( a1 @ SV39 @ SY616 )
| ( SV24 @ SY616 ) ) )
= $true )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(223,plain,
! [SV24: $i > $o,SV45: $i,SV12: $i] :
( ( ( ~ ( a1 @ SV12 @ SV45 ) )
= $true )
| ( ( ! [SY620: $i] :
( ~ ( a1 @ SV45 @ SY620 )
| ( SV24 @ SY620 ) ) )
= $true )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(224,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
= $true )
| ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(225,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) )
= $true )
| ( ( a1 @ SV13 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(226,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( ~ ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(227,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( ~ ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) ) )
= $false )
| ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(228,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
= $true )
| ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(229,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) )
= $true )
| ( ( a2 @ SV14 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(230,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( ~ ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(231,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( ~ ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) ) )
= $false )
| ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(232,plain,
! [SV1: $i,SV27: $i,SV32: $i,SV15: mu] :
( ( ( q @ SV15 @ SV32 )
= $false )
| ( ( a2 @ SV27 @ SV32 )
= $false )
| ( ( p @ SV15 @ SV27 )
= $true )
| ( ( a2 @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(233,plain,
! [SV3: $i,SV17: mu,SV40: $i,SV29: $i] :
( ( ( a1 @ SV29 @ SV40 )
= $false )
| ( ( r @ SV17 @ SV40 )
= $true )
| ( ( s @ SV17 @ SV29 )
= $false )
| ( ( a1 @ SV3 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(234,plain,
! [SV18: $i > $o,SV41: $i,SV4: $i] :
( ( ( a1 @ SV4 @ SV41 )
= $false )
| ( ( SV18 @ SV41 )
= $true )
| ( ( SV18 @ ( sK9_SY352 @ SV18 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(235,plain,
! [SV30: $i,SV5: $i,SV19: $i > $o,SV34: $i] :
( ( ( ~ ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
| ~ ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) )
= $false )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(236,plain,
! [SV6: $i,SV20: $i > $o,SV46: $i,SV35: $i] :
( ( ( ~ ( a1 @ SV35 @ SV46 )
| ( SV20 @ SV46 ) )
= $true )
| ( ( a2 @ SV6 @ SV35 )
= $false )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(237,plain,
! [SV20: $i > $o,SV42: $i,SV6: $i] :
( ( ( a2 @ SV6 @ SV42 )
= $false )
| ( ( ! [SY617: $i] :
( ~ ( a1 @ SV42 @ SY617 )
| ( SV20 @ SY617 ) ) )
= $true )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(238,plain,
! [SV7: $i,SV21: $i > $o,SV47: $i,SV36: $i] :
( ( ( ~ ( a2 @ SV36 @ SV47 )
| ( SV21 @ SV47 ) )
= $true )
| ( ( a1 @ SV7 @ SV36 )
= $false )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(239,plain,
! [SV21: $i > $o,SV43: $i,SV7: $i] :
( ( ( a1 @ SV7 @ SV43 )
= $false )
| ( ( ! [SY618: $i] :
( ~ ( a2 @ SV43 @ SY618 )
| ( SV21 @ SY618 ) ) )
= $true )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(240,plain,
! [SV31: $i,SV10: $i,SV22: $i > $o,SV37: $i] :
( ( ( ~ ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
| ~ ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) )
= $false )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(241,plain,
! [SV11: $i,SV23: $i > $o,SV48: $i,SV38: $i] :
( ( ( ~ ( a2 @ SV38 @ SV48 )
| ( SV23 @ SV48 ) )
= $true )
| ( ( a2 @ SV11 @ SV38 )
= $false )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(242,plain,
! [SV23: $i > $o,SV44: $i,SV11: $i] :
( ( ( a2 @ SV11 @ SV44 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( a2 @ SV44 @ SY619 )
| ( SV23 @ SY619 ) ) )
= $true )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(243,plain,
! [SV12: $i,SV24: $i > $o,SV49: $i,SV39: $i] :
( ( ( ~ ( a1 @ SV39 @ SV49 )
| ( SV24 @ SV49 ) )
= $true )
| ( ( a1 @ SV12 @ SV39 )
= $false )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(244,plain,
! [SV24: $i > $o,SV45: $i,SV12: $i] :
( ( ( a1 @ SV12 @ SV45 )
= $false )
| ( ( ! [SY620: $i] :
( ~ ( a1 @ SV45 @ SY620 )
| ( SV24 @ SY620 ) ) )
= $true )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(245,plain,
! [SV25: $i > $o,SV13: $i] :
( ( ( a1 @ SV13 @ ( sK12_SY433 @ SV25 @ SV13 ) )
= $true )
| ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(246,plain,
! [SV13: $i,SV25: $i > $o] :
( ( ( SV25 @ ( sK12_SY433 @ SV25 @ SV13 ) )
= $true )
| ( ( SV25 @ ( sK13_SY432 @ SV25 @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(247,plain,
! [SV26: $i > $o,SV14: $i] :
( ( ( a2 @ SV14 @ ( sK10_SY393 @ SV26 @ SV14 ) )
= $true )
| ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(248,plain,
! [SV14: $i,SV26: $i > $o] :
( ( ( SV26 @ ( sK10_SY393 @ SV26 @ SV14 ) )
= $true )
| ( ( SV26 @ ( sK11_SY392 @ SV26 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(249,plain,
! [SV30: $i,SV5: $i,SV19: $i > $o,SV34: $i] :
( ( ( ~ ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) )
= $false )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(250,plain,
! [SV30: $i,SV5: $i,SV34: $i,SV19: $i > $o] :
( ( ( ~ ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) )
= $false )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(251,plain,
! [SV6: $i,SV20: $i > $o,SV46: $i,SV35: $i] :
( ( ( ~ ( a1 @ SV35 @ SV46 ) )
= $true )
| ( ( SV20 @ SV46 )
= $true )
| ( ( a2 @ SV6 @ SV35 )
= $false )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV6: $i,SV20: $i > $o,SV50: $i,SV42: $i] :
( ( ( ~ ( a1 @ SV42 @ SV50 )
| ( SV20 @ SV50 ) )
= $true )
| ( ( a2 @ SV6 @ SV42 )
= $false )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV7: $i,SV21: $i > $o,SV47: $i,SV36: $i] :
( ( ( ~ ( a2 @ SV36 @ SV47 ) )
= $true )
| ( ( SV21 @ SV47 )
= $true )
| ( ( a1 @ SV7 @ SV36 )
= $false )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV7: $i,SV21: $i > $o,SV51: $i,SV43: $i] :
( ( ( ~ ( a2 @ SV43 @ SV51 )
| ( SV21 @ SV51 ) )
= $true )
| ( ( a1 @ SV7 @ SV43 )
= $false )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV31: $i,SV10: $i,SV22: $i > $o,SV37: $i] :
( ( ( ~ ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) )
= $false )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(256,plain,
! [SV31: $i,SV10: $i,SV37: $i,SV22: $i > $o] :
( ( ( ~ ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) )
= $false )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(257,plain,
! [SV11: $i,SV23: $i > $o,SV48: $i,SV38: $i] :
( ( ( ~ ( a2 @ SV38 @ SV48 ) )
= $true )
| ( ( SV23 @ SV48 )
= $true )
| ( ( a2 @ SV11 @ SV38 )
= $false )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(258,plain,
! [SV11: $i,SV23: $i > $o,SV52: $i,SV44: $i] :
( ( ( ~ ( a2 @ SV44 @ SV52 )
| ( SV23 @ SV52 ) )
= $true )
| ( ( a2 @ SV11 @ SV44 )
= $false )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(259,plain,
! [SV12: $i,SV24: $i > $o,SV49: $i,SV39: $i] :
( ( ( ~ ( a1 @ SV39 @ SV49 ) )
= $true )
| ( ( SV24 @ SV49 )
= $true )
| ( ( a1 @ SV12 @ SV39 )
= $false )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(260,plain,
! [SV12: $i,SV24: $i > $o,SV53: $i,SV45: $i] :
( ( ( ~ ( a1 @ SV45 @ SV53 )
| ( SV24 @ SV53 ) )
= $true )
| ( ( a1 @ SV12 @ SV45 )
= $false )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(261,plain,
! [SV30: $i,SV5: $i,SV19: $i > $o,SV34: $i] :
( ( ( a2 @ SV34 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
= $true )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV30: $i,SV5: $i,SV34: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) ) )
= $true )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV6: $i,SV20: $i > $o,SV46: $i,SV35: $i] :
( ( ( a1 @ SV35 @ SV46 )
= $false )
| ( ( SV20 @ SV46 )
= $true )
| ( ( a2 @ SV6 @ SV35 )
= $false )
| ( ( a1 @ SV6 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(264,plain,
! [SV6: $i,SV20: $i > $o,SV50: $i,SV42: $i] :
( ( ( ~ ( a1 @ SV42 @ SV50 ) )
= $true )
| ( ( SV20 @ SV50 )
= $true )
| ( ( a2 @ SV6 @ SV42 )
= $false )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(265,plain,
! [SV7: $i,SV21: $i > $o,SV47: $i,SV36: $i] :
( ( ( a2 @ SV36 @ SV47 )
= $false )
| ( ( SV21 @ SV47 )
= $true )
| ( ( a1 @ SV7 @ SV36 )
= $false )
| ( ( a2 @ SV7 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(266,plain,
! [SV7: $i,SV21: $i > $o,SV51: $i,SV43: $i] :
( ( ( ~ ( a2 @ SV43 @ SV51 ) )
= $true )
| ( ( SV21 @ SV51 )
= $true )
| ( ( a1 @ SV7 @ SV43 )
= $false )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(267,plain,
! [SV31: $i,SV10: $i,SV22: $i > $o,SV37: $i] :
( ( ( a1 @ SV37 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
= $true )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(268,plain,
! [SV31: $i,SV10: $i,SV37: $i,SV22: $i > $o] :
( ( ( ~ ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) ) )
= $true )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(269,plain,
! [SV11: $i,SV23: $i > $o,SV48: $i,SV38: $i] :
( ( ( a2 @ SV38 @ SV48 )
= $false )
| ( ( SV23 @ SV48 )
= $true )
| ( ( a2 @ SV11 @ SV38 )
= $false )
| ( ( a2 @ SV11 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(270,plain,
! [SV11: $i,SV23: $i > $o,SV52: $i,SV44: $i] :
( ( ( ~ ( a2 @ SV44 @ SV52 ) )
= $true )
| ( ( SV23 @ SV52 )
= $true )
| ( ( a2 @ SV11 @ SV44 )
= $false )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(271,plain,
! [SV12: $i,SV24: $i > $o,SV49: $i,SV39: $i] :
( ( ( a1 @ SV39 @ SV49 )
= $false )
| ( ( SV24 @ SV49 )
= $true )
| ( ( a1 @ SV12 @ SV39 )
= $false )
| ( ( a1 @ SV12 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(272,plain,
! [SV12: $i,SV24: $i > $o,SV53: $i,SV45: $i] :
( ( ( ~ ( a1 @ SV45 @ SV53 ) )
= $true )
| ( ( SV24 @ SV53 )
= $true )
| ( ( a1 @ SV12 @ SV45 )
= $false )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(273,plain,
! [SV30: $i,SV5: $i,SV34: $i,SV19: $i > $o] :
( ( ( SV19 @ ( sK3_SY63 @ SV34 @ SV19 @ SV5 ) )
= $false )
| ( ( a2 @ SV5 @ SV34 )
= $false )
| ( ( SV19 @ SV30 )
= $true )
| ( ( a2 @ SV5 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV6: $i,SV20: $i > $o,SV50: $i,SV42: $i] :
( ( ( a1 @ SV42 @ SV50 )
= $false )
| ( ( SV20 @ SV50 )
= $true )
| ( ( a2 @ SV6 @ SV42 )
= $false )
| ( ( SV20 @ ( sK7_SY265 @ SV20 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(275,plain,
! [SV7: $i,SV21: $i > $o,SV51: $i,SV43: $i] :
( ( ( a2 @ SV43 @ SV51 )
= $false )
| ( ( SV21 @ SV51 )
= $true )
| ( ( a1 @ SV7 @ SV43 )
= $false )
| ( ( SV21 @ ( sK6_SY217 @ SV21 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(276,plain,
! [SV31: $i,SV10: $i,SV37: $i,SV22: $i > $o] :
( ( ( SV22 @ ( sK4_SY115 @ SV37 @ SV22 @ SV10 ) )
= $false )
| ( ( a1 @ SV10 @ SV37 )
= $false )
| ( ( SV22 @ SV31 )
= $true )
| ( ( a1 @ SV10 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV11: $i,SV23: $i > $o,SV52: $i,SV44: $i] :
( ( ( a2 @ SV44 @ SV52 )
= $false )
| ( ( SV23 @ SV52 )
= $true )
| ( ( a2 @ SV11 @ SV44 )
= $false )
| ( ( SV23 @ ( sK5_SY169 @ SV23 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(278,plain,
! [SV12: $i,SV24: $i > $o,SV53: $i,SV45: $i] :
( ( ( a1 @ SV45 @ SV53 )
= $false )
| ( ( SV24 @ SV53 )
= $true )
| ( ( a1 @ SV12 @ SV45 )
= $false )
| ( ( SV24 @ ( sK8_SY313 @ SV24 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(279,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[121,278,277,276,275,274,273,271,269,267,265,263,261,248,247,246,245,234,233,232,229,228,225,224,212,210,140,123,122]) ).
thf(280,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT027^1 : 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
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 17:55:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.42/0.46
% 1.42/0.46 No.of.Axioms: 13
% 1.42/0.46
% 1.42/0.46 Length.of.Defs: 5324
% 1.42/0.46
% 1.42/0.46 Contains.Choice.Funs: false
% 1.42/0.46 ...............
% 1.42/0.46
% 1.42/0.46 ********************************
% 1.42/0.46 * All subproblems solved! *
% 1.42/0.46 ********************************
% 1.42/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:279,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.42/0.46
% 1.42/0.46 %**** Beginning of derivation protocol ****
% 1.42/0.46 % SZS output start CNFRefutation
% See solution above
% 1.42/0.47
% 1.42/0.47 %**** End of derivation protocol ****
% 1.42/0.47 %**** no. of clauses in derivation: 280 ****
% 1.42/0.47 %**** clause counter: 279 ****
% 1.42/0.47
% 1.42/0.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:279,loop_count:0,foatp_calls:1,translation:fof_full)
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