%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : AGT027^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 3.64s 0.88s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 206 ( 88 unt; 0 typ; 31 def)
% Number of atoms : 1345 ( 394 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 2282 ( 368 ~; 464 |; 8 &;1434 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 166 ( 166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 5 con; 0-3 aty)
% Number of variables : 697 ( 59 ^; 632 !; 6 ?; 697 :)
% 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_sK1_SY19,type,
sK1_SY19: $i ).
thf(tp_sK2_SY387,type,
sK2_SY387: $i > $i ).
thf(tp_sK3_SY407,type,
sK3_SY407: mu > $i ).
thf(tp_sK4_SY413,type,
sK4_SY413: ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY415,type,
sK5_SY415: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY418,type,
sK6_SY418: ( $i > $o ) > $i > $i ).
thf(tp_sK7_SY421,type,
sK7_SY421: ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY424,type,
sK8_SY424: ( $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/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a2 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_a2_a2) ).
thf(2,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a2 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_a2_a1) ).
thf(3,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a1 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_a1_a2) ).
thf(4,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a1 @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4s_for_a1_a1) ).
thf(5,axiom,
( mvalid
@ ( mforall_prop
@ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_I_for_a2_a1) ).
thf(6,axiom,
mvalid @ ( mdia @ a1 @ ( s @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a4) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X ) @ ( mbox @ a1 @ ( r @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X ) @ ( s @ X ) ) @ ( q @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a2) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X ) ) @ ( p @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a1) ).
thf(10,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(11,negated_conjecture,
( ( mvalid
@ ( mexists_ind
@ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [SY19: $i] :
~ ! [SY20: mu] :
~ ! [SY21: $i] :
( ~ ( a1 @ SY19 @ SY21 )
| ( p @ SY20 @ SY21 ) ) )
= $false ),
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(13,plain,
( ( ! [SY63: $i,SY64: $i > $o] :
( ~ ! [SY65: $i] :
( ~ ( a2 @ SY63 @ SY65 )
| ( SY64 @ SY65 ) )
| ! [SY66: $i] :
( ~ ( a2 @ SY63 @ SY66 )
| ! [SY59: $i] :
( ~ ( a2 @ SY66 @ SY59 )
| ( SY64 @ SY59 ) ) ) ) )
= $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(14,plain,
( ( ! [SY111: $i,SY112: $i > $o] :
( ~ ! [SY113: $i] :
( ~ ( a2 @ SY111 @ SY113 )
| ( SY112 @ SY113 ) )
| ! [SY114: $i] :
( ~ ( a1 @ SY111 @ SY114 )
| ! [SY107: $i] :
( ~ ( a2 @ SY114 @ SY107 )
| ( SY112 @ SY107 ) ) ) ) )
= $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(15,plain,
( ( ! [SY159: $i,SY160: $i > $o] :
( ~ ! [SY161: $i] :
( ~ ( a1 @ SY159 @ SY161 )
| ( SY160 @ SY161 ) )
| ! [SY162: $i] :
( ~ ( a2 @ SY159 @ SY162 )
| ! [SY155: $i] :
( ~ ( a1 @ SY162 @ SY155 )
| ( SY160 @ SY155 ) ) ) ) )
= $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(16,plain,
( ( ! [SY207: $i,SY208: $i > $o] :
( ~ ! [SY209: $i] :
( ~ ( a1 @ SY207 @ SY209 )
| ( SY208 @ SY209 ) )
| ! [SY210: $i] :
( ~ ( a1 @ SY207 @ SY210 )
| ! [SY203: $i] :
( ~ ( a1 @ SY210 @ SY203 )
| ( SY208 @ SY203 ) ) ) ) )
= $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(17,plain,
( ( ! [SY246: $i,SY247: $i > $o] :
( ~ ! [SY248: $i] :
( ~ ( a2 @ SY246 @ SY248 )
| ( SY247 @ SY248 ) )
| ! [SY249: $i] :
( ~ ( a1 @ SY246 @ SY249 )
| ( SY247 @ SY249 ) ) ) )
= $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(18,plain,
( ( ! [SY265: $i] :
~ ! [SY266: $i] :
( ~ ( a1 @ SY265 @ SY266 )
| ~ ( s @ a @ SY266 ) ) )
= $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(19,plain,
( ( ! [SY295: $i,SY296: mu,SY297: $i] :
( ~ ( a1 @ SY295 @ SY297 )
| ~ ( s @ SY296 @ SY297 )
| ! [SY292: $i] :
( ~ ( a1 @ SY297 @ SY292 )
| ( r @ SY296 @ SY292 ) ) ) )
= $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(20,plain,
( ( ! [SY328: $i,SY329: mu,SY330: $i] :
( ~ ( a1 @ SY328 @ SY330 )
| ~ ~ ( ~ ( r @ SY329 @ SY330 )
| ~ ( s @ SY329 @ SY330 ) )
| ( q @ SY329 @ SY330 ) ) )
= $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(21,plain,
( ( ! [SY369: $i,SY370: mu,SY371: $i] :
( ~ ( a2 @ SY369 @ SY371 )
| ~ ~ ! [SY366: $i] :
( ~ ( a2 @ SY371 @ SY366 )
| ~ ( q @ SY370 @ SY366 ) )
| ( p @ SY370 @ SY371 ) ) )
= $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(22,plain,
( ( ~ ! [SY377: mu] :
~ ! [SY378: $i] :
( ~ ( a1 @ sK1_SY19 @ SY378 )
| ( p @ SY377 @ SY378 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [SY377: mu] :
~ ! [SY378: $i] :
( ~ ( a1 @ sK1_SY19 @ SY378 )
| ( p @ SY377 @ SY378 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [SY369: $i,SY370: mu,SY371: $i] :
( ~ ( a2 @ SY369 @ SY371 )
| ~ ~ ! [SY366: $i] :
( ~ ( a2 @ SY371 @ SY366 )
| ~ ( q @ SY370 @ SY366 ) )
| ( p @ SY370 @ SY371 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SY328: $i,SY329: mu,SY330: $i] :
( ~ ( a1 @ SY328 @ SY330 )
| ~ ~ ( ~ ( r @ SY329 @ SY330 )
| ~ ( s @ SY329 @ SY330 ) )
| ( q @ SY329 @ SY330 ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [SY295: $i,SY296: mu,SY297: $i] :
( ~ ( a1 @ SY295 @ SY297 )
| ~ ( s @ SY296 @ SY297 )
| ! [SY292: $i] :
( ~ ( a1 @ SY297 @ SY292 )
| ( r @ SY296 @ SY292 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [SY265: $i] :
~ ! [SY266: $i] :
( ~ ( a1 @ SY265 @ SY266 )
| ~ ( s @ a @ SY266 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ! [SY246: $i,SY247: $i > $o] :
( ~ ! [SY248: $i] :
( ~ ( a2 @ SY246 @ SY248 )
| ( SY247 @ SY248 ) )
| ! [SY249: $i] :
( ~ ( a1 @ SY246 @ SY249 )
| ( SY247 @ SY249 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [SY207: $i,SY208: $i > $o] :
( ~ ! [SY209: $i] :
( ~ ( a1 @ SY207 @ SY209 )
| ( SY208 @ SY209 ) )
| ! [SY210: $i] :
( ~ ( a1 @ SY207 @ SY210 )
| ! [SY203: $i] :
( ~ ( a1 @ SY210 @ SY203 )
| ( SY208 @ SY203 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
( ( ! [SY159: $i,SY160: $i > $o] :
( ~ ! [SY161: $i] :
( ~ ( a1 @ SY159 @ SY161 )
| ( SY160 @ SY161 ) )
| ! [SY162: $i] :
( ~ ( a2 @ SY159 @ SY162 )
| ! [SY155: $i] :
( ~ ( a1 @ SY162 @ SY155 )
| ( SY160 @ SY155 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [SY111: $i,SY112: $i > $o] :
( ~ ! [SY113: $i] :
( ~ ( a2 @ SY111 @ SY113 )
| ( SY112 @ SY113 ) )
| ! [SY114: $i] :
( ~ ( a1 @ SY111 @ SY114 )
| ! [SY107: $i] :
( ~ ( a2 @ SY114 @ SY107 )
| ( SY112 @ SY107 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [SY63: $i,SY64: $i > $o] :
( ~ ! [SY65: $i] :
( ~ ( a2 @ SY63 @ SY65 )
| ( SY64 @ SY65 ) )
| ! [SY66: $i] :
( ~ ( a2 @ SY63 @ SY66 )
| ! [SY59: $i] :
( ~ ( a2 @ SY66 @ SY59 )
| ( SY64 @ SY59 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [SY377: mu] :
~ ! [SY378: $i] :
( ~ ( a1 @ sK1_SY19 @ SY378 )
| ( p @ SY377 @ SY378 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY379: mu,SY380: $i] :
( ~ ( a2 @ SV1 @ SY380 )
| ~ ~ ! [SY366: $i] :
( ~ ( a2 @ SY380 @ SY366 )
| ~ ( q @ SY379 @ SY366 ) )
| ( p @ SY379 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY382: mu,SY383: $i] :
( ~ ( a1 @ SV2 @ SY383 )
| ~ ~ ( ~ ( r @ SY382 @ SY383 )
| ~ ( s @ SY382 @ SY383 ) )
| ( q @ SY382 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV3: $i] :
( ( ! [SY384: mu,SY385: $i] :
( ~ ( a1 @ SV3 @ SY385 )
| ~ ( s @ SY384 @ SY385 )
| ! [SY292: $i] :
( ~ ( a1 @ SY385 @ SY292 )
| ( r @ SY384 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV4: $i] :
( ( ~ ! [SY387: $i] :
( ~ ( a1 @ SV4 @ SY387 )
| ~ ( s @ a @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY388: $i > $o] :
( ~ ! [SY389: $i] :
( ~ ( a2 @ SV5 @ SY389 )
| ( SY388 @ SY389 ) )
| ! [SY390: $i] :
( ~ ( a1 @ SV5 @ SY390 )
| ( SY388 @ SY390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY391: $i > $o] :
( ~ ! [SY392: $i] :
( ~ ( a1 @ SV6 @ SY392 )
| ( SY391 @ SY392 ) )
| ! [SY393: $i] :
( ~ ( a1 @ SV6 @ SY393 )
| ! [SY203: $i] :
( ~ ( a1 @ SY393 @ SY203 )
| ( SY391 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV7: $i] :
( ( ! [SY395: $i > $o] :
( ~ ! [SY396: $i] :
( ~ ( a1 @ SV7 @ SY396 )
| ( SY395 @ SY396 ) )
| ! [SY397: $i] :
( ~ ( a2 @ SV7 @ SY397 )
| ! [SY155: $i] :
( ~ ( a1 @ SY397 @ SY155 )
| ( SY395 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV8: $i] :
( ( ! [SY399: $i > $o] :
( ~ ! [SY400: $i] :
( ~ ( a2 @ SV8 @ SY400 )
| ( SY399 @ SY400 ) )
| ! [SY401: $i] :
( ~ ( a1 @ SV8 @ SY401 )
| ! [SY107: $i] :
( ~ ( a2 @ SY401 @ SY107 )
| ( SY399 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV9: $i] :
( ( ! [SY403: $i > $o] :
( ~ ! [SY404: $i] :
( ~ ( a2 @ SV9 @ SY404 )
| ( SY403 @ SY404 ) )
| ! [SY405: $i] :
( ~ ( a2 @ SV9 @ SY405 )
| ! [SY59: $i] :
( ~ ( a2 @ SY405 @ SY59 )
| ( SY403 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV10: mu] :
( ( ~ ! [SY407: $i] :
( ~ ( a1 @ sK1_SY19 @ SY407 )
| ( p @ SV10 @ SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV11: mu,SV1: $i] :
( ( ! [SY408: $i] :
( ~ ( a2 @ SV1 @ SY408 )
| ~ ~ ! [SY409: $i] :
( ~ ( a2 @ SY408 @ SY409 )
| ~ ( q @ SV11 @ SY409 ) )
| ( p @ SV11 @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV12: mu,SV2: $i] :
( ( ! [SY410: $i] :
( ~ ( a1 @ SV2 @ SY410 )
| ~ ~ ( ~ ( r @ SV12 @ SY410 )
| ~ ( s @ SV12 @ SY410 ) )
| ( q @ SV12 @ SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV13: mu,SV3: $i] :
( ( ! [SY411: $i] :
( ~ ( a1 @ SV3 @ SY411 )
| ~ ( s @ SV13 @ SY411 )
| ! [SY412: $i] :
( ~ ( a1 @ SY411 @ SY412 )
| ( r @ SV13 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV4: $i] :
( ( ! [SY387: $i] :
( ~ ( a1 @ SV4 @ SY387 )
| ~ ( s @ a @ SY387 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(48,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ~ ! [SY413: $i] :
( ~ ( a2 @ SV5 @ SY413 )
| ( SV14 @ SY413 ) )
| ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ~ ! [SY415: $i] :
( ~ ( a1 @ SV6 @ SY415 )
| ( SV15 @ SY415 ) )
| ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ~ ! [SY418: $i] :
( ~ ( a1 @ SV7 @ SY418 )
| ( SV16 @ SY418 ) )
| ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ~ ! [SY421: $i] :
( ~ ( a2 @ SV8 @ SY421 )
| ( SV17 @ SY421 ) )
| ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ~ ! [SY424: $i] :
( ~ ( a2 @ SV9 @ SY424 )
| ( SV18 @ SY424 ) )
| ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV10: mu] :
( ( ! [SY407: $i] :
( ~ ( a1 @ sK1_SY19 @ SY407 )
| ( p @ SV10 @ SY407 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV11: mu,SV19: $i,SV1: $i] :
( ( ~ ( a2 @ SV1 @ SV19 )
| ~ ~ ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) )
| ( p @ SV11 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV12: mu,SV20: $i,SV2: $i] :
( ( ~ ( a1 @ SV2 @ SV20 )
| ~ ~ ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) )
| ( q @ SV12 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV13: mu,SV21: $i,SV3: $i] :
( ( ~ ( a1 @ SV3 @ SV21 )
| ~ ( s @ SV13 @ SV21 )
| ! [SY428: $i] :
( ~ ( a1 @ SV21 @ SY428 )
| ( r @ SV13 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV4: $i] :
( ( ~ ( a1 @ SV4 @ ( sK2_SY387 @ SV4 ) )
| ~ ( s @ a @ ( sK2_SY387 @ SV4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(58,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ( ~ ! [SY413: $i] :
( ~ ( a2 @ SV5 @ SY413 )
| ( SV14 @ SY413 ) ) )
= $true )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ( ~ ! [SY415: $i] :
( ~ ( a1 @ SV6 @ SY415 )
| ( SV15 @ SY415 ) ) )
= $true )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( a1 @ SV7 @ SY418 )
| ( SV16 @ SY418 ) ) )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( a2 @ SV8 @ SY421 )
| ( SV17 @ SY421 ) ) )
= $true )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ( ~ ! [SY424: $i] :
( ~ ( a2 @ SV9 @ SY424 )
| ( SV18 @ SY424 ) ) )
= $true )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV10: mu] :
( ( ~ ( a1 @ sK1_SY19 @ ( sK3_SY407 @ SV10 ) )
| ( p @ SV10 @ ( sK3_SY407 @ SV10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(64,plain,
! [SV11: mu,SV19: $i,SV1: $i] :
( ( ( ~ ( a2 @ SV1 @ SV19 ) )
= $true )
| ( ( ~ ~ ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) )
| ( p @ SV11 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV12: mu,SV20: $i,SV2: $i] :
( ( ( ~ ( a1 @ SV2 @ SV20 ) )
= $true )
| ( ( ~ ~ ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) )
| ( q @ SV12 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV13: mu,SV21: $i,SV3: $i] :
( ( ( ~ ( a1 @ SV3 @ SV21 ) )
= $true )
| ( ( ~ ( s @ SV13 @ SV21 )
| ! [SY428: $i] :
( ~ ( a1 @ SV21 @ SY428 )
| ( r @ SV13 @ SY428 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV4: $i] :
( ( ~ ( a1 @ SV4 @ ( sK2_SY387 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV4: $i] :
( ( ~ ( s @ a @ ( sK2_SY387 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(69,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ( ! [SY413: $i] :
( ~ ( a2 @ SV5 @ SY413 )
| ( SV14 @ SY413 ) ) )
= $false )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ( ! [SY415: $i] :
( ~ ( a1 @ SV6 @ SY415 )
| ( SV15 @ SY415 ) ) )
= $false )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ( ! [SY418: $i] :
( ~ ( a1 @ SV7 @ SY418 )
| ( SV16 @ SY418 ) ) )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ( ! [SY421: $i] :
( ~ ( a2 @ SV8 @ SY421 )
| ( SV17 @ SY421 ) ) )
= $false )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ( ! [SY424: $i] :
( ~ ( a2 @ SV9 @ SY424 )
| ( SV18 @ SY424 ) ) )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(74,plain,
! [SV10: mu] :
( ( ~ ( a1 @ sK1_SY19 @ ( sK3_SY407 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(75,plain,
! [SV10: mu] :
( ( p @ SV10 @ ( sK3_SY407 @ SV10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(76,plain,
! [SV11: mu,SV19: $i,SV1: $i] :
( ( ( a2 @ SV1 @ SV19 )
= $false )
| ( ( ~ ~ ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) )
| ( p @ SV11 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV12: mu,SV20: $i,SV2: $i] :
( ( ( a1 @ SV2 @ SV20 )
= $false )
| ( ( ~ ~ ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) )
| ( q @ SV12 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV13: mu,SV21: $i,SV3: $i] :
( ( ( a1 @ SV3 @ SV21 )
= $false )
| ( ( ~ ( s @ SV13 @ SV21 )
| ! [SY428: $i] :
( ~ ( a1 @ SV21 @ SY428 )
| ( r @ SV13 @ SY428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV4: $i] :
( ( a1 @ SV4 @ ( sK2_SY387 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(80,plain,
! [SV4: $i] :
( ( s @ a @ ( sK2_SY387 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(81,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) )
| ( SV14 @ ( sK4_SY413 @ SV14 @ SV5 ) ) )
= $false )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(82,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
| ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) ) )
= $false )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(83,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
| ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) ) )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(84,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ( ~ ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
| ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) ) )
= $false )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(85,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
| ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) ) )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(86,plain,
! [SV10: mu] :
( ( a1 @ sK1_SY19 @ ( sK3_SY407 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(87,plain,
! [SV1: $i,SV11: mu,SV19: $i] :
( ( ( ~ ~ ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) ) )
= $true )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( ~ ~ ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) ) )
= $true )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(89,plain,
! [SV3: $i,SV21: $i,SV13: mu] :
( ( ( ~ ( s @ SV13 @ SV21 ) )
= $true )
| ( ( ! [SY428: $i] :
( ~ ( a1 @ SV21 @ SY428 )
| ( r @ SV13 @ SY428 ) ) )
= $true )
| ( ( a1 @ SV3 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(90,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ( ~ ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) ) )
= $false )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV5: $i,SV14: $i > $o] :
( ( ( SV14 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $false )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) ) )
= $false )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV6: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(94,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ( ~ ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) ) )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(95,plain,
! [SV7: $i,SV16: $i > $o] :
( ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(96,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ( ~ ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) ) )
= $false )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(97,plain,
! [SV8: $i,SV17: $i > $o] :
( ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(98,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) ) )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(99,plain,
! [SV9: $i,SV18: $i > $o] :
( ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(100,plain,
! [SV1: $i,SV11: mu,SV19: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) ) )
= $false )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( ~ ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) ) )
= $false )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV3: $i,SV21: $i,SV13: mu] :
( ( ( s @ SV13 @ SV21 )
= $false )
| ( ( ! [SY428: $i] :
( ~ ( a1 @ SV21 @ SY428 )
| ( r @ SV13 @ SY428 ) ) )
= $true )
| ( ( a1 @ SV3 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV14: $i > $o,SV5: $i] :
( ( ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $true )
| ( ( ! [SY414: $i] :
( ~ ( a1 @ SV5 @ SY414 )
| ( SV14 @ SY414 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(104,plain,
! [SV14: $i > $o,SV22: $i,SV5: $i] :
( ( ( ~ ( a1 @ SV5 @ SV22 )
| ( SV14 @ SV22 ) )
= $true )
| ( ( SV14 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV15: $i > $o,SV6: $i] :
( ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true )
| ( ( ! [SY416: $i] :
( ~ ( a1 @ SV6 @ SY416 )
| ! [SY417: $i] :
( ~ ( a1 @ SY416 @ SY417 )
| ( SV15 @ SY417 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(106,plain,
! [SV15: $i > $o,SV23: $i,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ SV23 )
| ! [SY429: $i] :
( ~ ( a1 @ SV23 @ SY429 )
| ( SV15 @ SY429 ) ) )
= $true )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV16: $i > $o,SV7: $i] :
( ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true )
| ( ( ! [SY419: $i] :
( ~ ( a2 @ SV7 @ SY419 )
| ! [SY420: $i] :
( ~ ( a1 @ SY419 @ SY420 )
| ( SV16 @ SY420 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(108,plain,
! [SV16: $i > $o,SV24: $i,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ SV24 )
| ! [SY430: $i] :
( ~ ( a1 @ SV24 @ SY430 )
| ( SV16 @ SY430 ) ) )
= $true )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV17: $i > $o,SV8: $i] :
( ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true )
| ( ( ! [SY422: $i] :
( ~ ( a1 @ SV8 @ SY422 )
| ! [SY423: $i] :
( ~ ( a2 @ SY422 @ SY423 )
| ( SV17 @ SY423 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(110,plain,
! [SV17: $i > $o,SV25: $i,SV8: $i] :
( ( ( ~ ( a1 @ SV8 @ SV25 )
| ! [SY431: $i] :
( ~ ( a2 @ SV25 @ SY431 )
| ( SV17 @ SY431 ) ) )
= $true )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV18: $i > $o,SV9: $i] :
( ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true )
| ( ( ! [SY425: $i] :
( ~ ( a2 @ SV9 @ SY425 )
| ! [SY426: $i] :
( ~ ( a2 @ SY425 @ SY426 )
| ( SV18 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(112,plain,
! [SV18: $i > $o,SV26: $i,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ SV26 )
| ! [SY432: $i] :
( ~ ( a2 @ SV26 @ SY432 )
| ( SV18 @ SY432 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV1: $i,SV11: mu,SV19: $i] :
( ( ( ! [SY427: $i] :
( ~ ( a2 @ SV19 @ SY427 )
| ~ ( q @ SV11 @ SY427 ) ) )
= $true )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(114,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( ~ ( r @ SV12 @ SV20 )
| ~ ( s @ SV12 @ SV20 ) )
= $true )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(115,plain,
! [SV3: $i,SV13: mu,SV27: $i,SV21: $i] :
( ( ( ~ ( a1 @ SV21 @ SV27 )
| ( r @ SV13 @ SV27 ) )
= $true )
| ( ( s @ SV13 @ SV21 )
= $false )
| ( ( a1 @ SV3 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV14: $i > $o,SV28: $i,SV5: $i] :
( ( ( ~ ( a1 @ SV5 @ SV28 )
| ( SV14 @ SV28 ) )
= $true )
| ( ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV14: $i > $o,SV22: $i,SV5: $i] :
( ( ( ~ ( a1 @ SV5 @ SV22 ) )
= $true )
| ( ( SV14 @ SV22 )
= $true )
| ( ( SV14 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV15: $i > $o,SV29: $i,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ SV29 )
| ! [SY433: $i] :
( ~ ( a1 @ SV29 @ SY433 )
| ( SV15 @ SY433 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV15: $i > $o,SV23: $i,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ SV23 ) )
= $true )
| ( ( ! [SY429: $i] :
( ~ ( a1 @ SV23 @ SY429 )
| ( SV15 @ SY429 ) ) )
= $true )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV16: $i > $o,SV30: $i,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ SV30 )
| ! [SY434: $i] :
( ~ ( a1 @ SV30 @ SY434 )
| ( SV16 @ SY434 ) ) )
= $true )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV16: $i > $o,SV24: $i,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ SV24 ) )
= $true )
| ( ( ! [SY430: $i] :
( ~ ( a1 @ SV24 @ SY430 )
| ( SV16 @ SY430 ) ) )
= $true )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV17: $i > $o,SV31: $i,SV8: $i] :
( ( ( ~ ( a1 @ SV8 @ SV31 )
| ! [SY435: $i] :
( ~ ( a2 @ SV31 @ SY435 )
| ( SV17 @ SY435 ) ) )
= $true )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(123,plain,
! [SV17: $i > $o,SV25: $i,SV8: $i] :
( ( ( ~ ( a1 @ SV8 @ SV25 ) )
= $true )
| ( ( ! [SY431: $i] :
( ~ ( a2 @ SV25 @ SY431 )
| ( SV17 @ SY431 ) ) )
= $true )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV18: $i > $o,SV32: $i,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ SV32 )
| ! [SY436: $i] :
( ~ ( a2 @ SV32 @ SY436 )
| ( SV18 @ SY436 ) ) )
= $true )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV18: $i > $o,SV26: $i,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ SV26 ) )
= $true )
| ( ( ! [SY432: $i] :
( ~ ( a2 @ SV26 @ SY432 )
| ( SV18 @ SY432 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV1: $i,SV11: mu,SV33: $i,SV19: $i] :
( ( ( ~ ( a2 @ SV19 @ SV33 )
| ~ ( q @ SV11 @ SV33 ) )
= $true )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( ~ ( r @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ( s @ SV12 @ SV20 ) )
= $true )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV3: $i,SV13: mu,SV27: $i,SV21: $i] :
( ( ( ~ ( a1 @ SV21 @ SV27 ) )
= $true )
| ( ( r @ SV13 @ SV27 )
= $true )
| ( ( s @ SV13 @ SV21 )
= $false )
| ( ( a1 @ SV3 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV14: $i > $o,SV28: $i,SV5: $i] :
( ( ( ~ ( a1 @ SV5 @ SV28 ) )
= $true )
| ( ( SV14 @ SV28 )
= $true )
| ( ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV14: $i > $o,SV22: $i,SV5: $i] :
( ( ( a1 @ SV5 @ SV22 )
= $false )
| ( ( SV14 @ SV22 )
= $true )
| ( ( SV14 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV15: $i > $o,SV29: $i,SV6: $i] :
( ( ( ~ ( a1 @ SV6 @ SV29 ) )
= $true )
| ( ( ! [SY433: $i] :
( ~ ( a1 @ SV29 @ SY433 )
| ( SV15 @ SY433 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV15: $i > $o,SV23: $i,SV6: $i] :
( ( ( a1 @ SV6 @ SV23 )
= $false )
| ( ( ! [SY429: $i] :
( ~ ( a1 @ SV23 @ SY429 )
| ( SV15 @ SY429 ) ) )
= $true )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV16: $i > $o,SV30: $i,SV7: $i] :
( ( ( ~ ( a2 @ SV7 @ SV30 ) )
= $true )
| ( ( ! [SY434: $i] :
( ~ ( a1 @ SV30 @ SY434 )
| ( SV16 @ SY434 ) ) )
= $true )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV16: $i > $o,SV24: $i,SV7: $i] :
( ( ( a2 @ SV7 @ SV24 )
= $false )
| ( ( ! [SY430: $i] :
( ~ ( a1 @ SV24 @ SY430 )
| ( SV16 @ SY430 ) ) )
= $true )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV17: $i > $o,SV31: $i,SV8: $i] :
( ( ( ~ ( a1 @ SV8 @ SV31 ) )
= $true )
| ( ( ! [SY435: $i] :
( ~ ( a2 @ SV31 @ SY435 )
| ( SV17 @ SY435 ) ) )
= $true )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(136,plain,
! [SV17: $i > $o,SV25: $i,SV8: $i] :
( ( ( a1 @ SV8 @ SV25 )
= $false )
| ( ( ! [SY431: $i] :
( ~ ( a2 @ SV25 @ SY431 )
| ( SV17 @ SY431 ) ) )
= $true )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV18: $i > $o,SV32: $i,SV9: $i] :
( ( ( ~ ( a2 @ SV9 @ SV32 ) )
= $true )
| ( ( ! [SY436: $i] :
( ~ ( a2 @ SV32 @ SY436 )
| ( SV18 @ SY436 ) ) )
= $true )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(138,plain,
! [SV18: $i > $o,SV26: $i,SV9: $i] :
( ( ( a2 @ SV9 @ SV26 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( a2 @ SV26 @ SY432 )
| ( SV18 @ SY432 ) ) )
= $true )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV1: $i,SV11: mu,SV33: $i,SV19: $i] :
( ( ( ~ ( a2 @ SV19 @ SV33 ) )
= $true )
| ( ( ~ ( q @ SV11 @ SV33 ) )
= $true )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( r @ SV12 @ SV20 )
= $false )
| ( ( ~ ( s @ SV12 @ SV20 ) )
= $true )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV3: $i,SV13: mu,SV27: $i,SV21: $i] :
( ( ( a1 @ SV21 @ SV27 )
= $false )
| ( ( r @ SV13 @ SV27 )
= $true )
| ( ( s @ SV13 @ SV21 )
= $false )
| ( ( a1 @ SV3 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV14: $i > $o,SV28: $i,SV5: $i] :
( ( ( a1 @ SV5 @ SV28 )
= $false )
| ( ( SV14 @ SV28 )
= $true )
| ( ( a2 @ SV5 @ ( sK4_SY413 @ SV14 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV15: $i > $o,SV29: $i,SV6: $i] :
( ( ( a1 @ SV6 @ SV29 )
= $false )
| ( ( ! [SY433: $i] :
( ~ ( a1 @ SV29 @ SY433 )
| ( SV15 @ SY433 ) ) )
= $true )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV6: $i,SV15: $i > $o,SV34: $i,SV23: $i] :
( ( ( ~ ( a1 @ SV23 @ SV34 )
| ( SV15 @ SV34 ) )
= $true )
| ( ( a1 @ SV6 @ SV23 )
= $false )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV16: $i > $o,SV30: $i,SV7: $i] :
( ( ( a2 @ SV7 @ SV30 )
= $false )
| ( ( ! [SY434: $i] :
( ~ ( a1 @ SV30 @ SY434 )
| ( SV16 @ SY434 ) ) )
= $true )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV7: $i,SV16: $i > $o,SV35: $i,SV24: $i] :
( ( ( ~ ( a1 @ SV24 @ SV35 )
| ( SV16 @ SV35 ) )
= $true )
| ( ( a2 @ SV7 @ SV24 )
= $false )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV17: $i > $o,SV31: $i,SV8: $i] :
( ( ( a1 @ SV8 @ SV31 )
= $false )
| ( ( ! [SY435: $i] :
( ~ ( a2 @ SV31 @ SY435 )
| ( SV17 @ SY435 ) ) )
= $true )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV8: $i,SV17: $i > $o,SV36: $i,SV25: $i] :
( ( ( ~ ( a2 @ SV25 @ SV36 )
| ( SV17 @ SV36 ) )
= $true )
| ( ( a1 @ SV8 @ SV25 )
= $false )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV18: $i > $o,SV32: $i,SV9: $i] :
( ( ( a2 @ SV9 @ SV32 )
= $false )
| ( ( ! [SY436: $i] :
( ~ ( a2 @ SV32 @ SY436 )
| ( SV18 @ SY436 ) ) )
= $true )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV9: $i,SV18: $i > $o,SV37: $i,SV26: $i] :
( ( ( ~ ( a2 @ SV26 @ SV37 )
| ( SV18 @ SV37 ) )
= $true )
| ( ( a2 @ SV9 @ SV26 )
= $false )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV1: $i,SV11: mu,SV33: $i,SV19: $i] :
( ( ( a2 @ SV19 @ SV33 )
= $false )
| ( ( ~ ( q @ SV11 @ SV33 ) )
= $true )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV2: $i,SV20: $i,SV12: mu] :
( ( ( s @ SV12 @ SV20 )
= $false )
| ( ( r @ SV12 @ SV20 )
= $false )
| ( ( q @ SV12 @ SV20 )
= $true )
| ( ( a1 @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV6: $i,SV15: $i > $o,SV38: $i,SV29: $i] :
( ( ( ~ ( a1 @ SV29 @ SV38 )
| ( SV15 @ SV38 ) )
= $true )
| ( ( a1 @ SV6 @ SV29 )
= $false )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV6: $i,SV15: $i > $o,SV34: $i,SV23: $i] :
( ( ( ~ ( a1 @ SV23 @ SV34 ) )
= $true )
| ( ( SV15 @ SV34 )
= $true )
| ( ( a1 @ SV6 @ SV23 )
= $false )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV7: $i,SV16: $i > $o,SV39: $i,SV30: $i] :
( ( ( ~ ( a1 @ SV30 @ SV39 )
| ( SV16 @ SV39 ) )
= $true )
| ( ( a2 @ SV7 @ SV30 )
= $false )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV7: $i,SV16: $i > $o,SV35: $i,SV24: $i] :
( ( ( ~ ( a1 @ SV24 @ SV35 ) )
= $true )
| ( ( SV16 @ SV35 )
= $true )
| ( ( a2 @ SV7 @ SV24 )
= $false )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV8: $i,SV17: $i > $o,SV40: $i,SV31: $i] :
( ( ( ~ ( a2 @ SV31 @ SV40 )
| ( SV17 @ SV40 ) )
= $true )
| ( ( a1 @ SV8 @ SV31 )
= $false )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV8: $i,SV17: $i > $o,SV36: $i,SV25: $i] :
( ( ( ~ ( a2 @ SV25 @ SV36 ) )
= $true )
| ( ( SV17 @ SV36 )
= $true )
| ( ( a1 @ SV8 @ SV25 )
= $false )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV9: $i,SV18: $i > $o,SV41: $i,SV32: $i] :
( ( ( ~ ( a2 @ SV32 @ SV41 )
| ( SV18 @ SV41 ) )
= $true )
| ( ( a2 @ SV9 @ SV32 )
= $false )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV9: $i,SV18: $i > $o,SV37: $i,SV26: $i] :
( ( ( ~ ( a2 @ SV26 @ SV37 ) )
= $true )
| ( ( SV18 @ SV37 )
= $true )
| ( ( a2 @ SV9 @ SV26 )
= $false )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV1: $i,SV19: $i,SV33: $i,SV11: mu] :
( ( ( q @ SV11 @ SV33 )
= $false )
| ( ( a2 @ SV19 @ SV33 )
= $false )
| ( ( p @ SV11 @ SV19 )
= $true )
| ( ( a2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV6: $i,SV15: $i > $o,SV38: $i,SV29: $i] :
( ( ( ~ ( a1 @ SV29 @ SV38 ) )
= $true )
| ( ( SV15 @ SV38 )
= $true )
| ( ( a1 @ SV6 @ SV29 )
= $false )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV6: $i,SV15: $i > $o,SV34: $i,SV23: $i] :
( ( ( a1 @ SV23 @ SV34 )
= $false )
| ( ( SV15 @ SV34 )
= $true )
| ( ( a1 @ SV6 @ SV23 )
= $false )
| ( ( SV15 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV7: $i,SV16: $i > $o,SV39: $i,SV30: $i] :
( ( ( ~ ( a1 @ SV30 @ SV39 ) )
= $true )
| ( ( SV16 @ SV39 )
= $true )
| ( ( a2 @ SV7 @ SV30 )
= $false )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV7: $i,SV16: $i > $o,SV35: $i,SV24: $i] :
( ( ( a1 @ SV24 @ SV35 )
= $false )
| ( ( SV16 @ SV35 )
= $true )
| ( ( a2 @ SV7 @ SV24 )
= $false )
| ( ( SV16 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV8: $i,SV17: $i > $o,SV40: $i,SV31: $i] :
( ( ( ~ ( a2 @ SV31 @ SV40 ) )
= $true )
| ( ( SV17 @ SV40 )
= $true )
| ( ( a1 @ SV8 @ SV31 )
= $false )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV8: $i,SV17: $i > $o,SV36: $i,SV25: $i] :
( ( ( a2 @ SV25 @ SV36 )
= $false )
| ( ( SV17 @ SV36 )
= $true )
| ( ( a1 @ SV8 @ SV25 )
= $false )
| ( ( SV17 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV9: $i,SV18: $i > $o,SV41: $i,SV32: $i] :
( ( ( ~ ( a2 @ SV32 @ SV41 ) )
= $true )
| ( ( SV18 @ SV41 )
= $true )
| ( ( a2 @ SV9 @ SV32 )
= $false )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV9: $i,SV18: $i > $o,SV37: $i,SV26: $i] :
( ( ( a2 @ SV26 @ SV37 )
= $false )
| ( ( SV18 @ SV37 )
= $true )
| ( ( a2 @ SV9 @ SV26 )
= $false )
| ( ( SV18 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV6: $i,SV15: $i > $o,SV38: $i,SV29: $i] :
( ( ( a1 @ SV29 @ SV38 )
= $false )
| ( ( SV15 @ SV38 )
= $true )
| ( ( a1 @ SV6 @ SV29 )
= $false )
| ( ( a1 @ SV6 @ ( sK5_SY415 @ SV15 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV7: $i,SV16: $i > $o,SV39: $i,SV30: $i] :
( ( ( a1 @ SV30 @ SV39 )
= $false )
| ( ( SV16 @ SV39 )
= $true )
| ( ( a2 @ SV7 @ SV30 )
= $false )
| ( ( a1 @ SV7 @ ( sK6_SY418 @ SV16 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(172,plain,
! [SV8: $i,SV17: $i > $o,SV40: $i,SV31: $i] :
( ( ( a2 @ SV31 @ SV40 )
= $false )
| ( ( SV17 @ SV40 )
= $true )
| ( ( a1 @ SV8 @ SV31 )
= $false )
| ( ( a2 @ SV8 @ ( sK7_SY421 @ SV17 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV9: $i,SV18: $i > $o,SV41: $i,SV32: $i] :
( ( ( a2 @ SV32 @ SV41 )
= $false )
| ( ( SV18 @ SV41 )
= $true )
| ( ( a2 @ SV9 @ SV32 )
= $false )
| ( ( a2 @ SV9 @ ( sK8_SY424 @ SV18 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(174,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,173,172,171,170,169,167,165,163,161,152,142,141,130,86,80,79]) ).
thf(175,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : AGT027^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n009.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 17:59:53 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/0.88
% 3.64/0.88 No.of.Axioms: 9
% 3.64/0.88
% 3.64/0.88 Length.of.Defs: 5293
% 3.64/0.88
% 3.64/0.88 Contains.Choice.Funs: false
% 3.64/0.88 ........
% 3.64/0.88
% 3.64/0.88 ********************************
% 3.64/0.88 * All subproblems solved! *
% 3.64/0.88 ********************************
% 3.64/0.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:174,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.64/0.88
% 3.64/0.88 %**** Beginning of derivation protocol ****
% 3.64/0.88 % SZS output start CNFRefutation
% See solution above
% 3.64/0.88
% 3.64/0.88 %**** End of derivation protocol ****
% 3.64/0.88 %**** no. of clauses in derivation: 175 ****
% 3.64/0.88 %**** clause counter: 174 ****
% 3.64/0.88
% 3.64/0.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:174,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------