%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO449^1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n010.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 11:08:20 AM UTC 2026
% Result : Theorem 1.16s 0.40s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 37
% Syntax : Number of formulae : 223 ( 60 unt; 0 typ; 33 def)
% Number of atoms : 2209 ( 549 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 3502 ( 829 ~; 869 |; 10 &;1782 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 14 con; 0-3 aty)
% Number of variables : 554 ( 52 ^; 496 !; 6 ?; 554 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s5,type,
mbox_s5: ( $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_mdia_s5,type,
mdia_s5: ( $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: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_rel_s5,type,
rel_s5: $i > $i > $o ).
thf(tp_sK10_SY149,type,
sK10_SY149: $i ).
thf(tp_sK11_SY151,type,
sK11_SY151: $i ).
thf(tp_sK12_SY139,type,
sK12_SY139: $i > $i > $i ).
thf(tp_sK13_SY152,type,
sK13_SY152: $i ).
thf(tp_sK14_SY155,type,
sK14_SY155: $i > $i > $i ).
thf(tp_sK1_SY92,type,
sK1_SY92: $i ).
thf(tp_sK2_SY124,type,
sK2_SY124: $i ).
thf(tp_sK3_SY135,type,
sK3_SY135: $i ).
thf(tp_sK4_SY145,type,
sK4_SY145: $i ).
thf(tp_sK5_SY139,type,
sK5_SY139: $i ).
thf(tp_sK6_SY139,type,
sK6_SY139: $i ).
thf(tp_sK7_SY139,type,
sK7_SY139: $i ).
thf(tp_sK8_SY139,type,
sK8_SY139: $i ).
thf(tp_sK9_SY147,type,
sK9_SY147: $i ).
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(mbox_s5,definition,
( mbox_s5
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s5 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5) ).
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(mdia_s5,definition,
( mdia_s5
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5) ).
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,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(4,conjecture,
mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(5,negated_conjecture,
( ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [SY92: $i,SY93: $i] :
( ~ ( rel_s5 @ SY92 @ SY93 )
| ~ ( ~ ( ~ ! [SY84: $i] :
( ~ ( rel_s5 @ SY93 @ SY84 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY84 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY84 ) )
| ! [SY86: $i] :
( ~ ( rel_s5 @ SY93 @ SY86 )
| ~ ( p @ SY86 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY86 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY88: $i] :
( ~ ( rel_s5 @ SY93 @ SY88 )
| ~ ( p @ SY88 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY88 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY90: $i] :
( ~ ( rel_s5 @ SY93 @ SY90 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY90 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY90 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(7,plain,
( ( ! [SY112: $i,SY113: $i] :
( ( rel_s5 @ SY112 @ SY113 )
=> ( rel_s5 @ SY113 @ SY112 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(8,plain,
( ( ! [SY116: $i,SY117: $i,SY118: $i] :
( ( ( rel_s5 @ SY116 @ SY117 )
& ( rel_s5 @ SY117 @ SY118 ) )
=> ( rel_s5 @ SY116 @ SY118 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(9,plain,
( ( ! [SY122: $i] : ( rel_s5 @ SY122 @ SY122 ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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(10,plain,
( ( ! [SY124: $i] :
( ~ ( rel_s5 @ sK1_SY92 @ SY124 )
| ~ ( ~ ( ~ ! [SY84: $i] :
( ~ ( rel_s5 @ SY124 @ SY84 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY84 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY84 ) )
| ! [SY86: $i] :
( ~ ( rel_s5 @ SY124 @ SY86 )
| ~ ( p @ SY86 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY86 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY88: $i] :
( ~ ( rel_s5 @ SY124 @ SY88 )
| ~ ( p @ SY88 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY88 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY90: $i] :
( ~ ( rel_s5 @ SY124 @ SY90 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY90 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY90 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ~ ( rel_s5 @ sK1_SY92 @ sK2_SY124 )
| ~ ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ~ ( ~ ( rel_s5 @ sK1_SY92 @ sK2_SY124 )
| ~ ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [SY122: $i] : ( rel_s5 @ SY122 @ SY122 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [SY116: $i,SY117: $i,SY118: $i] :
( ( ( rel_s5 @ SY116 @ SY117 )
& ( rel_s5 @ SY117 @ SY118 ) )
=> ( rel_s5 @ SY116 @ SY118 ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [SY112: $i,SY113: $i] :
( ( rel_s5 @ SY112 @ SY113 )
=> ( rel_s5 @ SY113 @ SY112 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(16,plain,
( ( ~ ( ~ ( rel_s5 @ sK1_SY92 @ sK2_SY124 )
| ~ ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s5 @ SX0 @ SX1 )
| ~ ( rel_s5 @ SX1 @ SX2 ) )
| ( rel_s5 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s5 @ SX0 @ SX1 )
| ( rel_s5 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mbox_s5,mcountersatisfiable,mdia,mdia_s5,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,
! [SV1: $i] :
( ( rel_s5 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
( ( ~ ( rel_s5 @ sK1_SY92 @ sK2_SY124 )
| ~ ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ~ ( ~ ( rel_s5 @ SV2 @ SY141 )
| ~ ( rel_s5 @ SY141 @ SY142 ) )
| ( rel_s5 @ SV2 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY143: $i] :
( ~ ( rel_s5 @ SV3 @ SY143 )
| ( rel_s5 @ SY143 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( rel_s5 @ sK1_SY92 @ sK2_SY124 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY144: $i] :
( ~ ~ ( ~ ( rel_s5 @ SV2 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SY144 ) )
| ( rel_s5 @ SV2 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ( rel_s5 @ SV3 @ SV5 )
| ( rel_s5 @ SV5 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( rel_s5 @ sK1_SY92 @ sK2_SY124 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
| ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ~ ~ ( ~ ( rel_s5 @ SV2 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) )
| ( rel_s5 @ SV2 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( rel_s5 @ SV3 @ SV5 ) )
= $true )
| ( ( rel_s5 @ SV5 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ( ~ ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( rel_s5 @ SV2 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) ) )
= $true )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV5: $i,SV3: $i] :
( ( ( rel_s5 @ SV3 @ SV5 )
= $false )
| ( ( rel_s5 @ SV5 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) )
| ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( ~ ( rel_s5 @ SV2 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) ) )
= $false )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ~ ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ( ! [SY135: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY135 )
| ~ ( p @ SY135 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY135 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( rel_s5 @ SV2 @ SV4 )
| ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ( ! [SY133: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY133 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY133 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY133 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
| ~ ( p @ sK3_SY135 )
| ! [SY145: $i] :
( ~ ( rel_s5 @ sK3_SY135 @ SY145 )
| ( q @ SY145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(41,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( rel_s5 @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV7: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV7 )
| ~ ~ ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) )
| ( q @ SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK3_SY135 ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ( ~ ( p @ sK3_SY135 )
| ! [SY145: $i] :
( ~ ( rel_s5 @ sK3_SY135 @ SY145 )
| ( q @ SY145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( rel_s5 @ SV2 @ SV4 )
= $false )
| ( ( ~ ( rel_s5 @ SV4 @ SV6 ) )
= $true )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV7: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV7 ) )
= $true )
| ( ( ~ ~ ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) )
| ( q @ SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ( ~ ( p @ sK3_SY135 ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ( ! [SY145: $i] :
( ~ ( rel_s5 @ sK3_SY135 @ SY145 )
| ( q @ SY145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( rel_s5 @ SV4 @ SV6 )
= $false )
| ( ( rel_s5 @ SV2 @ SV4 )
= $false )
| ( ( rel_s5 @ SV2 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV7: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ~ ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) )
| ( q @ SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
( ( ( p @ sK3_SY135 )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ( ~ ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
| ( q @ sK4_SY145 ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(55,plain,
! [SV7: $i] :
( ( ( ~ ~ ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) ) )
= $true )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(57,plain,
( ( ( ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( ( ~ ( rel_s5 @ sK3_SY135 @ sK4_SY145 ) )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( ( q @ sK4_SY145 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV7: $i] :
( ( ( ~ ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) ) )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(62,plain,
( ( ( ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(63,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK5_SY139 )
| ~ ~ ! [SY147: $i] :
( ~ ( rel_s5 @ sK5_SY139 @ SY147 )
| ~ ( p @ SY147 ) )
| ( q @ sK5_SY139 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(64,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
( ( ( ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
( ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(67,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV7: $i] :
( ( ( ! [SY146: $i] :
( ~ ( rel_s5 @ SV7 @ SY146 )
| ~ ( p @ SY146 ) ) )
= $true )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV8: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV8 )
| ~ ( p @ SV8 )
| ! [SY148: $i] :
( ~ ( rel_s5 @ SV8 @ SY148 )
| ( q @ SY148 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(70,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK5_SY139 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(71,plain,
( ( ( ~ ~ ! [SY147: $i] :
( ~ ( rel_s5 @ sK5_SY139 @ SY147 )
| ~ ( p @ SY147 ) )
| ( q @ sK5_SY139 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(72,plain,
( ( ( ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(73,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK6_SY139 )
| ~ ~ ! [SY149: $i] :
( ~ ( rel_s5 @ sK6_SY139 @ SY149 )
| ~ ( p @ SY149 ) )
| ( q @ sK6_SY139 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(74,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(76,plain,
( ( ( ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(77,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( rel_s5 @ SV7 @ SV9 )
| ~ ( p @ SV9 ) )
= $true )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV8: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV8 ) )
= $true )
| ( ( ~ ( p @ SV8 )
| ! [SY148: $i] :
( ~ ( rel_s5 @ SV8 @ SY148 )
| ( q @ SY148 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
( ( ( rel_s5 @ sK2_SY124 @ sK5_SY139 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
( ( ( ~ ~ ! [SY147: $i] :
( ~ ( rel_s5 @ sK5_SY139 @ SY147 )
| ~ ( p @ SY147 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(81,plain,
( ( ( q @ sK5_SY139 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(82,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV10 )
| ~ ( p @ SV10 )
| ! [SY150: $i] :
( ~ ( rel_s5 @ SV10 @ SY150 )
| ( q @ SY150 ) ) )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK6_SY139 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(84,plain,
( ( ( ~ ~ ! [SY149: $i] :
( ~ ( rel_s5 @ sK6_SY139 @ SY149 )
| ~ ( p @ SY149 ) )
| ( q @ sK6_SY139 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(86,plain,
( ( ( ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(87,plain,
( ( ( ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(88,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK7_SY139 )
| ~ ~ ! [SY151: $i] :
( ~ ( rel_s5 @ sK7_SY139 @ SY151 )
| ~ ( p @ SY151 ) )
| ( q @ sK7_SY139 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(89,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( rel_s5 @ SV7 @ SV9 ) )
= $true )
| ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(90,plain,
! [SV8: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( ~ ( p @ SV8 )
| ! [SY148: $i] :
( ~ ( rel_s5 @ SV8 @ SY148 )
| ( q @ SY148 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(91,plain,
( ( ( ~ ! [SY147: $i] :
( ~ ( rel_s5 @ sK5_SY139 @ SY147 )
| ~ ( p @ SY147 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(92,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV10 ) )
= $true )
| ( ( ~ ( p @ SV10 )
| ! [SY150: $i] :
( ~ ( rel_s5 @ SV10 @ SY150 )
| ( q @ SY150 ) ) )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(93,plain,
( ( ( rel_s5 @ sK2_SY124 @ sK6_SY139 )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
( ( ( ~ ~ ! [SY149: $i] :
( ~ ( rel_s5 @ sK6_SY139 @ SY149 )
| ~ ( p @ SY149 ) ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(95,plain,
( ( ( q @ sK6_SY139 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(96,plain,
( ( ( ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(97,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK8_SY139 )
| ~ ~ ! [SY152: $i] :
( ~ ( rel_s5 @ sK8_SY139 @ SY152 )
| ~ ( p @ SY152 ) )
| ( q @ sK8_SY139 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(98,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV11 )
| ~ ( p @ SV11 )
| ! [SY153: $i] :
( ~ ( rel_s5 @ SV11 @ SY153 )
| ( q @ SY153 ) ) )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(99,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK7_SY139 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(100,plain,
( ( ( ~ ~ ! [SY151: $i] :
( ~ ( rel_s5 @ sK7_SY139 @ SY151 )
| ~ ( p @ SY151 ) )
| ( q @ sK7_SY139 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(101,plain,
! [SV9: $i,SV7: $i] :
( ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV8: $i] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( ! [SY148: $i] :
( ~ ( rel_s5 @ SV8 @ SY148 )
| ( q @ SY148 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(103,plain,
( ( ( ! [SY147: $i] :
( ~ ( rel_s5 @ sK5_SY139 @ SY147 )
| ~ ( p @ SY147 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV10: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( ~ ( p @ SV10 )
| ! [SY150: $i] :
( ~ ( rel_s5 @ SV10 @ SY150 )
| ( q @ SY150 ) ) )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(105,plain,
( ( ( ~ ! [SY149: $i] :
( ~ ( rel_s5 @ sK6_SY139 @ SY149 )
| ~ ( p @ SY149 ) ) )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(106,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV12 )
| ~ ( p @ SV12 )
| ! [SY154: $i] :
( ~ ( rel_s5 @ SV12 @ SY154 )
| ( q @ SY154 ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(107,plain,
( ( ( ~ ( rel_s5 @ sK2_SY124 @ sK8_SY139 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(108,plain,
( ( ( ~ ~ ! [SY152: $i] :
( ~ ( rel_s5 @ sK8_SY139 @ SY152 )
| ~ ( p @ SY152 ) )
| ( q @ sK8_SY139 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(109,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV11 ) )
= $true )
| ( ( ~ ( p @ SV11 )
| ! [SY153: $i] :
( ~ ( rel_s5 @ SV11 @ SY153 )
| ( q @ SY153 ) ) )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(110,plain,
( ( ( rel_s5 @ sK2_SY124 @ sK7_SY139 )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(111,plain,
( ( ( ~ ~ ! [SY151: $i] :
( ~ ( rel_s5 @ sK7_SY139 @ SY151 )
| ~ ( p @ SY151 ) ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(112,plain,
( ( ( q @ sK7_SY139 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(113,plain,
! [SV7: $i,SV9: $i] :
( ( ( p @ SV9 )
= $false )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV8: $i] :
( ( ( p @ SV8 )
= $false )
| ( ( ! [SY148: $i] :
( ~ ( rel_s5 @ SV8 @ SY148 )
| ( q @ SY148 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
( ( ( ~ ( rel_s5 @ sK5_SY139 @ sK9_SY147 )
| ~ ( p @ sK9_SY147 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[103]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( ~ ( p @ SV10 ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( rel_s5 @ SV10 @ SY150 )
| ( q @ SY150 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
( ( ( ! [SY149: $i] :
( ~ ( rel_s5 @ sK6_SY139 @ SY149 )
| ~ ( p @ SY149 ) ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV12 ) )
= $true )
| ( ( ~ ( p @ SV12 )
| ! [SY154: $i] :
( ~ ( rel_s5 @ SV12 @ SY154 )
| ( q @ SY154 ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(119,plain,
( ( ( rel_s5 @ sK2_SY124 @ sK8_SY139 )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(120,plain,
( ( ( ~ ~ ! [SY152: $i] :
( ~ ( rel_s5 @ sK8_SY139 @ SY152 )
| ~ ( p @ SY152 ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(121,plain,
( ( ( q @ sK8_SY139 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(122,plain,
! [SV11: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( ~ ( p @ SV11 )
| ! [SY153: $i] :
( ~ ( rel_s5 @ SV11 @ SY153 )
| ( q @ SY153 ) ) )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(123,plain,
( ( ( ~ ! [SY151: $i] :
( ~ ( rel_s5 @ sK7_SY139 @ SY151 )
| ~ ( p @ SY151 ) ) )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(124,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) )
| ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( rel_s5 @ SV8 @ SV13 )
| ( q @ SV13 ) )
= $true )
| ( ( p @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(126,plain,
( ( ( ~ ( rel_s5 @ sK5_SY139 @ sK9_SY147 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(127,plain,
( ( ( ~ ( p @ sK9_SY147 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(128,plain,
! [SV10: $i] :
( ( ( p @ SV10 )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( rel_s5 @ SV10 @ SY150 )
| ( q @ SY150 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
( ( ( ~ ( rel_s5 @ sK6_SY139 @ sK10_SY149 )
| ~ ( p @ sK10_SY149 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(130,plain,
! [SV12: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( ~ ( p @ SV12 )
| ! [SY154: $i] :
( ~ ( rel_s5 @ SV12 @ SY154 )
| ( q @ SY154 ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
( ( ( ~ ! [SY152: $i] :
( ~ ( rel_s5 @ sK8_SY139 @ SY152 )
| ~ ( p @ SY152 ) ) )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV11: $i] :
( ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( ! [SY153: $i] :
( ~ ( rel_s5 @ SV11 @ SY153 )
| ( q @ SY153 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(133,plain,
( ( ( ! [SY151: $i] :
( ~ ( rel_s5 @ sK7_SY139 @ SY151 )
| ~ ( p @ SY151 ) ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV9: $i,SV7: $i] :
( ( ( ! [SY139: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY139 )
| ~ ~ ! [SY17: $i] :
( ~ ( rel_s5 @ SY139 @ SY17 )
| ~ ( p @ SY17 ) )
| ( q @ SY139 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( rel_s5 @ SV8 @ SV13 ) )
= $true )
| ( ( q @ SV13 )
= $true )
| ( ( p @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(137,plain,
( ( ( rel_s5 @ sK5_SY139 @ sK9_SY147 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
( ( ( p @ sK9_SY147 )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( rel_s5 @ SV10 @ SV14 )
| ( q @ SV14 ) )
= $true )
| ( ( p @ SV10 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(140,plain,
( ( ( ~ ( rel_s5 @ sK6_SY139 @ sK10_SY149 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(141,plain,
( ( ( ~ ( p @ sK10_SY149 ) )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $true )
| ( ( ! [SY154: $i] :
( ~ ( rel_s5 @ SV12 @ SY154 )
| ( q @ SY154 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
( ( ( ! [SY152: $i] :
( ~ ( rel_s5 @ sK8_SY139 @ SY152 )
| ~ ( p @ SY152 ) ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV11: $i] :
( ( ( p @ SV11 )
= $false )
| ( ( ! [SY153: $i] :
( ~ ( rel_s5 @ SV11 @ SY153 )
| ( q @ SY153 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
( ( ( ~ ( rel_s5 @ sK7_SY139 @ sK11_SY151 )
| ~ ( p @ sK11_SY151 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(146,plain,
! [SV9: $i,SV7: $i] :
( ( ( ! [SY137: $i] :
( ~ ( rel_s5 @ sK2_SY124 @ SY137 )
| ~ ( p @ SY137 )
| ! [SY72: $i] :
( ~ ( rel_s5 @ SY137 @ SY72 )
| ( q @ SY72 ) ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(147,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ ( sK12_SY139 @ SV9 @ SV7 ) )
| ~ ~ ! [SY155: $i] :
( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ SY155 )
| ~ ( p @ SY155 ) )
| ( q @ ( sK12_SY139 @ SV9 @ SV7 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(148,plain,
! [SV13: $i,SV8: $i] :
( ( ( rel_s5 @ SV8 @ SV13 )
= $false )
| ( ( q @ SV13 )
= $true )
| ( ( p @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV8 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( rel_s5 @ SV10 @ SV14 ) )
= $true )
| ( ( q @ SV14 )
= $true )
| ( ( p @ SV10 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(150,plain,
( ( ( rel_s5 @ sK6_SY139 @ sK10_SY149 )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(151,plain,
( ( ( p @ sK10_SY149 )
= $true )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV12: $i] :
( ( ( p @ SV12 )
= $false )
| ( ( ! [SY154: $i] :
( ~ ( rel_s5 @ SV12 @ SY154 )
| ( q @ SY154 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(153,plain,
( ( ( ~ ( rel_s5 @ sK8_SY139 @ sK13_SY152 )
| ~ ( p @ sK13_SY152 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(154,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ( rel_s5 @ SV11 @ SV15 )
| ( q @ SV15 ) )
= $true )
| ( ( p @ SV11 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
( ( ( ~ ( rel_s5 @ sK7_SY139 @ sK11_SY151 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(156,plain,
( ( ( ~ ( p @ sK11_SY151 ) )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(157,plain,
! [SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV16 )
| ~ ( p @ SV16 )
| ! [SY156: $i] :
( ~ ( rel_s5 @ SV16 @ SY156 )
| ( q @ SY156 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ ( sK12_SY139 @ SV9 @ SV7 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(159,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY155: $i] :
( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ SY155 )
| ~ ( p @ SY155 ) )
| ( q @ ( sK12_SY139 @ SV9 @ SV7 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(160,plain,
! [SV14: $i,SV10: $i] :
( ( ( rel_s5 @ SV10 @ SV14 )
= $false )
| ( ( q @ SV14 )
= $true )
| ( ( p @ SV10 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV10 )
= $false )
| ( ( p @ sK3_SY135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV17: $i,SV12: $i] :
( ( ( ~ ( rel_s5 @ SV12 @ SV17 )
| ( q @ SV17 ) )
= $true )
| ( ( p @ SV12 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(162,plain,
( ( ( ~ ( rel_s5 @ sK8_SY139 @ sK13_SY152 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(163,plain,
( ( ( ~ ( p @ sK13_SY152 ) )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV15: $i,SV11: $i] :
( ( ( ~ ( rel_s5 @ SV11 @ SV15 ) )
= $true )
| ( ( q @ SV15 )
= $true )
| ( ( p @ SV11 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(165,plain,
( ( ( rel_s5 @ sK7_SY139 @ sK11_SY151 )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(166,plain,
( ( ( p @ sK11_SY151 )
= $true )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( rel_s5 @ sK2_SY124 @ SV16 ) )
= $true )
| ( ( ~ ( p @ SV16 )
| ! [SY156: $i] :
( ~ ( rel_s5 @ SV16 @ SY156 )
| ( q @ SY156 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV7: $i,SV9: $i] :
( ( ( rel_s5 @ sK2_SY124 @ ( sK12_SY139 @ SV9 @ SV7 ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(169,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY155: $i] :
( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ SY155 )
| ~ ( p @ SY155 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(170,plain,
! [SV7: $i,SV9: $i] :
( ( ( q @ ( sK12_SY139 @ SV9 @ SV7 ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(171,plain,
! [SV17: $i,SV12: $i] :
( ( ( ~ ( rel_s5 @ SV12 @ SV17 ) )
= $true )
| ( ( q @ SV17 )
= $true )
| ( ( p @ SV12 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
( ( ( rel_s5 @ sK8_SY139 @ sK13_SY152 )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(173,plain,
( ( ( p @ sK13_SY152 )
= $true )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(174,plain,
! [SV15: $i,SV11: $i] :
( ( ( rel_s5 @ SV11 @ SV15 )
= $false )
| ( ( q @ SV15 )
= $true )
| ( ( p @ SV11 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV11 )
= $false )
| ( ( q @ sK4_SY145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV9: $i,SV7: $i,SV16: $i] :
( ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( ~ ( p @ SV16 )
| ! [SY156: $i] :
( ~ ( rel_s5 @ SV16 @ SY156 )
| ( q @ SY156 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ! [SY155: $i] :
( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ SY155 )
| ~ ( p @ SY155 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(177,plain,
! [SV17: $i,SV12: $i] :
( ( ( rel_s5 @ SV12 @ SV17 )
= $false )
| ( ( q @ SV17 )
= $true )
| ( ( p @ SV12 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV12 )
= $false )
| ( ( rel_s5 @ sK3_SY135 @ sK4_SY145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(178,plain,
! [SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( ! [SY156: $i] :
( ~ ( rel_s5 @ SV16 @ SY156 )
| ( q @ SY156 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(179,plain,
! [SV7: $i,SV9: $i] :
( ( ( ! [SY155: $i] :
( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ SY155 )
| ~ ( p @ SY155 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV9: $i,SV7: $i,SV16: $i] :
( ( ( p @ SV16 )
= $false )
| ( ( ! [SY156: $i] :
( ~ ( rel_s5 @ SV16 @ SY156 )
| ( q @ SY156 ) ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(181,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ ( sK14_SY155 @ SV7 @ SV9 ) )
| ~ ( p @ ( sK14_SY155 @ SV7 @ SV9 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[179]) ).
thf(182,plain,
! [SV9: $i,SV7: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( rel_s5 @ SV16 @ SV18 )
| ( q @ SV18 ) )
= $true )
| ( ( p @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(183,plain,
! [SV7: $i,SV9: $i] :
( ( ( ~ ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ ( sK14_SY155 @ SV7 @ SV9 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(184,plain,
! [SV9: $i,SV7: $i] :
( ( ( ~ ( p @ ( sK14_SY155 @ SV7 @ SV9 ) ) )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(185,plain,
! [SV9: $i,SV7: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( rel_s5 @ SV16 @ SV18 ) )
= $true )
| ( ( q @ SV18 )
= $true )
| ( ( p @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV7: $i,SV9: $i] :
( ( ( rel_s5 @ ( sK12_SY139 @ SV9 @ SV7 ) @ ( sK14_SY155 @ SV7 @ SV9 ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(187,plain,
! [SV9: $i,SV7: $i] :
( ( ( p @ ( sK14_SY155 @ SV7 @ SV9 ) )
= $true )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(188,plain,
! [SV9: $i,SV7: $i,SV18: $i,SV16: $i] :
( ( ( rel_s5 @ SV16 @ SV18 )
= $false )
| ( ( q @ SV18 )
= $true )
| ( ( p @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV16 )
= $false )
| ( ( rel_s5 @ sK2_SY124 @ SV7 )
= $false )
| ( ( q @ SV7 )
= $true )
| ( ( rel_s5 @ SV7 @ SV9 )
= $false )
| ( ( p @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,188,187,186,177,174,173,172,170,168,166,165,160,151,150,148,138,137,121,119,112,110,95,93,81,79,50,33,27]) ).
thf(190,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO449^1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:39:55 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.16/0.40
% 1.16/0.40 No.of.Axioms: 3
% 1.16/0.40
% 1.16/0.40 Length.of.Defs: 5612
% 1.16/0.40
% 1.16/0.40 Contains.Choice.Funs: false
% 1.16/0.40 ......
% 1.16/0.40
% 1.16/0.40 ********************************
% 1.16/0.40 * All subproblems solved! *
% 1.16/0.40 ********************************
% 1.16/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:189,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.16/0.40
% 1.16/0.40 %**** Beginning of derivation protocol ****
% 1.16/0.40 % SZS output start CNFRefutation
% See solution above
% 1.16/0.40
% 1.16/0.40 %**** End of derivation protocol ****
% 1.16/0.40 %**** no. of clauses in derivation: 190 ****
% 1.16/0.40 %**** clause counter: 189 ****
% 1.16/0.40
% 1.16/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:189,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------