%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET027^7 : TPTP v9.3.1. Released v5.5.0.
% 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 : n007.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 10:39:03 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 35
% Syntax : Number of formulae : 102 ( 71 unt; 0 typ; 32 def)
% Number of atoms : 717 ( 175 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1462 ( 221 ~; 225 |; 8 &; 974 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 6 con; 0-3 aty)
% Number of variables : 258 ( 59 ^; 193 !; 6 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $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_mbox_s4,type,
mbox_s4: ( $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_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_member,type,
member: 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_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY32,type,
sK1_SY32: $i ).
thf(tp_sK2_SY109,type,
sK2_SY109: mu ).
thf(tp_sK3_SX0,type,
sK3_SX0: mu ).
thf(tp_sK4_SY119,type,
sK4_SY119: mu ).
thf(tp_sK5_SY124,type,
sK5_SY124: mu > mu > $i > mu ).
thf(tp_subset,type,
subset: mu > mu > $i > $o ).
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_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
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_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).
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] :
( ( exists_in_world @ X @ W )
=> ( 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_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(7,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(8,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY32: $i,SY33: mu] :
( ( exists_in_world @ SY33 @ SY32 )
=> ! [SY34: mu] :
( ( exists_in_world @ SY34 @ SY32 )
=> ! [SY35: mu] :
( ( exists_in_world @ SY35 @ SY32 )
=> ( ~ ~ ( ~ ( subset @ SY33 @ SY34 @ SY32 )
| ~ ( subset @ SY34 @ SY35 @ SY32 ) )
| ( subset @ SY33 @ SY35 @ SY32 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,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,
( ( ! [SY43: $i,SY44: mu] :
( ( exists_in_world @ SY44 @ SY43 )
=> ( subset @ SY44 @ SY44 @ SY43 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(11,plain,
( ( ! [SY99: $i,SY100: mu] :
( ( exists_in_world @ SY100 @ SY99 )
=> ! [SY101: mu] :
( ( exists_in_world @ SY101 @ SY99 )
=> ~ ( ~ ( ~ ( subset @ SY100 @ SY101 @ SY99 )
| ! [SY102: mu] :
( ( exists_in_world @ SY102 @ SY99 )
=> ( ~ ( member @ SY102 @ SY100 @ SY99 )
| ( member @ SY102 @ SY101 @ SY99 ) ) ) )
| ~ ( ~ ! [SY103: mu] :
( ( exists_in_world @ SY103 @ SY99 )
=> ( ~ ( member @ SY103 @ SY100 @ SY99 )
| ( member @ SY103 @ SY101 @ SY99 ) ) )
| ( subset @ SY100 @ SY101 @ SY99 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,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(12,plain,
( ( ! [SY109: mu] :
( ( exists_in_world @ SY109 @ sK1_SY32 )
=> ! [SY110: mu] :
( ( exists_in_world @ SY110 @ sK1_SY32 )
=> ! [SY111: mu] :
( ( exists_in_world @ SY111 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( subset @ SY109 @ SY110 @ sK1_SY32 )
| ~ ( subset @ SY110 @ SY111 @ sK1_SY32 ) )
| ( subset @ SY109 @ SY111 @ sK1_SY32 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(13,plain,
( ( ( exists_in_world @ sK2_SY109 @ sK1_SY32 )
=> ! [SY112: mu] :
( ( exists_in_world @ SY112 @ sK1_SY32 )
=> ! [SY113: mu] :
( ( exists_in_world @ SY113 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY109 @ SY112 @ sK1_SY32 )
| ~ ( subset @ SY112 @ SY113 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY113 @ sK1_SY32 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( exists_in_world @ sK2_SY109 @ sK1_SY32 )
= $true ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SY112: mu] :
( ( exists_in_world @ SY112 @ sK1_SY32 )
=> ! [SY113: mu] :
( ( exists_in_world @ SY113 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY109 @ SY112 @ sK1_SY32 )
| ~ ( subset @ SY112 @ SY113 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY113 @ sK1_SY32 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY112: mu] :
( ( exists_in_world @ SY112 @ sK1_SY32 )
=> ! [SY113: mu] :
( ( exists_in_world @ SY113 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY109 @ SY112 @ sK1_SY32 )
| ~ ( subset @ SY112 @ SY113 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY113 @ sK1_SY32 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [SY99: $i,SY100: mu] :
( ( exists_in_world @ SY100 @ SY99 )
=> ! [SY101: mu] :
( ( exists_in_world @ SY101 @ SY99 )
=> ~ ( ~ ( ~ ( subset @ SY100 @ SY101 @ SY99 )
| ! [SY102: mu] :
( ( exists_in_world @ SY102 @ SY99 )
=> ( ~ ( member @ SY102 @ SY100 @ SY99 )
| ( member @ SY102 @ SY101 @ SY99 ) ) ) )
| ~ ( ~ ! [SY103: mu] :
( ( exists_in_world @ SY103 @ SY99 )
=> ( ~ ( member @ SY103 @ SY100 @ SY99 )
| ( member @ SY103 @ SY101 @ SY99 ) ) )
| ( subset @ SY100 @ SY101 @ SY99 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [SY43: $i,SY44: mu] :
( ( exists_in_world @ SY44 @ SY43 )
=> ( subset @ SY44 @ SY44 @ SY43 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( exists_in_world @ sK2_SY109 @ sK1_SY32 )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ~ ! [SY112: mu] :
( ( exists_in_world @ SY112 @ sK1_SY32 )
=> ! [SY113: mu] :
( ( exists_in_world @ SY113 @ sK1_SY32 )
=> ( ~ ~ ( ~ ( subset @ sK2_SY109 @ SY112 @ sK1_SY32 )
| ~ ( subset @ SY112 @ SY113 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY113 @ sK1_SY32 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY32 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY32 )
| ~ ~ ( ~ ( subset @ sK2_SY109 @ SX0 @ sK1_SY32 )
| ~ ( subset @ SX0 @ SX1 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SX1 @ sK1_SY32 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,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,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ( subset @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( subset @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(24,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY32 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK1_SY32 )
| ~ ~ ( ~ ( subset @ sK2_SY109 @ SX0 @ sK1_SY32 )
| ~ ( subset @ SX0 @ SX1 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SX1 @ sK1_SY32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY114: mu] :
( ~ ( exists_in_world @ SY114 @ SV1 )
| ! [SY115: mu] :
( ~ ( exists_in_world @ SY115 @ SV1 )
| ~ ( ~ ( ~ ( subset @ SY114 @ SY115 @ SV1 )
| ! [SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SV1 )
| ~ ( member @ SY116 @ SY114 @ SV1 )
| ( member @ SY116 @ SY115 @ SV1 ) ) )
| ~ ( ~ ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SV1 )
| ~ ( member @ SY117 @ SY114 @ SV1 )
| ( member @ SY117 @ SY115 @ SV1 ) )
| ( subset @ SY114 @ SY115 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SV2 )
| ( subset @ SY118 @ SY118 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY32 )
| ! [SY119: mu] :
( ~ ( exists_in_world @ SY119 @ sK1_SY32 )
| ~ ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ SY119 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY119 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(28,plain,
! [SV1: $i,SV3: mu] :
( ( ~ ( exists_in_world @ SV3 @ SV1 )
| ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV1 )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY120 @ SV1 )
| ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV1 )
| ~ ( member @ SY121 @ SV3 @ SV1 )
| ( member @ SY121 @ SY120 @ SV1 ) ) )
| ~ ( ~ ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV1 )
| ~ ( member @ SY122 @ SV3 @ SV1 )
| ( member @ SY122 @ SY120 @ SV1 ) )
| ( subset @ SV3 @ SY120 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: $i,SV4: mu] :
( ( ~ ( exists_in_world @ SV4 @ SV2 )
| ( subset @ SV4 @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SY119: mu] :
( ~ ( exists_in_world @ SY119 @ sK1_SY32 )
| ~ ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ SY119 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ SY119 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i,SV3: mu] :
( ( ( ~ ( exists_in_world @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV1 )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY120 @ SV1 )
| ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV1 )
| ~ ( member @ SY121 @ SV3 @ SV1 )
| ( member @ SY121 @ SY120 @ SV1 ) ) )
| ~ ( ~ ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV1 )
| ~ ( member @ SY122 @ SV3 @ SV1 )
| ( member @ SY122 @ SY120 @ SV1 ) )
| ( subset @ SV3 @ SY120 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i,SV4: mu] :
( ( ( ~ ( exists_in_world @ SV4 @ SV2 ) )
= $true )
| ( ( subset @ SV4 @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
( ( exists_in_world @ sK3_SX0 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( exists_in_world @ sK4_SY119 @ sK1_SY32 )
| ~ ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ sK4_SY119 @ sK1_SY32 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
! [SV1: $i,SV3: mu] :
( ( ( exists_in_world @ SV3 @ SV1 )
= $false )
| ( ( ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV1 )
| ~ ( ~ ( ~ ( subset @ SV3 @ SY120 @ SV1 )
| ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV1 )
| ~ ( member @ SY121 @ SV3 @ SV1 )
| ( member @ SY121 @ SY120 @ SV1 ) ) )
| ~ ( ~ ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV1 )
| ~ ( member @ SY122 @ SV3 @ SV1 )
| ( member @ SY122 @ SY120 @ SV1 ) )
| ( subset @ SV3 @ SY120 @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV2: $i,SV4: mu] :
( ( ( exists_in_world @ SV4 @ SV2 )
= $false )
| ( ( subset @ SV4 @ SV4 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( exists_in_world @ sK4_SY119 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) )
| ( subset @ sK2_SY109 @ sK4_SY119 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV3: mu,SV1: $i,SV5: mu] :
( ( ( ~ ( exists_in_world @ SV5 @ SV1 )
| ~ ( ~ ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
| ~ ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) ) ) )
= $true )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( exists_in_world @ sK4_SY119 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ~ ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( subset @ sK2_SY109 @ sK4_SY119 @ sK1_SY32 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV3: mu,SV1: $i,SV5: mu] :
( ( ( ~ ( exists_in_world @ SV5 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
| ~ ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) ) ) )
= $true )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: mu,SV1: $i,SV5: mu] :
( ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
| ~ ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) ) ) )
= $true )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
| ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV1: $i,SV5: mu,SV3: mu] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
| ~ ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) ) )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV1: $i,SV5: mu,SV3: mu] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) ) )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV5: mu,SV3: mu,SV1: $i] :
( ( ( ~ ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) ) )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( subset @ sK2_SY109 @ sK3_SX0 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( subset @ sK3_SX0 @ sK4_SY119 @ sK1_SY32 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV1: $i,SV5: mu,SV3: mu] :
( ( ( ~ ( subset @ SV3 @ SV5 @ SV1 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: mu,SV3: mu,SV1: $i] :
( ( ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) )
| ( subset @ SV3 @ SV5 @ SV1 ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV1: $i,SV5: mu,SV3: mu] :
( ( ( ~ ( subset @ SV3 @ SV5 @ SV1 ) )
= $true )
| ( ( ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV5: mu,SV3: mu,SV1: $i] :
( ( ( ~ ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) ) )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(59,plain,
! [SV1: $i,SV5: mu,SV3: mu] :
( ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV1 )
| ~ ( member @ SY123 @ SV3 @ SV1 )
| ( member @ SY123 @ SV5 @ SV1 ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV5: mu,SV3: mu,SV1: $i] :
( ( ( ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV1 )
| ~ ( member @ SY124 @ SV3 @ SV1 )
| ( member @ SY124 @ SV5 @ SV1 ) ) )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
! [SV5: mu,SV3: mu,SV1: $i,SV6: mu] :
( ( ( ~ ( exists_in_world @ SV6 @ SV1 )
| ~ ( member @ SV6 @ SV3 @ SV1 )
| ( member @ SV6 @ SV5 @ SV1 ) )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(62,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV1 )
| ~ ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV3 @ SV1 )
| ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV5 @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(63,plain,
! [SV5: mu,SV3: mu,SV1: $i,SV6: mu] :
( ( ( ~ ( exists_in_world @ SV6 @ SV1 ) )
= $true )
| ( ( ~ ( member @ SV6 @ SV3 @ SV1 )
| ( member @ SV6 @ SV5 @ SV1 ) )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(65,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( ~ ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV3 @ SV1 )
| ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV5 @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(66,plain,
! [SV5: mu,SV3: mu,SV1: $i,SV6: mu] :
( ( ( exists_in_world @ SV6 @ SV1 )
= $false )
| ( ( ~ ( member @ SV6 @ SV3 @ SV1 )
| ( member @ SV6 @ SV5 @ SV1 ) )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( exists_in_world @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( ~ ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV3 @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV5 @ SV1 )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: mu,SV1: $i,SV3: mu,SV6: mu] :
( ( ( ~ ( member @ SV6 @ SV3 @ SV1 ) )
= $true )
| ( ( member @ SV6 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV6 @ SV1 )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV1: $i,SV3: mu,SV5: mu] :
( ( ( member @ ( sK5_SY124 @ SV5 @ SV3 @ SV1 ) @ SV3 @ SV1 )
= $true )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(72,plain,
! [SV5: mu,SV1: $i,SV3: mu,SV6: mu] :
( ( ( member @ SV6 @ SV3 @ SV1 )
= $false )
| ( ( member @ SV6 @ SV5 @ SV1 )
= $true )
| ( ( exists_in_world @ SV6 @ SV1 )
= $false )
| ( ( subset @ SV3 @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV5 @ SV1 )
= $false )
| ( ( exists_in_world @ SV3 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,72,71,69,67,54,53,43,41,37,34]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^7 : TPTP v9.3.1. Released v5.5.0.
% 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
% 0.06/0.18 % Computer : n007.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 14:25:30 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.24
% 0.06/0.24 No.of.Axioms: 2
% 0.06/0.24
% 0.06/0.24 Length.of.Defs: 5508
% 0.06/0.24
% 0.06/0.24 Contains.Choice.Funs: false
% 0.06/0.24 ....
% 0.06/0.24
% 0.06/0.24 ********************************
% 0.06/0.24 * All subproblems solved! *
% 0.06/0.24 ********************************
% 0.06/0.24 % 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:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.24
% 0.06/0.24 %**** Beginning of derivation protocol ****
% 0.06/0.24 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24
% 0.06/0.24 %**** End of derivation protocol ****
% 0.06/0.24 %**** no. of clauses in derivation: 70 ****
% 0.06/0.24 %**** clause counter: 73 ****
% 0.06/0.24
% 0.06/0.24 % 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:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------