TSTP Solution File: SET027^7 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET027^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:58:18 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 83
% Syntax : Number of formulae : 173 ( 85 unt; 44 typ; 32 def)
% Number of atoms : 861 ( 214 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1585 ( 249 ~; 257 |; 9 &;1060 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 43 usr; 6 con; 0-3 aty)
% Number of variables : 317 ( 69 ^ 241 !; 7 ?; 317 :)
% 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_X,type,
sK1_X: $i > mu ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: mu ).
thf(tp_sK4_SY17,type,
sK4_SY17: mu ).
thf(tp_sK5_SY21,type,
sK5_SY21: mu ).
thf(tp_sK6_SY20,type,
sK6_SY20: 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/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(3,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(4,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(5,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(6,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
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/sandbox2/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,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[3]) ).
thf(11,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(17,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] : ( subset @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(18,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(19,plain,
( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(20,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,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(21,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)],[16,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 )
| ( subset @ SX1 @ SX1 @ 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 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX3 @ SX0 ) )
| ( subset @ SX1 @ SX3 @ 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,
! [SV1: $i] :
( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(25,plain,
! [SV2: mu] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( exists_in_world @ SV2 @ SY0 )
| ~ ( rel_s4 @ SY0 @ SY1 )
| ( exists_in_world @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(26,plain,
! [SV3: $i] :
( ( rel_s4 @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV4: $i] :
( ( ! [SY2: $i,SY3: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV4 @ SY2 )
| ~ ( rel_s4 @ SY2 @ SY3 ) )
| ( rel_s4 @ SV4 @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV5: $i] :
( ( ! [SY4: mu] :
( ~ ( exists_in_world @ SY4 @ SV5 )
| ! [SY5: mu] :
( ~ ( exists_in_world @ SY5 @ SV5 )
| ~ ( ~ ( ~ ( subset @ SY4 @ SY5 @ SV5 )
| ! [SY6: mu] :
( ~ ( exists_in_world @ SY6 @ SV5 )
| ~ ( member @ SY6 @ SY4 @ SV5 )
| ( member @ SY6 @ SY5 @ SV5 ) ) )
| ~ ( ~ ! [SY7: mu] :
( ~ ( exists_in_world @ SY7 @ SV5 )
| ~ ( member @ SY7 @ SY4 @ SV5 )
| ( member @ SY7 @ SY5 @ SV5 ) )
| ( subset @ SY4 @ SY5 @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV6: $i] :
( ( ! [SY8: mu] :
( ~ ( exists_in_world @ SY8 @ SV6 )
| ( subset @ SY8 @ SY8 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX3 @ SX0 ) )
| ( subset @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV7: $i,SV2: mu] :
( ( ! [SY9: $i] :
( ~ ( exists_in_world @ SV2 @ SV7 )
| ~ ( rel_s4 @ SV7 @ SY9 )
| ( exists_in_world @ SV2 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY10: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( rel_s4 @ SV8 @ SY10 ) )
| ( rel_s4 @ SV4 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV5: $i,SV9: mu] :
( ( ~ ( exists_in_world @ SV9 @ SV5 )
| ! [SY11: mu] :
( ~ ( exists_in_world @ SY11 @ SV5 )
| ~ ( ~ ( ~ ( subset @ SV9 @ SY11 @ SV5 )
| ! [SY12: mu] :
( ~ ( exists_in_world @ SY12 @ SV5 )
| ~ ( member @ SY12 @ SV9 @ SV5 )
| ( member @ SY12 @ SY11 @ SV5 ) ) )
| ~ ( ~ ! [SY13: mu] :
( ~ ( exists_in_world @ SY13 @ SV5 )
| ~ ( member @ SY13 @ SV9 @ SV5 )
| ( member @ SY13 @ SY11 @ SV5 ) )
| ( subset @ SV9 @ SY11 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV6: $i,SV10: mu] :
( ( ~ ( exists_in_world @ SV10 @ SV6 )
| ( subset @ SV10 @ SV10 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SY14: mu] :
( ~ ( exists_in_world @ SY14 @ sK2_SX0 )
| ! [SY15: mu] :
( ~ ( exists_in_world @ SY15 @ sK2_SX0 )
| ! [SY16: mu] :
( ~ ( exists_in_world @ SY16 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ SY14 @ SY15 @ sK2_SX0 )
| ~ ( subset @ SY15 @ SY16 @ sK2_SX0 ) )
| ( subset @ SY14 @ SY16 @ sK2_SX0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(36,plain,
! [SV11: $i,SV7: $i,SV2: mu] :
( ( ~ ( exists_in_world @ SV2 @ SV7 )
| ~ ( rel_s4 @ SV7 @ SV11 )
| ( exists_in_world @ SV2 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( rel_s4 @ SV8 @ SV12 ) )
| ( rel_s4 @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: $i,SV9: mu] :
( ( ( ~ ( exists_in_world @ SV9 @ SV5 ) )
= $true )
| ( ( ! [SY11: mu] :
( ~ ( exists_in_world @ SY11 @ SV5 )
| ~ ( ~ ( ~ ( subset @ SV9 @ SY11 @ SV5 )
| ! [SY12: mu] :
( ~ ( exists_in_world @ SY12 @ SV5 )
| ~ ( member @ SY12 @ SV9 @ SV5 )
| ( member @ SY12 @ SY11 @ SV5 ) ) )
| ~ ( ~ ! [SY13: mu] :
( ~ ( exists_in_world @ SY13 @ SV5 )
| ~ ( member @ SY13 @ SV9 @ SV5 )
| ( member @ SY13 @ SY11 @ SV5 ) )
| ( subset @ SV9 @ SY11 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV6: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV6 ) )
= $true )
| ( ( subset @ SV10 @ SV10 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( ~ ( exists_in_world @ sK3_SY14 @ sK2_SX0 )
| ! [SY17: mu] :
( ~ ( exists_in_world @ SY17 @ sK2_SX0 )
| ! [SY18: mu] :
( ~ ( exists_in_world @ SY18 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ sK3_SY14 @ SY17 @ sK2_SX0 )
| ~ ( subset @ SY17 @ SY18 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ SY18 @ sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(41,plain,
! [SV11: $i,SV7: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV7 )
| ~ ( rel_s4 @ SV7 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( rel_s4 @ SV8 @ SV12 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV5: $i,SV9: mu] :
( ( ( exists_in_world @ SV9 @ SV5 )
= $false )
| ( ( ! [SY11: mu] :
( ~ ( exists_in_world @ SY11 @ SV5 )
| ~ ( ~ ( ~ ( subset @ SV9 @ SY11 @ SV5 )
| ! [SY12: mu] :
( ~ ( exists_in_world @ SY12 @ SV5 )
| ~ ( member @ SY12 @ SV9 @ SV5 )
| ( member @ SY12 @ SY11 @ SV5 ) ) )
| ~ ( ~ ! [SY13: mu] :
( ~ ( exists_in_world @ SY13 @ SV5 )
| ~ ( member @ SY13 @ SV9 @ SV5 )
| ( member @ SY13 @ SY11 @ SV5 ) )
| ( subset @ SV9 @ SY11 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV6: $i,SV10: mu] :
( ( ( exists_in_world @ SV10 @ SV6 )
= $false )
| ( ( subset @ SV10 @ SV10 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( exists_in_world @ sK3_SY14 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
( ( ! [SY17: mu] :
( ~ ( exists_in_world @ SY17 @ sK2_SX0 )
| ! [SY18: mu] :
( ~ ( exists_in_world @ SY18 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ sK3_SY14 @ SY17 @ sK2_SX0 )
| ~ ( subset @ SY17 @ SY18 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ SY18 @ sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(47,plain,
! [SV11: $i,SV7: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV7 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( rel_s4 @ SV8 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV9: mu,SV5: $i,SV13: mu] :
( ( ( ~ ( exists_in_world @ SV13 @ SV5 )
| ~ ( ~ ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
| ~ ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( exists_in_world @ sK3_SY14 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( ~ ( exists_in_world @ sK4_SY17 @ sK2_SX0 )
| ! [SY21: mu] :
( ~ ( exists_in_world @ SY21 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ SY21 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ SY21 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
! [SV11: $i,SV7: $i,SV2: mu] :
( ( ( exists_in_world @ SV2 @ SV7 )
= $false )
| ( ( ~ ( rel_s4 @ SV7 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( rel_s4 @ SV8 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV9: mu,SV5: $i,SV13: mu] :
( ( ( ~ ( exists_in_world @ SV13 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
| ~ ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
( ( ~ ( exists_in_world @ sK4_SY17 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
( ( ! [SY21: mu] :
( ~ ( exists_in_world @ SY21 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ SY21 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ SY21 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: mu,SV11: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV11 )
= $false )
| ( ( exists_in_world @ SV2 @ SV7 )
= $false )
| ( ( exists_in_world @ SV2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV8 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV9: mu,SV5: $i,SV13: mu] :
( ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
| ~ ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(60,plain,
( ( exists_in_world @ sK4_SY17 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(61,plain,
( ( ~ ( exists_in_world @ sK5_SY21 @ sK2_SX0 )
| ~ ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ sK5_SY21 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(62,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( ~ ( rel_s4 @ SV8 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV5: $i,SV13: mu,SV9: mu] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
| ~ ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) ) )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( ~ ( exists_in_world @ sK5_SY21 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) )
| ( subset @ sK3_SY14 @ sK5_SY21 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV12 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV5: $i,SV13: mu,SV9: mu] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) ) )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV13: mu,SV9: mu,SV5: $i] :
( ( ( ~ ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) ) )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
( ( exists_in_world @ sK5_SY21 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(70,plain,
( ( ~ ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(71,plain,
( ( subset @ sK3_SY14 @ sK5_SY21 @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: $i,SV13: mu,SV9: mu] :
( ( ( ~ ( subset @ SV9 @ SV13 @ SV5 )
| ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV13: mu,SV9: mu,SV5: $i] :
( ( ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) )
| ( subset @ SV9 @ SV13 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( ~ ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV5: $i,SV13: mu,SV9: mu] :
( ( ( ~ ( subset @ SV9 @ SV13 @ SV5 ) )
= $true )
| ( ( ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV13: mu,SV9: mu,SV5: $i] :
( ( ( ~ ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) ) )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
| ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV5: $i,SV13: mu,SV9: mu] :
( ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV5 )
| ~ ( member @ SY19 @ SV9 @ SV5 )
| ( member @ SY19 @ SV13 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV13: mu,SV9: mu,SV5: $i] :
( ( ( ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV5 )
| ~ ( member @ SY20 @ SV9 @ SV5 )
| ( member @ SY20 @ SV13 @ SV5 ) ) )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
( ( ~ ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(81,plain,
( ( ~ ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV13: mu,SV9: mu,SV5: $i,SV14: mu] :
( ( ( ~ ( exists_in_world @ SV14 @ SV5 )
| ~ ( member @ SV14 @ SV9 @ SV5 )
| ( member @ SV14 @ SV13 @ SV5 ) )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV5 )
| ~ ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV9 @ SV5 )
| ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV13 @ SV5 ) )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(84,plain,
( ( subset @ sK3_SY14 @ sK4_SY17 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
( ( subset @ sK4_SY17 @ sK5_SY21 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV13: mu,SV9: mu,SV5: $i,SV14: mu] :
( ( ( ~ ( exists_in_world @ SV14 @ SV5 ) )
= $true )
| ( ( ~ ( member @ SV14 @ SV9 @ SV5 )
| ( member @ SV14 @ SV13 @ SV5 ) )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV5 ) )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( ~ ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV9 @ SV5 )
| ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV13 @ SV5 ) )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV13: mu,SV9: mu,SV5: $i,SV14: mu] :
( ( ( exists_in_world @ SV14 @ SV5 )
= $false )
| ( ( ~ ( member @ SV14 @ SV9 @ SV5 )
| ( member @ SV14 @ SV13 @ SV5 ) )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( exists_in_world @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(91,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( ~ ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV9 @ SV5 ) )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(92,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV13 @ SV5 )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
! [SV13: mu,SV5: $i,SV9: mu,SV14: mu] :
( ( ( ~ ( member @ SV14 @ SV9 @ SV5 ) )
= $true )
| ( ( member @ SV14 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV5: $i,SV9: mu,SV13: mu] :
( ( ( member @ ( sK6_SY20 @ SV13 @ SV9 @ SV5 ) @ SV9 @ SV5 )
= $true )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV13: mu,SV5: $i,SV9: mu,SV14: mu] :
( ( ( member @ SV14 @ SV9 @ SV5 )
= $false )
| ( ( member @ SV14 @ SV13 @ SV5 )
= $true )
| ( ( exists_in_world @ SV14 @ SV5 )
= $false )
| ( ( subset @ SV9 @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV13 @ SV5 )
= $false )
| ( ( exists_in_world @ SV9 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,95,94,92,90,85,84,71,69,66,60,57,50,44,26]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET027^7 : TPTP v8.1.0. Released v5.5.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 16:44:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.34
% 0.18/0.34 No.of.Axioms: 6
% 0.18/0.34
% 0.18/0.34 Length.of.Defs: 5540
% 0.18/0.34
% 0.18/0.34 Contains.Choice.Funs: false
% 0.18/0.35 (rf:0,axioms:6,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.18/0.46
% 0.18/0.46 ********************************
% 0.18/0.46 * All subproblems solved! *
% 0.18/0.46 ********************************
% 0.18/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.46
% 0.18/0.46 %**** Beginning of derivation protocol ****
% 0.18/0.46 % SZS output start CNFRefutation
% See solution above
% 0.18/0.46
% 0.18/0.46 %**** End of derivation protocol ****
% 0.18/0.46 %**** no. of clauses in derivation: 97 ****
% 0.18/0.46 %**** clause counter: 96 ****
% 0.18/0.46
% 0.18/0.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------