TSTP Solution File: KRS277^7 by cvc5---1.0.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : KRS277^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n032.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  : 300s
% DateTime : Thu Aug 31 05:42:01 EDT 2023

% Result   : CounterSatisfiable 35.51s 35.79s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : KRS277^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.12  % Command    : do_cvc5 %s %d
% 0.14/0.32  % Computer : n032.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Mon Aug 28 02:32:30 EDT 2023
% 0.14/0.32  % CPUTime    : 
% 0.16/0.41  %----Proving TH0
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % File     : KRS277^7 : TPTP v8.1.2. Released v5.5.0.
% 0.16/0.42  % Domain   : Knowledge Representation
% 0.16/0.42  % Problem  : Database querying
% 0.16/0.42  % Version  : [Ben12] axioms.
% 0.16/0.42  % English  :
% 0.16/0.42  
% 0.16/0.42  % Refs     : [Rei92] Reiter (1992), What Should a Database Know?
% 0.16/0.42  %          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.16/0.42  % Source   : [Ben12]
% 0.16/0.42  % Names    : s4-cumul-APM010+1 [Ben12]
% 0.16/0.42  
% 0.16/0.42  % Status   : CounterCounterSatisfiable
% 0.16/0.42  % Rating   : 0.50 v8.1.0, 0.40 v7.5.0, 0.20 v7.4.0, 0.25 v7.2.0, 0.00 v6.4.0, 0.33 v6.3.0, 0.00 v6.0.0, 0.33 v5.5.0
% 0.16/0.42  % Syntax   : Number of formulae    :   87 (  39 unt;  43 typ;  32 def)
% 0.16/0.42  %            Number of atoms       :  129 (  36 equ;   0 cnn)
% 0.16/0.42  %            Maximal formula atoms :   10 (   2 avg)
% 0.16/0.42  %            Number of connectives :  185 (   5   ~;   5   |;   9   &; 156   @)
% 0.16/0.42  %                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
% 0.16/0.42  %            Maximal formula depth :   10 (   2 avg)
% 0.16/0.42  %            Number of types       :    3 (   1 usr)
% 0.16/0.42  %            Number of type conns  :  183 ( 183   >;   0   *;   0   +;   0  <<)
% 0.16/0.42  %            Number of symbols     :   50 (  48 usr;  13 con; 0-3 aty)
% 0.16/0.42  %            Number of variables   :   98 (  51   ^;  40   !;   7   ?;  98   :)
% 0.16/0.42  % SPC      : TH0_CSA_EQU_NAR
% 0.16/0.42  
% 0.16/0.42  % Comments : 
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %----Include axioms for Modal logic S4 under cumulative domains
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %----Declaration of additional base type mu
% 0.16/0.42  thf(mu_type,type,
% 0.16/0.42      mu: $tType ).
% 0.16/0.42  
% 0.16/0.42  %----Equality
% 0.16/0.42  thf(qmltpeq_type,type,
% 0.16/0.42      qmltpeq: mu > mu > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  % originale Definition
% 0.16/0.42  %thf(qmltpeq,definition,
% 0.16/0.42  %    ( qmltpeq
% 0.16/0.42  %    = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.16/0.42  
% 0.16/0.42  % erweiterte Leibnitz-Definition
% 0.16/0.42  %thf(qmltpeq,definition,
% 0.16/0.42  % ( qmltpeq
% 0.16/0.42  % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.16/0.42  
% 0.16/0.42  %  Leibnitz-Definition
% 0.16/0.42  %thf(qmltpeq,definition,
% 0.16/0.42  % ( qmltpeq
% 0.16/0.42  %  = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.16/0.42  
% 0.16/0.42  thf(meq_prop_type,type,
% 0.16/0.42      meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(meq_prop,definition,
% 0.16/0.42      ( meq_prop
% 0.16/0.42      = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.16/0.42            ( ( X @ W )
% 0.16/0.42            = ( Y @ W ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Modal operators not, or, box, Pi 
% 0.16/0.42  thf(mnot_type,type,
% 0.16/0.42      mnot: ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mnot,definition,
% 0.16/0.42      ( mnot
% 0.16/0.42      = ( ^ [Phi: $i > $o,W: $i] :
% 0.16/0.42            ~ ( Phi @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mor_type,type,
% 0.16/0.42      mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mor,definition,
% 0.16/0.42      ( mor
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.16/0.42            ( ( Phi @ W )
% 0.16/0.42            | ( Psi @ W ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mbox_type,type,
% 0.16/0.42      mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mbox,definition,
% 0.16/0.42      ( mbox
% 0.16/0.42      = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.16/0.42          ! [V: $i] :
% 0.16/0.42            ( ~ ( R @ W @ V )
% 0.16/0.42            | ( Phi @ V ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mforall_prop_type,type,
% 0.16/0.42      mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mforall_prop,definition,
% 0.16/0.42      ( mforall_prop
% 0.16/0.42      = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.16/0.42          ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Further modal operators
% 0.16/0.42  thf(mtrue_type,type,
% 0.16/0.42      mtrue: $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mtrue,definition,
% 0.16/0.42      ( mtrue
% 0.16/0.42      = ( ^ [W: $i] : $true ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mfalse_type,type,
% 0.16/0.42      mfalse: $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mfalse,definition,
% 0.16/0.42      ( mfalse
% 0.16/0.42      = ( mnot @ mtrue ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mand_type,type,
% 0.16/0.42      mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mand,definition,
% 0.16/0.42      ( mand
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mimplies_type,type,
% 0.16/0.42      mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mimplies,definition,
% 0.16/0.42      ( mimplies
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mimplied_type,type,
% 0.16/0.42      mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mimplied,definition,
% 0.16/0.42      ( mimplied
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mequiv_type,type,
% 0.16/0.42      mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mequiv,definition,
% 0.16/0.42      ( mequiv
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mxor_type,type,
% 0.16/0.42      mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mxor,definition,
% 0.16/0.42      ( mxor
% 0.16/0.42      = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mdia_type,type,
% 0.16/0.42      mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mdia,definition,
% 0.16/0.42      ( mdia
% 0.16/0.42      = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %--- (new for cumulative)
% 0.16/0.42  %---Declaration of existence predicate for simulating cumulative domain
% 0.16/0.42  thf(exists_in_world_type,type,
% 0.16/0.42      exists_in_world: mu > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  %----The domains are non-empty
% 0.16/0.42  thf(nonempty_ax,axiom,
% 0.16/0.42      ! [V: $i] :
% 0.16/0.42      ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mforall_ind_type,type,
% 0.16/0.42      mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  %--- (new for cumulative)
% 0.16/0.42  thf(mforall_ind,definition,
% 0.16/0.42      ( mforall_ind
% 0.16/0.42      = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.16/0.42          ! [X: mu] :
% 0.16/0.42            ( ( exists_in_world @ X @ W )
% 0.16/0.42           => ( Phi @ X @ W ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %thf(mforall_ind,definition,
% 0.16/0.42  %    ( mforall_ind
% 0.16/0.42  %    = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.16/0.42  %        ! [X: mu] :
% 0.16/0.42  %          ( Phi @ X @ W ) ) )).
% 0.16/0.42  
% 0.16/0.42  thf(mexists_ind_type,type,
% 0.16/0.42      mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mexists_ind,definition,
% 0.16/0.42      ( mexists_ind
% 0.16/0.42      = ( ^ [Phi: mu > $i > $o] :
% 0.16/0.42            ( mnot
% 0.16/0.42            @ ( mforall_ind
% 0.16/0.42              @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mexists_prop_type,type,
% 0.16/0.42      mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mexists_prop,definition,
% 0.16/0.42      ( mexists_prop
% 0.16/0.42      = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.16/0.42            ( mnot
% 0.16/0.42            @ ( mforall_prop
% 0.16/0.42              @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Definition of properties of accessibility relations
% 0.16/0.42  thf(mreflexive_type,type,
% 0.16/0.42      mreflexive: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mreflexive,definition,
% 0.16/0.42      ( mreflexive
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(msymmetric_type,type,
% 0.16/0.42      msymmetric: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(msymmetric,definition,
% 0.16/0.42      ( msymmetric
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i] :
% 0.16/0.42            ( ( R @ S @ T )
% 0.16/0.42           => ( R @ T @ S ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mserial_type,type,
% 0.16/0.42      mserial: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mserial,definition,
% 0.16/0.42      ( mserial
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i] :
% 0.16/0.42          ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mtransitive_type,type,
% 0.16/0.42      mtransitive: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mtransitive,definition,
% 0.16/0.42      ( mtransitive
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( ( R @ S @ T )
% 0.16/0.42              & ( R @ T @ U ) )
% 0.16/0.42           => ( R @ S @ U ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(meuclidean_type,type,
% 0.16/0.42      meuclidean: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(meuclidean,definition,
% 0.16/0.42      ( meuclidean
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( ( R @ S @ T )
% 0.16/0.42              & ( R @ S @ U ) )
% 0.16/0.42           => ( R @ T @ U ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mpartially_functional_type,type,
% 0.16/0.42      mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mpartially_functional,definition,
% 0.16/0.42      ( mpartially_functional
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( ( R @ S @ T )
% 0.16/0.42              & ( R @ S @ U ) )
% 0.16/0.42           => ( T = U ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mfunctional_type,type,
% 0.16/0.42      mfunctional: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mfunctional,definition,
% 0.16/0.42      ( mfunctional
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i] :
% 0.16/0.42          ? [T: $i] :
% 0.16/0.42            ( ( R @ S @ T )
% 0.16/0.42            & ! [U: $i] :
% 0.16/0.42                ( ( R @ S @ U )
% 0.16/0.42               => ( T = U ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_dense_type,type,
% 0.16/0.42      mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_dense,definition,
% 0.16/0.42      ( mweakly_dense
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( R @ S @ T )
% 0.16/0.42           => ? [U: $i] :
% 0.16/0.42                ( ( R @ S @ U )
% 0.16/0.42                & ( R @ U @ T ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_connected_type,type,
% 0.16/0.42      mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_connected,definition,
% 0.16/0.42      ( mweakly_connected
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( ( R @ S @ T )
% 0.16/0.42              & ( R @ S @ U ) )
% 0.16/0.42           => ( ( R @ T @ U )
% 0.16/0.42              | ( T = U )
% 0.16/0.42              | ( R @ U @ T ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_directed_type,type,
% 0.16/0.42      mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mweakly_directed,definition,
% 0.16/0.42      ( mweakly_directed
% 0.16/0.42      = ( ^ [R: $i > $i > $o] :
% 0.16/0.42          ! [S: $i,T: $i,U: $i] :
% 0.16/0.42            ( ( ( R @ S @ T )
% 0.16/0.42              & ( R @ S @ U ) )
% 0.16/0.42           => ? [V: $i] :
% 0.16/0.42                ( ( R @ T @ V )
% 0.16/0.42                & ( R @ U @ V ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Definition of validity
% 0.16/0.42  thf(mvalid_type,type,
% 0.16/0.42      mvalid: ( $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mvalid,definition,
% 0.16/0.42      ( mvalid
% 0.16/0.42      = ( ^ [Phi: $i > $o] :
% 0.16/0.42          ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Definition of satisfiability
% 0.16/0.42  thf(msatisfiable_type,type,
% 0.16/0.42      msatisfiable: ( $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(msatisfiable,definition,
% 0.16/0.42      ( msatisfiable
% 0.16/0.42      = ( ^ [Phi: $i > $o] :
% 0.16/0.42          ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Definition of countersatisfiability
% 0.16/0.42  thf(mcountersatisfiable_type,type,
% 0.16/0.42      mcountersatisfiable: ( $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mcountersatisfiable,definition,
% 0.16/0.42      ( mcountersatisfiable
% 0.16/0.42      = ( ^ [Phi: $i > $o] :
% 0.16/0.42          ? [W: $i] :
% 0.16/0.42            ~ ( Phi @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----Definition of invalidity
% 0.16/0.42  thf(minvalid_type,type,
% 0.16/0.42      minvalid: ( $i > $o ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(minvalid,definition,
% 0.16/0.42      ( minvalid
% 0.16/0.42      = ( ^ [Phi: $i > $o] :
% 0.16/0.42          ! [W: $i] :
% 0.16/0.42            ~ ( Phi @ W ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %----We reserve an accessibility relation constant rel_s4
% 0.16/0.42  thf(rel_s4_type,type,
% 0.16/0.42      rel_s4: $i > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.16/0.42  thf(mbox_s4_type,type,
% 0.16/0.42      mbox_s4: ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mbox_s4,definition,
% 0.16/0.42      ( mbox_s4
% 0.16/0.42      = ( ^ [Phi: $i > $o,W: $i] :
% 0.16/0.42          ! [V: $i] :
% 0.16/0.42            ( ~ ( rel_s4 @ W @ V )
% 0.16/0.42            | ( Phi @ V ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mdia_s4_type,type,
% 0.16/0.42      mdia_s4: ( $i > $o ) > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(mdia_s4,definition,
% 0.16/0.42      ( mdia_s4
% 0.16/0.42      = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %----We have now two options for stating the B conditions: 
% 0.16/0.42  %----We can (i) directly formulate conditions for the accessibility relation
% 0.16/0.42  %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.16/0.42  thf(a1,axiom,
% 0.16/0.42      mreflexive @ rel_s4 ).
% 0.16/0.42  
% 0.16/0.42  thf(a2,axiom,
% 0.16/0.42      mtransitive @ rel_s4 ).
% 0.16/0.42  
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  thf(cumulative_ax,axiom,
% 0.16/0.42      ! [X: mu,V: $i,W: $i] :
% 0.16/0.42        ( ( ( exists_in_world @ X @ V )
% 0.16/0.42          & ( rel_s4 @ V @ W ) )
% 0.16/0.42       => ( exists_in_world @ X @ W ) ) ).
% 0.16/0.42  
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  thf(teach_type,type,
% 0.16/0.42      teach: mu > mu > $i > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sue_type,type,
% 0.16/0.42      sue: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_sue_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ sue @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(mary_type,type,
% 0.16/0.42      mary: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_mary_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ mary @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(math_type,type,
% 0.16/0.42      math: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_math_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ math @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(john_type,type,
% 0.16/0.42      john: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_john_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ john @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(cs_type,type,
% 0.16/0.42      cs: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_cs_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ cs @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(psych_type,type,
% 0.16/0.42      psych: mu ).
% 0.16/0.42  
% 0.16/0.42  thf(existence_of_psych_ax,axiom,
% 0.16/0.42      ! [V: $i] : ( exists_in_world @ psych @ V ) ).
% 0.16/0.42  
% 0.16/0.42  thf(db,axiom,
% 0.16/0.42      ( mvalid
% 0.16/0.42      @ ( mbox_s4
% 0.16/0.42        @ ( mand @ ( teach @ john @ math )
% 0.16/0.42          @ ( mand
% 0.16/0.42            @ ( mexists_ind
% 0.16/0.42              @ ^ [X: mu] : ( teach @ X @ cs ) )
% 0.16/0.42            @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  thf(query,conjecture,
% 0.16/0.42      ( mvalid
% 0.16/0.42      @ ( mexists_ind
% 0.16/0.42        @ ^ [X: mu] : ( mand @ ( teach @ X @ psych ) @ ( mnot @ ( mbox_s4 @ ( teach @ X @ cs ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.pGZCTOymFQ/cvc5---1.0.5_30864.p...
% 0.16/0.42  (declare-sort $$unsorted 0)
% 0.16/0.42  (declare-sort tptp.mu 0)
% 0.16/0.42  (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.16/0.42  (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.16/0.42  (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.16/0.42  (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.16/0.42  (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.16/0.42  (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.16/0.42  (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.16/0.42  (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.16/0.42  (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.16/0.42  (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.16/0.42  (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.16/0.42  (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.16/0.42  (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.16/0.42  (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.16/0.42  (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.16/0.42  (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.16/0.42  (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.16/0.42  (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.16/0.42  (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.16/0.42  (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.16/0.42  (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.16/0.42  (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.16/0.42  (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.16/0.42  (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.16/0.42  (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.16/0.42  (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.16/0.42  (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.16/0.42  (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.16/0.42  (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.16/0.42  (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.42  (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.16/0.42  (assert (@ tptp.mreflexive tptp.rel_s4))
% 35.51/35.79  (assert (@ tptp.mtransitive tptp.rel_s4))
% 35.51/35.79  (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 35.51/35.79  (declare-fun tptp.teach (tptp.mu tptp.mu $$unsorted) Bool)
% 35.51/35.79  (declare-fun tptp.sue () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.sue) V)))
% 35.51/35.79  (declare-fun tptp.mary () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.mary) V)))
% 35.51/35.79  (declare-fun tptp.math () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.math) V)))
% 35.51/35.79  (declare-fun tptp.john () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.john) V)))
% 35.51/35.79  (declare-fun tptp.cs () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.cs) V)))
% 35.51/35.79  (declare-fun tptp.psych () tptp.mu)
% 35.51/35.79  (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.psych) V)))
% 35.51/35.79  (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.mand (@ (@ tptp.teach tptp.john) tptp.math)) (@ (@ tptp.mand (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.teach X) tptp.cs) __flatten_var_0)))) (@ (@ tptp.mand (@ (@ tptp.teach tptp.mary) tptp.psych)) (@ (@ tptp.teach tptp.sue) tptp.psych)))))))
% 35.51/35.79  (assert (not (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.teach X))) (@ (@ (@ tptp.mand (@ _let_1 tptp.psych)) (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_1 tptp.cs)))) __flatten_var_0)))))))
% 35.51/35.79  (set-info :filename cvc5---1.0.5_30864)
% 35.51/35.79  (check-sat-assuming ( true ))
% 35.51/35.79  ------- get file name : TPTP file name is KRS277^7
% 35.51/35.79  ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30864.smt2...
% 35.51/35.79  --- Run --ho-elim --full-saturate-quant at 10...
% 35.51/35.79  --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 35.51/35.79  --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 35.51/35.79  --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.51/35.79  --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 35.51/35.79  % SZS status CounterSatisfiable for KRS277^7
% 35.51/35.79  % cvc5---1.0.5 exiting
% 35.51/35.79  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------