TSTP Solution File: SYN036^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN036^7 : TPTP v8.1.2. Bugfixed v7.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 : Fri Sep 1 02:00:56 EDT 2023
% Result : CounterSatisfiable 37.63s 38.00s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN036^7 : TPTP v8.1.2. Bugfixed v7.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 22:18:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : SYN036^7 : TPTP v8.1.2. Bugfixed v7.1.0.
% 0.21/0.51 % Domain : Syntactic
% 0.21/0.51 % Problem : Andrews Challenge Problem
% 0.21/0.51 % Version : [Ben12] axioms.
% 0.21/0.51 % English :
% 0.21/0.51
% 0.21/0.51 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.21/0.51 % : [And86] Andrews (1986), An Introduction to Mathematical Logic
% 0.21/0.51 % : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch
% 0.21/0.51 % : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.21/0.51 % : [Pel88] Pelletier (1988), Errata
% 0.21/0.51 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.21/0.51 % Source : [Ben12]
% 0.21/0.51 % Names : s4-cumul-GSY036+1 [Ben12]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % Rating : 1.00 v7.1.0
% 0.21/0.51 % Syntax : Number of formulae : 75 ( 33 unt; 38 typ; 32 def)
% 0.21/0.51 % Number of atoms : 412 ( 36 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 306 ( 11 avg)
% 0.21/0.51 % Number of connectives : 515 ( 5 ~; 5 |; 9 &; 486 @)
% 0.21/0.51 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 24 ( 2 avg)
% 0.21/0.51 % Number of types : 3 ( 1 usr)
% 0.21/0.51 % Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 45 ( 43 usr; 7 con; 0-3 aty)
% 0.21/0.51 % Number of variables : 138 ( 97 ^; 34 !; 7 ?; 138 :)
% 0.21/0.51 % SPC : TH0_THM_EQU_NAR
% 0.21/0.51
% 0.21/0.51 % Comments : Goedel translation of SYN036+1
% 0.21/0.51 % Bugfixes : Reordered includes to get signature of mnot before use
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----Include axioms for Modal logic S4 under cumulative domains
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----Declaration of additional base type mu
% 0.21/0.51 thf(mu_type,type,
% 0.21/0.51 mu: $tType ).
% 0.21/0.51
% 0.21/0.51 %----Equality
% 0.21/0.51 thf(qmltpeq_type,type,
% 0.21/0.51 qmltpeq: mu > mu > $i > $o ).
% 0.21/0.51
% 0.21/0.51 % originale Definition
% 0.21/0.51 %thf(qmltpeq,definition,
% 0.21/0.51 % ( qmltpeq
% 0.21/0.51 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.21/0.51
% 0.21/0.51 % erweiterte Leibnitz-Definition
% 0.21/0.51 %thf(qmltpeq,definition,
% 0.21/0.51 % ( qmltpeq
% 0.21/0.51 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.21/0.51
% 0.21/0.51 % Leibnitz-Definition
% 0.21/0.51 %thf(qmltpeq,definition,
% 0.21/0.51 % ( qmltpeq
% 0.21/0.51 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.21/0.51
% 0.21/0.51 thf(meq_prop_type,type,
% 0.21/0.51 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(meq_prop,definition,
% 0.21/0.51 ( meq_prop
% 0.21/0.51 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.21/0.51 ( ( X @ W )
% 0.21/0.51 = ( Y @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Modal operators not, or, box, Pi
% 0.21/0.51 thf(mnot_type,type,
% 0.21/0.51 mnot: ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mnot,definition,
% 0.21/0.51 ( mnot
% 0.21/0.51 = ( ^ [Phi: $i > $o,W: $i] :
% 0.21/0.51 ~ ( Phi @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mor_type,type,
% 0.21/0.51 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mor,definition,
% 0.21/0.51 ( mor
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.21/0.51 ( ( Phi @ W )
% 0.21/0.51 | ( Psi @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mbox_type,type,
% 0.21/0.51 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mbox,definition,
% 0.21/0.51 ( mbox
% 0.21/0.51 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.21/0.51 ! [V: $i] :
% 0.21/0.51 ( ~ ( R @ W @ V )
% 0.21/0.51 | ( Phi @ V ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mforall_prop_type,type,
% 0.21/0.51 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mforall_prop,definition,
% 0.21/0.51 ( mforall_prop
% 0.21/0.51 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.21/0.51 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Further modal operators
% 0.21/0.51 thf(mtrue_type,type,
% 0.21/0.51 mtrue: $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mtrue,definition,
% 0.21/0.51 ( mtrue
% 0.21/0.51 = ( ^ [W: $i] : $true ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mfalse_type,type,
% 0.21/0.51 mfalse: $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mfalse,definition,
% 0.21/0.51 ( mfalse
% 0.21/0.51 = ( mnot @ mtrue ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mand_type,type,
% 0.21/0.51 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mand,definition,
% 0.21/0.51 ( mand
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mimplies_type,type,
% 0.21/0.51 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mimplies,definition,
% 0.21/0.51 ( mimplies
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mimplied_type,type,
% 0.21/0.51 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mimplied,definition,
% 0.21/0.51 ( mimplied
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mequiv_type,type,
% 0.21/0.51 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mequiv,definition,
% 0.21/0.51 ( mequiv
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mxor_type,type,
% 0.21/0.51 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mxor,definition,
% 0.21/0.51 ( mxor
% 0.21/0.51 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mdia_type,type,
% 0.21/0.51 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mdia,definition,
% 0.21/0.51 ( mdia
% 0.21/0.51 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %--- (new for cumulative)
% 0.21/0.51 %---Declaration of existence predicate for simulating cumulative domain
% 0.21/0.51 thf(exists_in_world_type,type,
% 0.21/0.51 exists_in_world: mu > $i > $o ).
% 0.21/0.51
% 0.21/0.51 %----The domains are non-empty
% 0.21/0.51 thf(nonempty_ax,axiom,
% 0.21/0.51 ! [V: $i] :
% 0.21/0.51 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.21/0.51
% 0.21/0.51 thf(mforall_ind_type,type,
% 0.21/0.51 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 %--- (new for cumulative)
% 0.21/0.51 thf(mforall_ind,definition,
% 0.21/0.51 ( mforall_ind
% 0.21/0.51 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.21/0.51 ! [X: mu] :
% 0.21/0.51 ( ( exists_in_world @ X @ W )
% 0.21/0.51 => ( Phi @ X @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %thf(mforall_ind,definition,
% 0.21/0.51 % ( mforall_ind
% 0.21/0.51 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.21/0.51 % ! [X: mu] :
% 0.21/0.51 % ( Phi @ X @ W ) ) )).
% 0.21/0.51
% 0.21/0.51 thf(mexists_ind_type,type,
% 0.21/0.51 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mexists_ind,definition,
% 0.21/0.51 ( mexists_ind
% 0.21/0.51 = ( ^ [Phi: mu > $i > $o] :
% 0.21/0.51 ( mnot
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mexists_prop_type,type,
% 0.21/0.51 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mexists_prop,definition,
% 0.21/0.51 ( mexists_prop
% 0.21/0.51 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.21/0.51 ( mnot
% 0.21/0.51 @ ( mforall_prop
% 0.21/0.51 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of properties of accessibility relations
% 0.21/0.51 thf(mreflexive_type,type,
% 0.21/0.51 mreflexive: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mreflexive,definition,
% 0.21/0.51 ( mreflexive
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(msymmetric_type,type,
% 0.21/0.51 msymmetric: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(msymmetric,definition,
% 0.21/0.51 ( msymmetric
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i] :
% 0.21/0.51 ( ( R @ S @ T )
% 0.21/0.51 => ( R @ T @ S ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mserial_type,type,
% 0.21/0.51 mserial: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mserial,definition,
% 0.21/0.51 ( mserial
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i] :
% 0.21/0.51 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mtransitive_type,type,
% 0.21/0.51 mtransitive: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mtransitive,definition,
% 0.21/0.51 ( mtransitive
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( ( R @ S @ T )
% 0.21/0.51 & ( R @ T @ U ) )
% 0.21/0.51 => ( R @ S @ U ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(meuclidean_type,type,
% 0.21/0.51 meuclidean: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(meuclidean,definition,
% 0.21/0.51 ( meuclidean
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( ( R @ S @ T )
% 0.21/0.51 & ( R @ S @ U ) )
% 0.21/0.51 => ( R @ T @ U ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mpartially_functional_type,type,
% 0.21/0.51 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mpartially_functional,definition,
% 0.21/0.51 ( mpartially_functional
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( ( R @ S @ T )
% 0.21/0.51 & ( R @ S @ U ) )
% 0.21/0.51 => ( T = U ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mfunctional_type,type,
% 0.21/0.51 mfunctional: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mfunctional,definition,
% 0.21/0.51 ( mfunctional
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i] :
% 0.21/0.51 ? [T: $i] :
% 0.21/0.51 ( ( R @ S @ T )
% 0.21/0.51 & ! [U: $i] :
% 0.21/0.51 ( ( R @ S @ U )
% 0.21/0.51 => ( T = U ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_dense_type,type,
% 0.21/0.51 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_dense,definition,
% 0.21/0.51 ( mweakly_dense
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( R @ S @ T )
% 0.21/0.51 => ? [U: $i] :
% 0.21/0.51 ( ( R @ S @ U )
% 0.21/0.51 & ( R @ U @ T ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_connected_type,type,
% 0.21/0.51 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_connected,definition,
% 0.21/0.51 ( mweakly_connected
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( ( R @ S @ T )
% 0.21/0.51 & ( R @ S @ U ) )
% 0.21/0.51 => ( ( R @ T @ U )
% 0.21/0.51 | ( T = U )
% 0.21/0.51 | ( R @ U @ T ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_directed_type,type,
% 0.21/0.51 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mweakly_directed,definition,
% 0.21/0.51 ( mweakly_directed
% 0.21/0.51 = ( ^ [R: $i > $i > $o] :
% 0.21/0.51 ! [S: $i,T: $i,U: $i] :
% 0.21/0.51 ( ( ( R @ S @ T )
% 0.21/0.51 & ( R @ S @ U ) )
% 0.21/0.51 => ? [V: $i] :
% 0.21/0.51 ( ( R @ T @ V )
% 0.21/0.51 & ( R @ U @ V ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of validity
% 0.21/0.51 thf(mvalid_type,type,
% 0.21/0.51 mvalid: ( $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mvalid,definition,
% 0.21/0.51 ( mvalid
% 0.21/0.51 = ( ^ [Phi: $i > $o] :
% 0.21/0.51 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of satisfiability
% 0.21/0.51 thf(msatisfiable_type,type,
% 0.21/0.51 msatisfiable: ( $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(msatisfiable,definition,
% 0.21/0.51 ( msatisfiable
% 0.21/0.51 = ( ^ [Phi: $i > $o] :
% 0.21/0.51 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of countersatisfiability
% 0.21/0.51 thf(mcountersatisfiable_type,type,
% 0.21/0.51 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mcountersatisfiable,definition,
% 0.21/0.51 ( mcountersatisfiable
% 0.21/0.51 = ( ^ [Phi: $i > $o] :
% 0.21/0.51 ? [W: $i] :
% 0.21/0.51 ~ ( Phi @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----Definition of invalidity
% 0.21/0.51 thf(minvalid_type,type,
% 0.21/0.51 minvalid: ( $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(minvalid,definition,
% 0.21/0.51 ( minvalid
% 0.21/0.51 = ( ^ [Phi: $i > $o] :
% 0.21/0.51 ! [W: $i] :
% 0.21/0.51 ~ ( Phi @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----We reserve an accessibility relation constant rel_s4
% 0.21/0.51 thf(rel_s4_type,type,
% 0.21/0.51 rel_s4: $i > $i > $o ).
% 0.21/0.51
% 0.21/0.51 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.21/0.51 thf(mbox_s4_type,type,
% 0.21/0.51 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mbox_s4,definition,
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 = ( ^ [Phi: $i > $o,W: $i] :
% 0.21/0.51 ! [V: $i] :
% 0.21/0.51 ( ~ ( rel_s4 @ W @ V )
% 0.21/0.51 | ( Phi @ V ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mdia_s4_type,type,
% 0.21/0.51 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mdia_s4,definition,
% 0.21/0.51 ( mdia_s4
% 0.21/0.51 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %----We have now two options for stating the B conditions:
% 0.21/0.51 %----We can (i) directly formulate conditions for the accessibility relation
% 0.21/0.51 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.21/0.51 thf(a1,axiom,
% 0.21/0.51 mreflexive @ rel_s4 ).
% 0.21/0.51
% 0.21/0.51 thf(a2,axiom,
% 0.21/0.51 mtransitive @ rel_s4 ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 thf(cumulative_ax,axiom,
% 0.21/0.51 ! [X: mu,V: $i,W: $i] :
% 0.21/0.51 ( ( ( exists_in_world @ X @ V )
% 0.21/0.51 & ( rel_s4 @ V @ W ) )
% 0.21/0.51 => ( exists_in_world @ X @ W ) ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 thf(big_q_type,type,
% 0.21/0.51 big_q: mu > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(big_p_type,type,
% 0.21/0.51 big_p: mu > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(pel34,conjecture,
% 0.21/0.51 ( mvalid
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X1: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X1: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X1: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W1: mu] : ( mbox_s4 @ ( big_p @ W1 ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U1: mu] : ( mbox_s4 @ ( big_p @ U1 ) ) ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X1: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y1: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ X1 ) ) @ ( mbox_s4 @ ( big_q @ Y1 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_q @ Y1 ) ) @ ( mbox_s4 @ ( big_q @ X1 ) ) ) ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mand
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) ) ) )
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mimplies
% 0.21/0.51 @ ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [W: mu] : ( mbox_s4 @ ( big_q @ W ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [U: mu] : ( mbox_s4 @ ( big_q @ U ) ) ) ) ) )
% 0.21/0.51 @ ( mexists_ind
% 0.21/0.51 @ ^ [X: mu] :
% 0.21/0.51 ( mbox_s4
% 0.21/0.51 @ ( mforall_ind
% 0.21/0.51 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ X ) ) @ ( mbox_s4 @ ( big_p @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ Y ) ) @ ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.DO3nvSBDpG/cvc5---1.0.5_13712.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.mu 0)
% 0.21/0.53 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.21/0.53 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.21/0.53 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.21/0.53 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.21/0.53 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.21/0.53 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.21/0.53 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.21/0.53 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.21/0.53 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.21/0.53 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.21/0.53 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.21/0.53 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.21/0.53 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.21/0.53 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.21/0.53 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.21/0.53 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.21/0.53 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.21/0.53 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.21/0.53 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.21/0.53 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.21/0.53 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.21/0.53 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.21/0.53 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.21/0.53 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.53 (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)))))))))
% 0.21/0.53 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.21/0.53 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.21/0.53 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.21/0.53 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.53 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.21/0.53 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.21/0.53 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.21/0.53 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.21/0.53 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.21/0.53 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.21/0.53 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.21/0.53 (declare-fun tptp.big_q (tptp.mu $$unsorted) Bool)
% 0.21/0.53 (declare-fun tptp.big_p (tptp.mu $$unsorted) Bool)
% 0.21/0.53 (assert (not (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_p X)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_p Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0))))))) (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_p X)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_p Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((X1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y1 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_q X1)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_q Y1)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0))))))) (@ tptp.mexists_ind (lambda ((X1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y1 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_q X1)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_q Y1)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((X1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y1 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_q X1)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_q Y1)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p W1)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_p U1)) __flatten_var_0))))))) (@ tptp.mexists_ind (lambda ((X1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y1 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_q X1)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_q Y1)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_p X)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_p Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0)))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q W)) __flatten_var_0))))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.big_q U)) __flatten_var_0))))))) (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ tptp.big_p X)))) (let ((_let_2 (@ tptp.mbox_s4 (@ tptp.big_p Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))))))))
% 37.63/38.00 (set-info :filename cvc5---1.0.5_13712)
% 37.63/38.00 (check-sat-assuming ( true ))
% 37.63/38.00 ------- get file name : TPTP file name is SYN036^7
% 37.63/38.00 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13712.smt2...
% 37.63/38.00 --- Run --ho-elim --full-saturate-quant at 10...
% 37.63/38.00 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 37.63/38.00 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 37.63/38.00 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 37.63/38.00 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 37.63/38.00 % SZS status CounterSatisfiable for SYN036^7
% 37.63/38.00 % cvc5---1.0.5 exiting
% 37.63/38.00 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------