TSTP Solution File: AGT027^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : AGT027^2 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 : Wed Aug 30 15:52:57 EDT 2023
% Result : Timeout 299.99s 300.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : AGT027^2 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Aug 27 17:25:23 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : AGT027^2 : TPTP v8.1.2. Released v5.2.0.
% 0.22/0.52 % Domain : Agents
% 0.22/0.52 % Problem : Two different degrees of belief
% 0.22/0.52 % Version : [Ben11] axioms : Reduced > Complete.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% 0.22/0.52 % : [Ben11] Benzmueller (2011), Combining and Automating Classical
% 0.22/0.52 % Source : [Ben11]
% 0.22/0.52 % Names : Ex_10_1_KI4s [Ben11]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.62 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.78 v7.2.0, 0.75 .0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 .0, 0.57 v6.0.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0
% 0.22/0.52 % Syntax : Number of formulae : 81 ( 31 unt; 40 typ; 31 def)
% 0.22/0.52 % Number of atoms : 171 ( 36 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 9 ( 4 avg)
% 0.22/0.52 % Number of connectives : 211 ( 4 ~; 4 |; 8 &; 187 @)
% 0.22/0.52 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 10 ( 3 avg)
% 0.22/0.52 % Number of types : 3 ( 1 usr)
% 0.22/0.52 % Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 49 ( 47 usr; 11 con; 0-3 aty)
% 0.22/0.52 % Number of variables : 93 ( 58 ^; 29 !; 6 ?; 93 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments :
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----Include embedding of quantified multimodal logic in simple type theory
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----Declaration of additional base type mu
% 0.22/0.52 thf(mu_type,type,
% 0.22/0.52 mu: $tType ).
% 0.22/0.52
% 0.22/0.52 %----Equality
% 0.22/0.52 thf(meq_ind_type,type,
% 0.22/0.52 meq_ind: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(meq_ind,definition,
% 0.22/0.52 ( meq_ind
% 0.22/0.52 = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(meq_prop_type,type,
% 0.22/0.52 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(meq_prop,definition,
% 0.22/0.52 ( meq_prop
% 0.22/0.52 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.22/0.52 ( ( X @ W )
% 0.22/0.52 = ( Y @ W ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Modal operators not, or, box, Pi
% 0.22/0.52 thf(mnot_type,type,
% 0.22/0.52 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mnot,definition,
% 0.22/0.52 ( mnot
% 0.22/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.52 ~ ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mor_type,type,
% 0.22/0.52 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mor,definition,
% 0.22/0.52 ( mor
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.22/0.52 ( ( Phi @ W )
% 0.22/0.52 | ( Psi @ W ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mand_type,type,
% 0.22/0.52 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mand,definition,
% 0.22/0.52 ( mand
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mimplies_type,type,
% 0.22/0.52 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mimplies,definition,
% 0.22/0.52 ( mimplies
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mimplied_type,type,
% 0.22/0.52 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mimplied,definition,
% 0.22/0.52 ( mimplied
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mequiv_type,type,
% 0.22/0.52 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mequiv,definition,
% 0.22/0.52 ( mequiv
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mxor_type,type,
% 0.22/0.52 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mxor,definition,
% 0.22/0.52 ( mxor
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Universal quantification: individuals
% 0.22/0.52 thf(mforall_ind_type,type,
% 0.22/0.52 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_ind,definition,
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.52 ! [X: mu] : ( Phi @ X @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_prop_type,type,
% 0.22/0.52 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_prop,definition,
% 0.22/0.52 ( mforall_prop
% 0.22/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.22/0.52 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_ind_type,type,
% 0.22/0.52 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_ind,definition,
% 0.22/0.52 ( mexists_ind
% 0.22/0.52 = ( ^ [Phi: mu > $i > $o] :
% 0.22/0.52 ( mnot
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_prop_type,type,
% 0.22/0.52 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_prop,definition,
% 0.22/0.52 ( mexists_prop
% 0.22/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.22/0.52 ( mnot
% 0.22/0.52 @ ( mforall_prop
% 0.22/0.52 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mtrue_type,type,
% 0.22/0.52 mtrue: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mtrue,definition,
% 0.22/0.52 ( mtrue
% 0.22/0.52 = ( ^ [W: $i] : $true ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mfalse_type,type,
% 0.22/0.52 mfalse: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mfalse,definition,
% 0.22/0.52 ( mfalse
% 0.22/0.52 = ( mnot @ mtrue ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mbox_type,type,
% 0.22/0.52 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mbox,definition,
% 0.22/0.52 ( mbox
% 0.22/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.22/0.52 ! [V: $i] :
% 0.22/0.52 ( ~ ( R @ W @ V )
% 0.22/0.52 | ( Phi @ V ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mdia_type,type,
% 0.22/0.52 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mdia,definition,
% 0.22/0.52 ( mdia
% 0.22/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of properties of accessibility relations
% 0.22/0.52 thf(mreflexive_type,type,
% 0.22/0.52 mreflexive: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mreflexive,definition,
% 0.22/0.52 ( mreflexive
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(msymmetric_type,type,
% 0.22/0.52 msymmetric: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(msymmetric,definition,
% 0.22/0.52 ( msymmetric
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 => ( R @ T @ S ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mserial_type,type,
% 0.22/0.52 mserial: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mserial,definition,
% 0.22/0.52 ( mserial
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] :
% 0.22/0.52 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mtransitive_type,type,
% 0.22/0.52 mtransitive: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mtransitive,definition,
% 0.22/0.52 ( mtransitive
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ T @ U ) )
% 0.22/0.52 => ( R @ S @ U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(meuclidean_type,type,
% 0.22/0.52 meuclidean: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(meuclidean,definition,
% 0.22/0.52 ( meuclidean
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( R @ T @ U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mpartially_functional_type,type,
% 0.22/0.52 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mpartially_functional,definition,
% 0.22/0.52 ( mpartially_functional
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( T = U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mfunctional_type,type,
% 0.22/0.52 mfunctional: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mfunctional,definition,
% 0.22/0.52 ( mfunctional
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] :
% 0.22/0.52 ? [T: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 & ! [U: $i] :
% 0.22/0.52 ( ( R @ S @ U )
% 0.22/0.52 => ( T = U ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_dense_type,type,
% 0.22/0.52 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_dense,definition,
% 0.22/0.52 ( mweakly_dense
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 => ? [U: $i] :
% 0.22/0.52 ( ( R @ S @ U )
% 0.22/0.52 & ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_connected_type,type,
% 0.22/0.52 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_connected,definition,
% 0.22/0.52 ( mweakly_connected
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( ( R @ T @ U )
% 0.22/0.52 | ( T = U )
% 0.22/0.52 | ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_directed_type,type,
% 0.22/0.52 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_directed,definition,
% 0.22/0.52 ( mweakly_directed
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ? [V: $i] :
% 0.22/0.52 ( ( R @ T @ V )
% 0.22/0.52 & ( R @ U @ V ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of validity
% 0.22/0.52 thf(mvalid_type,type,
% 0.22/0.52 mvalid: ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mvalid,definition,
% 0.22/0.52 ( mvalid
% 0.22/0.52 = ( ^ [Phi: $i > $o] :
% 0.22/0.52 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of invalidity
% 0.22/0.54 thf(minvalid_type,type,
% 0.22/0.54 minvalid: ( $i > $o ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(minvalid,definition,
% 0.22/0.54 ( minvalid
% 0.22/0.54 = ( ^ [Phi: $i > $o] :
% 0.22/0.54 ! [W: $i] :
% 0.22/0.54 ~ ( Phi @ W ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %----Definition of satisfiability
% 0.22/0.54 thf(msatisfiable_type,type,
% 0.22/0.54 msatisfiable: ( $i > $o ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(msatisfiable,definition,
% 0.22/0.54 ( msatisfiable
% 0.22/0.54 = ( ^ [Phi: $i > $o] :
% 0.22/0.54 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %----Definition of countersatisfiability
% 0.22/0.54 thf(mcountersatisfiable_type,type,
% 0.22/0.54 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.54
% 0.22/0.54 thf(mcountersatisfiable,definition,
% 0.22/0.54 ( mcountersatisfiable
% 0.22/0.54 = ( ^ [Phi: $i > $o] :
% 0.22/0.54 ? [W: $i] :
% 0.22/0.54 ~ ( Phi @ W ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 thf(a1,type,
% 0.22/0.54 a1: $i > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(a2,type,
% 0.22/0.54 a2: $i > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(a,type,
% 0.22/0.54 a: mu ).
% 0.22/0.54
% 0.22/0.54 thf(tom,type,
% 0.22/0.54 tom: mu ).
% 0.22/0.54
% 0.22/0.54 thf(p,type,
% 0.22/0.54 p: mu > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(q,type,
% 0.22/0.54 q: mu > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(r,type,
% 0.22/0.54 r: mu > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(s,type,
% 0.22/0.54 s: mu > $i > $o ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_a1,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( mdia @ a2 @ ( q @ X ) ) @ ( p @ X ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_a2,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mand @ ( r @ X ) @ ( s @ X ) ) @ ( q @ X ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_a3,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( s @ X ) @ ( mbox @ a1 @ ( r @ X ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_a4,axiom,
% 0.22/0.54 mvalid @ ( mdia @ a1 @ ( s @ a ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_I_for_a2_a1,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_prop
% 0.22/0.54 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ Phi ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_4s_for_a1_a1,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_prop
% 0.22/0.54 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a1 @ Phi ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_4s_for_a1_a2,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_prop
% 0.22/0.54 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a1 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a1 @ Phi ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_4s_for_a2_a1,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_prop
% 0.22/0.54 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a1 @ ( mbox @ a2 @ Phi ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(axiom_4s_for_a2_a2,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_prop
% 0.22/0.54 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a2 @ Phi ) @ ( mbox @ a2 @ ( mbox @ a2 @ Phi ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(conj,conjecture,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mexists_ind
% 0.22/0.54 @ ^ [X: mu] : ( mbox @ a1 @ ( p @ X ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DHKuR5YZkl/cvc5---1.0.5_31080.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.mu 0)
% 0.22/0.54 (declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.22/0.54 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.22/0.54 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.22/0.54 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.22/0.54 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.22/0.54 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (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 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.22/0.54 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.22/0.54 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.22/0.54 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.22/0.54 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.22/0.54 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.22/0.54 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.22/0.54 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.meuclidean (lambda ((R (-> $$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)))))))
% 0.22/0.54 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.22/0.54 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (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))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.22/0.54 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.54 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.54 (declare-fun tptp.a1 ($$unsorted $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.a2 ($$unsorted $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.a () tptp.mu)
% 0.22/0.54 (declare-fun tptp.tom () tptp.mu)
% 0.22/0.54 (declare-fun tptp.p (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.q (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.r (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.s (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.a2) (@ (@ tptp.mimplies (@ (@ tptp.mdia tptp.a2) (@ tptp.q X))) (@ tptp.p X))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.a1) (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.r X)) (@ tptp.s X))) (@ tptp.q X))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.a1))) (@ (@ _let_1 (@ (@ tptp.mimplies (@ tptp.s X)) (@ _let_1 (@ tptp.r X)))) __flatten_var_0))))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ (@ tptp.mdia tptp.a1) (@ tptp.s tptp.a))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.a2) Phi)) (@ (@ tptp.mbox tptp.a1) Phi)) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.a1))) (let ((_let_2 (@ _let_1 Phi))) (@ (@ (@ tptp.mimplies _let_2) (@ _let_1 _let_2)) __flatten_var_0)))))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a1) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a2) _let_1)) __flatten_var_0))))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a2) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a1) _let_1)) __flatten_var_0))))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 31244 Alarm clock ( read result; case "$result" in
% 299.99/300.21 unsat)
% 299.99/300.21 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.99/300.21 ;;
% 299.99/300.21 sat)
% 299.99/300.21 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.99/300.21 ;;
% 299.99/300.21 esac; exit 1 )
% 299.99/300.21 Alarm clock
% 299.99/300.21 % cvc5---1.0.5 exiting
% 299.99/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------