TSTP Solution File: ALG022^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG022^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 16:07:54 EDT 2023
% Result : Timeout 299.67s 300.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : ALG022^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.17 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n021.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Mon Aug 28 05:08:43 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 % File : ALG022^7 : TPTP v8.1.2. Released v5.5.0.
% 0.25/0.56 % Domain : General Algebra
% 0.25/0.56 % Problem : Groups 4: REPRESENTATIVES-SATISFY-PROPS-PROBLEM-2
% 0.25/0.56 % Version : [Ben12] axioms.
% 0.25/0.56 % English :
% 0.25/0.56
% 0.25/0.56 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.25/0.56 % : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% 0.25/0.56 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.25/0.56 % Source : [Ben12]
% 0.25/0.56 % Names : s4-cumul-GAL022+1 [Ben12]
% 0.25/0.56
% 0.25/0.56 % Status : Theorem
% 0.25/0.56 % Rating : 1.00 v5.5.0
% 0.25/0.56 % Syntax : Number of formulae : 97 ( 40 unt; 43 typ; 32 def)
% 0.25/0.56 % Number of atoms : 817 ( 36 equ; 0 cnn)
% 0.25/0.56 % Maximal formula atoms : 542 ( 15 avg)
% 0.25/0.56 % Number of connectives : 2068 ( 5 ~; 5 |; 9 &;2039 @)
% 0.25/0.56 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.25/0.56 % Maximal formula depth : 112 ( 6 avg)
% 0.25/0.56 % Number of types : 3 ( 1 usr)
% 0.25/0.56 % Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% 0.25/0.56 % Number of symbols : 53 ( 51 usr; 15 con; 0-3 aty)
% 0.25/0.56 % Number of variables : 114 ( 63 ^; 44 !; 7 ?; 114 :)
% 0.25/0.56 % SPC : TH0_THM_EQU_NAR
% 0.25/0.56
% 0.25/0.56 % Comments : Goedel translation of ALG022+1
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %----Include axioms for Modal logic S4 under cumulative domains
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %----Declaration of additional base type mu
% 0.25/0.56 thf(mu_type,type,
% 0.25/0.56 mu: $tType ).
% 0.25/0.56
% 0.25/0.56 %----Equality
% 0.25/0.56 thf(qmltpeq_type,type,
% 0.25/0.56 qmltpeq: mu > mu > $i > $o ).
% 0.25/0.56
% 0.25/0.56 % originale Definition
% 0.25/0.56 %thf(qmltpeq,definition,
% 0.25/0.56 % ( qmltpeq
% 0.25/0.56 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.25/0.56
% 0.25/0.56 % erweiterte Leibnitz-Definition
% 0.25/0.56 %thf(qmltpeq,definition,
% 0.25/0.56 % ( qmltpeq
% 0.25/0.56 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.25/0.56
% 0.25/0.56 % Leibnitz-Definition
% 0.25/0.56 %thf(qmltpeq,definition,
% 0.25/0.56 % ( qmltpeq
% 0.25/0.56 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.25/0.56
% 0.25/0.56 thf(meq_prop_type,type,
% 0.25/0.56 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(meq_prop,definition,
% 0.25/0.56 ( meq_prop
% 0.25/0.56 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.25/0.56 ( ( X @ W )
% 0.25/0.56 = ( Y @ W ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Modal operators not, or, box, Pi
% 0.25/0.56 thf(mnot_type,type,
% 0.25/0.56 mnot: ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mnot,definition,
% 0.25/0.56 ( mnot
% 0.25/0.56 = ( ^ [Phi: $i > $o,W: $i] :
% 0.25/0.56 ~ ( Phi @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mor_type,type,
% 0.25/0.56 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mor,definition,
% 0.25/0.56 ( mor
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.25/0.56 ( ( Phi @ W )
% 0.25/0.56 | ( Psi @ W ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mbox_type,type,
% 0.25/0.56 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mbox,definition,
% 0.25/0.56 ( mbox
% 0.25/0.56 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.25/0.56 ! [V: $i] :
% 0.25/0.56 ( ~ ( R @ W @ V )
% 0.25/0.56 | ( Phi @ V ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mforall_prop_type,type,
% 0.25/0.56 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mforall_prop,definition,
% 0.25/0.56 ( mforall_prop
% 0.25/0.56 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.25/0.56 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Further modal operators
% 0.25/0.56 thf(mtrue_type,type,
% 0.25/0.56 mtrue: $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mtrue,definition,
% 0.25/0.56 ( mtrue
% 0.25/0.56 = ( ^ [W: $i] : $true ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mfalse_type,type,
% 0.25/0.56 mfalse: $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mfalse,definition,
% 0.25/0.56 ( mfalse
% 0.25/0.56 = ( mnot @ mtrue ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mand_type,type,
% 0.25/0.56 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mand,definition,
% 0.25/0.56 ( mand
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mimplies_type,type,
% 0.25/0.56 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mimplies,definition,
% 0.25/0.56 ( mimplies
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mimplied_type,type,
% 0.25/0.56 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mimplied,definition,
% 0.25/0.56 ( mimplied
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mequiv_type,type,
% 0.25/0.56 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mequiv,definition,
% 0.25/0.56 ( mequiv
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mxor_type,type,
% 0.25/0.56 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mxor,definition,
% 0.25/0.56 ( mxor
% 0.25/0.56 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mdia_type,type,
% 0.25/0.56 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mdia,definition,
% 0.25/0.56 ( mdia
% 0.25/0.56 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %--- (new for cumulative)
% 0.25/0.56 %---Declaration of existence predicate for simulating cumulative domain
% 0.25/0.56 thf(exists_in_world_type,type,
% 0.25/0.56 exists_in_world: mu > $i > $o ).
% 0.25/0.56
% 0.25/0.56 %----The domains are non-empty
% 0.25/0.56 thf(nonempty_ax,axiom,
% 0.25/0.56 ! [V: $i] :
% 0.25/0.56 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(mforall_ind_type,type,
% 0.25/0.56 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 %--- (new for cumulative)
% 0.25/0.56 thf(mforall_ind,definition,
% 0.25/0.56 ( mforall_ind
% 0.25/0.56 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.25/0.56 ! [X: mu] :
% 0.25/0.56 ( ( exists_in_world @ X @ W )
% 0.25/0.56 => ( Phi @ X @ W ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %thf(mforall_ind,definition,
% 0.25/0.56 % ( mforall_ind
% 0.25/0.56 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.25/0.56 % ! [X: mu] :
% 0.25/0.56 % ( Phi @ X @ W ) ) )).
% 0.25/0.56
% 0.25/0.56 thf(mexists_ind_type,type,
% 0.25/0.56 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mexists_ind,definition,
% 0.25/0.56 ( mexists_ind
% 0.25/0.56 = ( ^ [Phi: mu > $i > $o] :
% 0.25/0.56 ( mnot
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mexists_prop_type,type,
% 0.25/0.56 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mexists_prop,definition,
% 0.25/0.56 ( mexists_prop
% 0.25/0.56 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.25/0.56 ( mnot
% 0.25/0.56 @ ( mforall_prop
% 0.25/0.56 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Definition of properties of accessibility relations
% 0.25/0.56 thf(mreflexive_type,type,
% 0.25/0.56 mreflexive: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mreflexive,definition,
% 0.25/0.56 ( mreflexive
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(msymmetric_type,type,
% 0.25/0.56 msymmetric: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(msymmetric,definition,
% 0.25/0.56 ( msymmetric
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i] :
% 0.25/0.56 ( ( R @ S @ T )
% 0.25/0.56 => ( R @ T @ S ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mserial_type,type,
% 0.25/0.56 mserial: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mserial,definition,
% 0.25/0.56 ( mserial
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i] :
% 0.25/0.56 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mtransitive_type,type,
% 0.25/0.56 mtransitive: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mtransitive,definition,
% 0.25/0.56 ( mtransitive
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( ( R @ S @ T )
% 0.25/0.56 & ( R @ T @ U ) )
% 0.25/0.56 => ( R @ S @ U ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(meuclidean_type,type,
% 0.25/0.56 meuclidean: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(meuclidean,definition,
% 0.25/0.56 ( meuclidean
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( ( R @ S @ T )
% 0.25/0.56 & ( R @ S @ U ) )
% 0.25/0.56 => ( R @ T @ U ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mpartially_functional_type,type,
% 0.25/0.56 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mpartially_functional,definition,
% 0.25/0.56 ( mpartially_functional
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( ( R @ S @ T )
% 0.25/0.56 & ( R @ S @ U ) )
% 0.25/0.56 => ( T = U ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mfunctional_type,type,
% 0.25/0.56 mfunctional: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mfunctional,definition,
% 0.25/0.56 ( mfunctional
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i] :
% 0.25/0.56 ? [T: $i] :
% 0.25/0.56 ( ( R @ S @ T )
% 0.25/0.56 & ! [U: $i] :
% 0.25/0.56 ( ( R @ S @ U )
% 0.25/0.56 => ( T = U ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_dense_type,type,
% 0.25/0.56 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_dense,definition,
% 0.25/0.56 ( mweakly_dense
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( R @ S @ T )
% 0.25/0.56 => ? [U: $i] :
% 0.25/0.56 ( ( R @ S @ U )
% 0.25/0.56 & ( R @ U @ T ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_connected_type,type,
% 0.25/0.56 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_connected,definition,
% 0.25/0.56 ( mweakly_connected
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( ( R @ S @ T )
% 0.25/0.56 & ( R @ S @ U ) )
% 0.25/0.56 => ( ( R @ T @ U )
% 0.25/0.56 | ( T = U )
% 0.25/0.56 | ( R @ U @ T ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_directed_type,type,
% 0.25/0.56 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mweakly_directed,definition,
% 0.25/0.56 ( mweakly_directed
% 0.25/0.56 = ( ^ [R: $i > $i > $o] :
% 0.25/0.56 ! [S: $i,T: $i,U: $i] :
% 0.25/0.56 ( ( ( R @ S @ T )
% 0.25/0.56 & ( R @ S @ U ) )
% 0.25/0.56 => ? [V: $i] :
% 0.25/0.56 ( ( R @ T @ V )
% 0.25/0.56 & ( R @ U @ V ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Definition of validity
% 0.25/0.56 thf(mvalid_type,type,
% 0.25/0.56 mvalid: ( $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mvalid,definition,
% 0.25/0.56 ( mvalid
% 0.25/0.56 = ( ^ [Phi: $i > $o] :
% 0.25/0.56 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Definition of satisfiability
% 0.25/0.56 thf(msatisfiable_type,type,
% 0.25/0.56 msatisfiable: ( $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(msatisfiable,definition,
% 0.25/0.56 ( msatisfiable
% 0.25/0.56 = ( ^ [Phi: $i > $o] :
% 0.25/0.56 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Definition of countersatisfiability
% 0.25/0.56 thf(mcountersatisfiable_type,type,
% 0.25/0.56 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mcountersatisfiable,definition,
% 0.25/0.56 ( mcountersatisfiable
% 0.25/0.56 = ( ^ [Phi: $i > $o] :
% 0.25/0.56 ? [W: $i] :
% 0.25/0.56 ~ ( Phi @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----Definition of invalidity
% 0.25/0.56 thf(minvalid_type,type,
% 0.25/0.56 minvalid: ( $i > $o ) > $o ).
% 0.25/0.56
% 0.25/0.56 thf(minvalid,definition,
% 0.25/0.56 ( minvalid
% 0.25/0.56 = ( ^ [Phi: $i > $o] :
% 0.25/0.56 ! [W: $i] :
% 0.25/0.56 ~ ( Phi @ W ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %----We reserve an accessibility relation constant rel_s4
% 0.25/0.56 thf(rel_s4_type,type,
% 0.25/0.56 rel_s4: $i > $i > $o ).
% 0.25/0.56
% 0.25/0.56 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.25/0.56 thf(mbox_s4_type,type,
% 0.25/0.56 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mbox_s4,definition,
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 = ( ^ [Phi: $i > $o,W: $i] :
% 0.25/0.56 ! [V: $i] :
% 0.25/0.56 ( ~ ( rel_s4 @ W @ V )
% 0.25/0.56 | ( Phi @ V ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(mdia_s4_type,type,
% 0.25/0.56 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.25/0.56
% 0.25/0.56 thf(mdia_s4,definition,
% 0.25/0.56 ( mdia_s4
% 0.25/0.56 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 %----We have now two options for stating the B conditions:
% 0.25/0.56 %----We can (i) directly formulate conditions for the accessibility relation
% 0.25/0.56 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.25/0.56 thf(a1,axiom,
% 0.25/0.56 mreflexive @ rel_s4 ).
% 0.25/0.56
% 0.25/0.56 thf(a2,axiom,
% 0.25/0.56 mtransitive @ rel_s4 ).
% 0.25/0.56
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 thf(cumulative_ax,axiom,
% 0.25/0.56 ! [X: mu,V: $i,W: $i] :
% 0.25/0.56 ( ( ( exists_in_world @ X @ V )
% 0.25/0.56 & ( rel_s4 @ V @ W ) )
% 0.25/0.56 => ( exists_in_world @ X @ W ) ) ).
% 0.25/0.56
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 %------------------------------------------------------------------------------
% 0.25/0.56 thf(inv_type,type,
% 0.25/0.56 inv: mu > mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_inv_ax,axiom,
% 0.25/0.56 ! [V: $i,V1: mu] : ( exists_in_world @ ( inv @ V1 ) @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(unit_type,type,
% 0.25/0.56 unit: mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_unit_ax,axiom,
% 0.25/0.56 ! [V: $i] : ( exists_in_world @ unit @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(e3_type,type,
% 0.25/0.56 e3: mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_e3_ax,axiom,
% 0.25/0.56 ! [V: $i] : ( exists_in_world @ e3 @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(e2_type,type,
% 0.25/0.56 e2: mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_e2_ax,axiom,
% 0.25/0.56 ! [V: $i] : ( exists_in_world @ e2 @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(e1_type,type,
% 0.25/0.56 e1: mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_e1_ax,axiom,
% 0.25/0.56 ! [V: $i] : ( exists_in_world @ e1 @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(e0_type,type,
% 0.25/0.56 e0: mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_e0_ax,axiom,
% 0.25/0.56 ! [V: $i] : ( exists_in_world @ e0 @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(op_type,type,
% 0.25/0.56 op: mu > mu > mu ).
% 0.25/0.56
% 0.25/0.56 thf(existence_of_op_ax,axiom,
% 0.25/0.56 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( op @ V2 @ V1 ) @ V ) ).
% 0.25/0.56
% 0.25/0.56 thf(reflexivity,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(symmetry,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [X: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(transitivity,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [X: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [Y: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(inv_substitution_1,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [A: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(op_substitution_1,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [A: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [B: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ A @ C ) @ ( op @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(op_substitution_2,axiom,
% 0.25/0.56 ( mvalid
% 0.25/0.56 @ ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [A: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [B: mu] :
% 0.25/0.56 ( mbox_s4
% 0.25/0.56 @ ( mforall_ind
% 0.25/0.56 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ C @ A ) @ ( op @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(ax1,axiom,
% 0.25/0.56 mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e1 @ e3 ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e2 @ e3 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(ax2,axiom,
% 0.25/0.56 mvalid @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(ax3,axiom,
% 0.25/0.56 mvalid @ ( mbox_s4 @ ( qmltpeq @ unit @ e0 ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(ax4,axiom,
% 0.25/0.56 mvalid @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 thf(co1,conjecture,
% 0.25/0.56 mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mor @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e0 ) @ ( op @ e0 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e1 ) @ ( op @ e0 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e2 ) @ ( op @ e0 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e3 ) @ ( op @ e0 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e0 ) @ ( op @ e0 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e1 ) @ ( op @ e0 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e2 ) @ ( op @ e0 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e3 ) @ ( op @ e0 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e0 ) @ ( op @ e0 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e1 ) @ ( op @ e0 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e2 ) @ ( op @ e0 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e3 ) @ ( op @ e0 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e0 ) @ ( op @ e0 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e1 ) @ ( op @ e0 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e2 ) @ ( op @ e0 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e3 ) @ ( op @ e0 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e0 ) @ ( op @ e1 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e1 ) @ ( op @ e1 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e2 ) @ ( op @ e1 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e3 ) @ ( op @ e1 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e0 ) @ ( op @ e1 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e1 ) @ ( op @ e1 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e2 ) @ ( op @ e1 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e3 ) @ ( op @ e1 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e0 ) @ ( op @ e1 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e1 ) @ ( op @ e1 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e2 ) @ ( op @ e1 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e3 ) @ ( op @ e1 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e0 ) @ ( op @ e1 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e1 ) @ ( op @ e1 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e2 ) @ ( op @ e1 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e3 ) @ ( op @ e1 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e0 ) @ ( op @ e2 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e1 ) @ ( op @ e2 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e2 ) @ ( op @ e2 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e3 ) @ ( op @ e2 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e0 ) @ ( op @ e2 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e1 ) @ ( op @ e2 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e2 ) @ ( op @ e2 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e3 ) @ ( op @ e2 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e0 ) @ ( op @ e2 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e1 ) @ ( op @ e2 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e2 ) @ ( op @ e2 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e3 ) @ ( op @ e2 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e0 ) @ ( op @ e2 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e1 ) @ ( op @ e2 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e2 ) @ ( op @ e2 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e3 ) @ ( op @ e2 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e0 ) @ ( op @ e3 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e1 ) @ ( op @ e3 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e2 ) @ ( op @ e3 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e3 ) @ ( op @ e3 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e0 ) @ ( op @ e3 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e1 ) @ ( op @ e3 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e2 ) @ ( op @ e3 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e3 ) @ ( op @ e3 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e0 ) @ ( op @ e3 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e1 ) @ ( op @ e3 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e2 ) @ ( op @ e3 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e3 ) @ ( op @ e3 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e0 ) @ ( op @ e3 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e1 ) @ ( op @ e3 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e2 ) @ ( op @ e3 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ unit @ e0 ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ unit ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ unit @ e1 ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ unit ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ unit @ e2 ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ unit ) @ e2 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ unit @ e3 ) @ e3 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ unit ) @ e3 ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ unit @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ ( inv @ e0 ) ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( inv @ e0 ) @ e0 ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ ( inv @ e1 ) ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( inv @ e1 ) @ e1 ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ ( inv @ e2 ) ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( inv @ e2 ) @ e2 ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ ( inv @ e3 ) ) @ unit ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( inv @ e3 ) @ e3 ) @ unit ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 %------------------------------------------------------------------------------
% 0.25/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YBZm1EX58M/cvc5---1.0.5_10761.p...
% 0.25/0.60 (declare-sort $$unsorted 0)
% 0.25/0.60 (declare-sort tptp.mu 0)
% 0.25/0.60 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.25/0.60 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.25/0.60 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.25/0.60 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.25/0.60 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.25/0.60 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.25/0.60 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.25/0.60 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.25/0.60 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.25/0.60 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.25/0.60 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.25/0.60 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.25/0.60 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.25/0.60 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.25/0.60 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.25/0.60 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.25/0.60 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.25/0.60 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.25/0.60 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.25/0.60 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.25/0.60 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.25/0.60 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.25/0.60 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.25/0.60 (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)))))))))
% 0.25/0.60 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.25/0.60 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.25/0.60 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.25/0.60 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.25/0.60 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.25/0.60 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.25/0.60 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.25/0.60 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.25/0.60 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.25/0.60 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.25/0.60 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.25/0.60 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.25/0.60 (declare-fun tptp.inv (tptp.mu) tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inv V1)) V)))
% 0.25/0.60 (declare-fun tptp.unit () tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.unit) V)))
% 0.25/0.60 (declare-fun tptp.e3 () tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e3) V)))
% 0.25/0.60 (declare-fun tptp.e2 () tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e2) V)))
% 0.25/0.60 (declare-fun tptp.e1 () tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e1) V)))
% 0.25/0.60 (declare-fun tptp.e0 () tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e0) V)))
% 0.25/0.60 (declare-fun tptp.op (tptp.mu tptp.mu) tptp.mu)
% 0.25/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.op V2) V1)) V)))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) Z)))) (@ tptp.mbox_s4 (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv A)) (@ tptp.inv B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op A) C)) (@ (@ tptp.op B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.op C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.25/0.60 (assert (let ((_let_1 (@ tptp.qmltpeq tptp.e1))) (let ((_let_2 (@ tptp.qmltpeq tptp.e0))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_2 tptp.e1))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_2 tptp.e2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_2 tptp.e3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_1 tptp.e2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_1 tptp.e3))))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) tptp.e3)))))))))))))
% 0.25/0.60 (assert (let ((_let_1 (@ tptp.op tptp.e3))) (let ((_let_2 (@ tptp.op tptp.e2))) (let ((_let_3 (@ tptp.op tptp.e1))) (let ((_let_4 (@ tptp.op tptp.e0))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_4 tptp.e0)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_4 tptp.e1)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_4 tptp.e2)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_4 tptp.e3)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e0)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e1)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e2)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e3)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e0)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e1)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e2)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e3)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 tptp.e0)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 tptp.e1)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 tptp.e2)) tptp.e1))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 tptp.e3)) tptp.e0)))))))))))))))))))))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.unit) tptp.e0))))
% 0.25/0.60 (assert (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv tptp.e0)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv tptp.e1)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv tptp.e2)) tptp.e1))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv tptp.e3)) tptp.e3)))))))
% 0.25/0.60 (assert (let ((_let_1 (@ tptp.inv tptp.e3))) (let ((_let_2 (@ tptp.qmltpeq _let_1))) (let ((_let_3 (@ tptp.inv tptp.e2))) (let ((_let_4 (@ tptp.qmltpeq _let_3))) (let ((_let_5 (@ tptp.inv tptp.e1))) (let ((_let_6 (@ tptp.qmltpeq _let_5))) (let ((_let_7 (@ tptp.inv tptp.e0))) (let ((_let_8 (@ tptp.qmltpeq _let_7))) (let ((_let_9 (@ tptp.op tptp.e3))) (let ((_let_10 (@ tptp.op tptp.e2))) (let ((_let_11 (@ tptp.op tptp.e1))) (let ((_let_12 (@ tptp.op tptp.e0))) (let ((_let_13 (@ tptp.qmltpeq tptp.unit))) (let ((_let_14 (@ tptp.op tptp.unit))) (let ((_let_15 (@ _let_9 tptp.e3))) (let ((_let_16 (@ tptp.op _let_15))) (let ((_let_17 (@ _let_9 tptp.e2))) (let ((_let_18 (@ _let_9 tptp.e1))) (let ((_let_19 (@ _let_9 tptp.e0))) (let ((_let_20 (@ _let_10 tptp.e3))) (let ((_let_21 (@ tptp.op _let_17))) (let ((_let_22 (@ _let_10 tptp.e2))) (let ((_let_23 (@ _let_10 tptp.e1))) (let ((_let_24 (@ _let_10 tptp.e0))) (let ((_let_25 (@ _let_11 tptp.e3))) (let ((_let_26 (@ tptp.op _let_18))) (let ((_let_27 (@ _let_11 tptp.e2))) (let ((_let_28 (@ _let_11 tptp.e1))) (let ((_let_29 (@ _let_11 tptp.e0))) (let ((_let_30 (@ _let_12 tptp.e3))) (let ((_let_31 (@ tptp.op _let_19))) (let ((_let_32 (@ _let_12 tptp.e2))) (let ((_let_33 (@ _let_12 tptp.e1))) (let ((_let_34 (@ _let_12 tptp.e0))) (let ((_let_35 (@ tptp.op _let_20))) (let ((_let_36 (@ tptp.op _let_22))) (let ((_let_37 (@ tptp.op _let_23))) (let ((_let_38 (@ tptp.op _let_24))) (let ((_let_39 (@ tptp.op _let_25))) (let ((_let_40 (@ tptp.op _let_27))) (let ((_let_41 (@ tptp.op _let_28))) (let ((_let_42 (@ tptp.op _let_29))) (let ((_let_43 (@ tptp.op _let_30))) (let ((_let_44 (@ tptp.op _let_32))) (let ((_let_45 (@ tptp.op _let_33))) (let ((_let_46 (@ tptp.op _let_34))) (let ((_let_47 (@ tptp.qmltpeq _let_15))) (let ((_let_48 (@ tptp.mbox_s4 (@ _let_47 tptp.e3)))) (let ((_let_49 (@ tptp.mbox_s4 (@ _let_47 tptp.e2)))) (let ((_let_50 (@ tptp.mbox_s4 (@ _let_47 tptp.e1)))) (let ((_let_51 (@ tptp.mbox_s4 (@ _let_47 tptp.e0)))) (let ((_let_52 (@ tptp.qmltpeq _let_17))) (let ((_let_53 (@ tptp.qmltpeq _let_18))) (let ((_let_54 (@ tptp.qmltpeq _let_19))) (let ((_let_55 (@ tptp.qmltpeq _let_20))) (let ((_let_56 (@ tptp.qmltpeq _let_22))) (let ((_let_57 (@ tptp.mbox_s4 (@ _let_56 tptp.e3)))) (let ((_let_58 (@ tptp.mbox_s4 (@ _let_56 tptp.e2)))) (let ((_let_59 (@ tptp.mbox_s4 (@ _let_56 tptp.e1)))) (let ((_let_60 (@ tptp.mbox_s4 (@ _let_56 tptp.e0)))) (let ((_let_61 (@ tptp.qmltpeq _let_23))) (let ((_let_62 (@ tptp.qmltpeq _let_24))) (let ((_let_63 (@ tptp.qmltpeq _let_25))) (let ((_let_64 (@ tptp.qmltpeq _let_27))) (let ((_let_65 (@ tptp.qmltpeq _let_28))) (let ((_let_66 (@ tptp.mbox_s4 (@ _let_65 tptp.e3)))) (let ((_let_67 (@ tptp.mbox_s4 (@ _let_65 tptp.e2)))) (let ((_let_68 (@ tptp.mbox_s4 (@ _let_65 tptp.e1)))) (let ((_let_69 (@ tptp.mbox_s4 (@ _let_65 tptp.e0)))) (let ((_let_70 (@ tptp.qmltpeq _let_29))) (let ((_let_71 (@ tptp.qmltpeq _let_30))) (let ((_let_72 (@ tptp.qmltpeq _let_32))) (let ((_let_73 (@ tptp.qmltpeq _let_33))) (let ((_let_74 (@ tptp.qmltpeq _let_34))) (let ((_let_75 (@ tptp.mbox_s4 (@ _let_74 tptp.e3)))) (let ((_let_76 (@ tptp.mbox_s4 (@ _let_74 tptp.e2)))) (let ((_let_77 (@ tptp.mbox_s4 (@ _let_74 tptp.e1)))) (let ((_let_78 (@ tptp.mbox_s4 (@ _let_74 tptp.e0)))) (not (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mor (@ (@ tptp.mand _let_78) (@ (@ tptp.mand _let_69) (@ (@ tptp.mand _let_60) _let_51)))) (@ (@ tptp.mor (@ (@ tptp.mand _let_77) (@ (@ tptp.mand _let_68) (@ (@ tptp.mand _let_59) _let_50)))) (@ (@ tptp.mor (@ (@ tptp.mand _let_76) (@ (@ tptp.mand _let_67) (@ (@ tptp.mand _let_58) _let_49)))) (@ (@ tptp.mand _let_75) (@ (@ tptp.mand _let_66) (@ (@ tptp.mand _let_57) _let_48))))))))) (@ (@ tptp.mand (@ (@ tptp.mor _let_78) (@ (@ tptp.mor _let_77) (@ (@ tptp.mor _let_76) _let_75)))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_73 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_73 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_73 tptp.e2))) (@ tptp.mbox_s4 (@ _let_73 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_72 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_72 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_72 tptp.e2))) (@ tptp.mbox_s4 (@ _let_72 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_71 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_71 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_71 tptp.e2))) (@ tptp.mbox_s4 (@ _let_71 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_70 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_70 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_70 tptp.e2))) (@ tptp.mbox_s4 (@ _let_70 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor _let_69) (@ (@ tptp.mor _let_68) (@ (@ tptp.mor _let_67) _let_66)))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_64 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_64 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_64 tptp.e2))) (@ tptp.mbox_s4 (@ _let_64 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_63 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_63 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_63 tptp.e2))) (@ tptp.mbox_s4 (@ _let_63 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_62 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_62 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_62 tptp.e2))) (@ tptp.mbox_s4 (@ _let_62 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_61 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_61 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_61 tptp.e2))) (@ tptp.mbox_s4 (@ _let_61 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor _let_60) (@ (@ tptp.mor _let_59) (@ (@ tptp.mor _let_58) _let_57)))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_55 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_55 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_55 tptp.e2))) (@ tptp.mbox_s4 (@ _let_55 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_54 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_54 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_54 tptp.e2))) (@ tptp.mbox_s4 (@ _let_54 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_53 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_53 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_53 tptp.e2))) (@ tptp.mbox_s4 (@ _let_53 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_52 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_52 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_52 tptp.e2))) (@ tptp.mbox_s4 (@ _let_52 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor _let_51) (@ (@ tptp.mor _let_50) (@ (@ tptp.mor _let_49) _let_48)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_46 tptp.e0)) (@ _let_12 _let_34)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_46 tptp.e1)) (@ _let_12 _let_33)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_46 tptp.e2)) (@ _let_12 _let_32)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_46 tptp.e3)) (@ _let_12 _let_30)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_45 tptp.e0)) (@ _let_12 _let_29)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_45 tptp.e1)) (@ _let_12 _let_28)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_45 tptp.e2)) (@ _let_12 _let_27)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_45 tptp.e3)) (@ _let_12 _let_25)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_44 tptp.e0)) (@ _let_12 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_44 tptp.e1)) (@ _let_12 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_44 tptp.e2)) (@ _let_12 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_44 tptp.e3)) (@ _let_12 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_43 tptp.e0)) (@ _let_12 _let_19)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_43 tptp.e1)) (@ _let_12 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_43 tptp.e2)) (@ _let_12 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_43 tptp.e3)) (@ _let_12 _let_15)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_42 tptp.e0)) (@ _let_11 _let_34)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_42 tptp.e1)) (@ _let_11 _let_33)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_42 tptp.e2)) (@ _let_11 _let_32)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_42 tptp.e3)) (@ _let_11 _let_30)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_41 tptp.e0)) (@ _let_11 _let_29)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_41 tptp.e1)) (@ _let_11 _let_28)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_41 tptp.e2)) (@ _let_11 _let_27)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_41 tptp.e3)) (@ _let_11 _let_25)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_40 tptp.e0)) (@ _let_11 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_40 tptp.e1)) (@ _let_11 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_40 tptp.e2)) (@ _let_11 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_40 tptp.e3)) (@ _let_11 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_39 tptp.e0)) (@ _let_11 _let_19)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_39 tptp.e1)) (@ _let_11 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_39 tptp.e2)) (@ _let_11 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_39 tptp.e3)) (@ _let_11 _let_15)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_38 tptp.e0)) (@ _let_10 _let_34)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_38 tptp.e1)) (@ _let_10 _let_33)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_38 tptp.e2)) (@ _let_10 _let_32)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_38 tptp.e3)) (@ _let_10 _let_30)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_37 tptp.e0)) (@ _let_10 _let_29)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_37 tptp.e1)) (@ _let_10 _let_28)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_37 tptp.e2)) (@ _let_10 _let_27)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_37 tptp.e3)) (@ _let_10 _let_25)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e0)) (@ _let_10 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e1)) (@ _let_10 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e2)) (@ _let_10 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e3)) (@ _let_10 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e0)) (@ _let_10 _let_19)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e1)) (@ _let_10 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e2)) (@ _let_10 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e3)) (@ _let_10 _let_15)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e0)) (@ _let_9 _let_34)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e1)) (@ _let_9 _let_33)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e2)) (@ _let_9 _let_32)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e3)) (@ _let_9 _let_30)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e0)) (@ _let_9 _let_29)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e1)) (@ _let_9 _let_28)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e2)) (@ _let_9 _let_27)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e3)) (@ _let_9 _let_25)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e0)) (@ _let_9 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e1)) (@ _let_9 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e2)) (@ _let_9 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e3)) (@ _let_9 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_16 tptp.e0)) (@ _let_9 _let_19)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_16 tptp.e1)) (@ _let_9 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_16 tptp.e2)) (@ _let_9 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_16 tptp.e3)) (@ _let_9 _let_15)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_14 tptp.e0)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_12 tptp.unit)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_14 tptp.e1)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_11 tptp.unit)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_14 t/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 16629 Alarm clock ( read result; case "$result" in
% 299.67/300.20 unsat)
% 299.67/300.20 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.67/300.20 ;;
% 299.67/300.20 sat)
% 299.67/300.20 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.67/300.20 ;;
% 299.67/300.20 esac; exit 1 )
% 299.67/300.20 ptp.e2)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.unit)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_14 tptp.e3)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 tptp.unit)) tptp.e3))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_13 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_13 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_13 tptp.e2))) (@ tptp.mbox_s4 (@ _let_13 tptp.e3)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_12 _let_7)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op _let_7) tptp.e0)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_11 _let_5)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op _let_5) tptp.e1)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 _let_3)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op _let_3) tptp.e2)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 _let_1)) tptp.unit))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op _let_1) tptp.e3)) tptp.unit))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_8 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_8 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_8 tptp.e2))) (@ tptp.mbox_s4 (@ _let_8 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_6 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_6 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_6 tptp.e2))) (@ tptp.mbox_s4 (@ _let_6 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_4 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_4 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_4 tptp.e2))) (@ tptp.mbox_s4 (@ _let_4 tptp.e3)))))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_2 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_2 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_2 tptp.e2))) (@ tptp.mbox_s4 (@ _let_2 tptp.e3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 299.67/300.20 (set-info :filename cvc5---1.0.5_10761)
% 299.67/300.20 (check-sat-assuming ( true ))
% 299.67/300.20 ------- get file name : TPTP file name is ALG022^7
% 299.67/300.20 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10761.smt2...
% 299.67/300.20 --- Run --ho-elim --full-saturate-quant at 10...
% 299.67/300.20 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.67/300.20 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.67/300.20 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.67/300.20 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.67/300.20 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.67/300.20 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.67/300.20 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.67/300.20 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.67/300.20 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.67/300.20 % cvc5---1.0.5 exiting
% 299.67/300.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------