TSTP Solution File: ALG023^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG023^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 299.74s 300.22s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : ALG023^7 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.17 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n010.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon Aug 28 05:26:04 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.23/0.55 %----Proving TH0
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 % File : ALG023^7 : TPTP v8.1.2. Released v5.5.0.
% 0.23/0.55 % Domain : General Algebra
% 0.23/0.55 % Problem : Groups 4: VERIFY-GEN-SYSES-PROBLEM-2
% 0.23/0.55 % Version : [Ben12] axioms.
% 0.23/0.55 % English :
% 0.23/0.55
% 0.23/0.55 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.23/0.55 % : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% 0.23/0.55 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.23/0.55 % Source : [Ben12]
% 0.23/0.55 % Names : s4-cumul-GAL023+1 [Ben12]
% 0.23/0.55
% 0.23/0.55 % Status : Unsatisfiable
% 0.23/0.55 % Rating : 1.00 v8.1.0, 0.86 v6.0.0, 1.00 v5.5.0
% 0.23/0.55 % Syntax : Number of formulae : 127 ( 40 unt; 43 typ; 32 def)
% 0.23/0.55 % Number of atoms : 1341 ( 36 equ; 0 cnn)
% 0.23/0.55 % Maximal formula atoms : 240 ( 15 avg)
% 0.23/0.55 % Number of connectives : 3103 ( 5 ~; 5 |; 9 &;3074 @)
% 0.23/0.55 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.23/0.55 % Maximal formula depth : 73 ( 8 avg)
% 0.23/0.55 % Number of types : 3 ( 1 usr)
% 0.23/0.55 % Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% 0.23/0.55 % Number of symbols : 53 ( 51 usr; 15 con; 0-3 aty)
% 0.23/0.55 % Number of variables : 114 ( 63 ^; 44 !; 7 ?; 114 :)
% 0.23/0.55 % SPC : TH0_UNS_EQU_NAR
% 0.23/0.55
% 0.23/0.55 % Comments : Goedel translation of ALG023+1
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %----Include axioms for Modal logic S4 under cumulative domains
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %----Declaration of additional base type mu
% 0.23/0.55 thf(mu_type,type,
% 0.23/0.55 mu: $tType ).
% 0.23/0.55
% 0.23/0.55 %----Equality
% 0.23/0.55 thf(qmltpeq_type,type,
% 0.23/0.55 qmltpeq: mu > mu > $i > $o ).
% 0.23/0.55
% 0.23/0.55 % originale Definition
% 0.23/0.55 %thf(qmltpeq,definition,
% 0.23/0.55 % ( qmltpeq
% 0.23/0.55 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.23/0.55
% 0.23/0.55 % erweiterte Leibnitz-Definition
% 0.23/0.55 %thf(qmltpeq,definition,
% 0.23/0.55 % ( qmltpeq
% 0.23/0.55 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.23/0.55
% 0.23/0.55 % Leibnitz-Definition
% 0.23/0.55 %thf(qmltpeq,definition,
% 0.23/0.55 % ( qmltpeq
% 0.23/0.55 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.23/0.55
% 0.23/0.55 thf(meq_prop_type,type,
% 0.23/0.55 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(meq_prop,definition,
% 0.23/0.55 ( meq_prop
% 0.23/0.55 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.23/0.55 ( ( X @ W )
% 0.23/0.55 = ( Y @ W ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Modal operators not, or, box, Pi
% 0.23/0.55 thf(mnot_type,type,
% 0.23/0.55 mnot: ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mnot,definition,
% 0.23/0.55 ( mnot
% 0.23/0.55 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.55 ~ ( Phi @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mor_type,type,
% 0.23/0.55 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mor,definition,
% 0.23/0.55 ( mor
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.23/0.55 ( ( Phi @ W )
% 0.23/0.55 | ( Psi @ W ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mbox_type,type,
% 0.23/0.55 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mbox,definition,
% 0.23/0.55 ( mbox
% 0.23/0.55 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.23/0.55 ! [V: $i] :
% 0.23/0.55 ( ~ ( R @ W @ V )
% 0.23/0.55 | ( Phi @ V ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mforall_prop_type,type,
% 0.23/0.55 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mforall_prop,definition,
% 0.23/0.55 ( mforall_prop
% 0.23/0.55 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.23/0.55 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Further modal operators
% 0.23/0.55 thf(mtrue_type,type,
% 0.23/0.55 mtrue: $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mtrue,definition,
% 0.23/0.55 ( mtrue
% 0.23/0.55 = ( ^ [W: $i] : $true ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mfalse_type,type,
% 0.23/0.55 mfalse: $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mfalse,definition,
% 0.23/0.55 ( mfalse
% 0.23/0.55 = ( mnot @ mtrue ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mand_type,type,
% 0.23/0.55 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mand,definition,
% 0.23/0.55 ( mand
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mimplies_type,type,
% 0.23/0.55 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mimplies,definition,
% 0.23/0.55 ( mimplies
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mimplied_type,type,
% 0.23/0.55 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mimplied,definition,
% 0.23/0.55 ( mimplied
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mequiv_type,type,
% 0.23/0.55 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mequiv,definition,
% 0.23/0.55 ( mequiv
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mxor_type,type,
% 0.23/0.55 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mxor,definition,
% 0.23/0.55 ( mxor
% 0.23/0.55 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mdia_type,type,
% 0.23/0.55 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mdia,definition,
% 0.23/0.55 ( mdia
% 0.23/0.55 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %--- (new for cumulative)
% 0.23/0.55 %---Declaration of existence predicate for simulating cumulative domain
% 0.23/0.55 thf(exists_in_world_type,type,
% 0.23/0.55 exists_in_world: mu > $i > $o ).
% 0.23/0.55
% 0.23/0.55 %----The domains are non-empty
% 0.23/0.55 thf(nonempty_ax,axiom,
% 0.23/0.55 ! [V: $i] :
% 0.23/0.55 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(mforall_ind_type,type,
% 0.23/0.55 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 %--- (new for cumulative)
% 0.23/0.55 thf(mforall_ind,definition,
% 0.23/0.55 ( mforall_ind
% 0.23/0.55 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.55 ! [X: mu] :
% 0.23/0.55 ( ( exists_in_world @ X @ W )
% 0.23/0.55 => ( Phi @ X @ W ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %thf(mforall_ind,definition,
% 0.23/0.55 % ( mforall_ind
% 0.23/0.55 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.55 % ! [X: mu] :
% 0.23/0.55 % ( Phi @ X @ W ) ) )).
% 0.23/0.55
% 0.23/0.55 thf(mexists_ind_type,type,
% 0.23/0.55 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mexists_ind,definition,
% 0.23/0.55 ( mexists_ind
% 0.23/0.55 = ( ^ [Phi: mu > $i > $o] :
% 0.23/0.55 ( mnot
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mexists_prop_type,type,
% 0.23/0.55 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mexists_prop,definition,
% 0.23/0.55 ( mexists_prop
% 0.23/0.55 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.23/0.55 ( mnot
% 0.23/0.55 @ ( mforall_prop
% 0.23/0.55 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Definition of properties of accessibility relations
% 0.23/0.55 thf(mreflexive_type,type,
% 0.23/0.55 mreflexive: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mreflexive,definition,
% 0.23/0.55 ( mreflexive
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(msymmetric_type,type,
% 0.23/0.55 msymmetric: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(msymmetric,definition,
% 0.23/0.55 ( msymmetric
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i] :
% 0.23/0.55 ( ( R @ S @ T )
% 0.23/0.55 => ( R @ T @ S ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mserial_type,type,
% 0.23/0.55 mserial: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mserial,definition,
% 0.23/0.55 ( mserial
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i] :
% 0.23/0.55 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mtransitive_type,type,
% 0.23/0.55 mtransitive: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mtransitive,definition,
% 0.23/0.55 ( mtransitive
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( ( R @ S @ T )
% 0.23/0.55 & ( R @ T @ U ) )
% 0.23/0.55 => ( R @ S @ U ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(meuclidean_type,type,
% 0.23/0.55 meuclidean: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(meuclidean,definition,
% 0.23/0.55 ( meuclidean
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( ( R @ S @ T )
% 0.23/0.55 & ( R @ S @ U ) )
% 0.23/0.55 => ( R @ T @ U ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mpartially_functional_type,type,
% 0.23/0.55 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mpartially_functional,definition,
% 0.23/0.55 ( mpartially_functional
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( ( R @ S @ T )
% 0.23/0.55 & ( R @ S @ U ) )
% 0.23/0.55 => ( T = U ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mfunctional_type,type,
% 0.23/0.55 mfunctional: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mfunctional,definition,
% 0.23/0.55 ( mfunctional
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i] :
% 0.23/0.55 ? [T: $i] :
% 0.23/0.55 ( ( R @ S @ T )
% 0.23/0.55 & ! [U: $i] :
% 0.23/0.55 ( ( R @ S @ U )
% 0.23/0.55 => ( T = U ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_dense_type,type,
% 0.23/0.55 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_dense,definition,
% 0.23/0.55 ( mweakly_dense
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( R @ S @ T )
% 0.23/0.55 => ? [U: $i] :
% 0.23/0.55 ( ( R @ S @ U )
% 0.23/0.55 & ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_connected_type,type,
% 0.23/0.55 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_connected,definition,
% 0.23/0.55 ( mweakly_connected
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( ( R @ S @ T )
% 0.23/0.55 & ( R @ S @ U ) )
% 0.23/0.55 => ( ( R @ T @ U )
% 0.23/0.55 | ( T = U )
% 0.23/0.55 | ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_directed_type,type,
% 0.23/0.55 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mweakly_directed,definition,
% 0.23/0.55 ( mweakly_directed
% 0.23/0.55 = ( ^ [R: $i > $i > $o] :
% 0.23/0.55 ! [S: $i,T: $i,U: $i] :
% 0.23/0.55 ( ( ( R @ S @ T )
% 0.23/0.55 & ( R @ S @ U ) )
% 0.23/0.55 => ? [V: $i] :
% 0.23/0.55 ( ( R @ T @ V )
% 0.23/0.55 & ( R @ U @ V ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Definition of validity
% 0.23/0.55 thf(mvalid_type,type,
% 0.23/0.55 mvalid: ( $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mvalid,definition,
% 0.23/0.55 ( mvalid
% 0.23/0.55 = ( ^ [Phi: $i > $o] :
% 0.23/0.55 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Definition of satisfiability
% 0.23/0.55 thf(msatisfiable_type,type,
% 0.23/0.55 msatisfiable: ( $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(msatisfiable,definition,
% 0.23/0.55 ( msatisfiable
% 0.23/0.55 = ( ^ [Phi: $i > $o] :
% 0.23/0.55 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Definition of countersatisfiability
% 0.23/0.55 thf(mcountersatisfiable_type,type,
% 0.23/0.55 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mcountersatisfiable,definition,
% 0.23/0.55 ( mcountersatisfiable
% 0.23/0.55 = ( ^ [Phi: $i > $o] :
% 0.23/0.55 ? [W: $i] :
% 0.23/0.55 ~ ( Phi @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----Definition of invalidity
% 0.23/0.55 thf(minvalid_type,type,
% 0.23/0.55 minvalid: ( $i > $o ) > $o ).
% 0.23/0.55
% 0.23/0.55 thf(minvalid,definition,
% 0.23/0.55 ( minvalid
% 0.23/0.55 = ( ^ [Phi: $i > $o] :
% 0.23/0.55 ! [W: $i] :
% 0.23/0.55 ~ ( Phi @ W ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %----We reserve an accessibility relation constant rel_s4
% 0.23/0.55 thf(rel_s4_type,type,
% 0.23/0.55 rel_s4: $i > $i > $o ).
% 0.23/0.55
% 0.23/0.55 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.23/0.55 thf(mbox_s4_type,type,
% 0.23/0.55 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mbox_s4,definition,
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.55 ! [V: $i] :
% 0.23/0.55 ( ~ ( rel_s4 @ W @ V )
% 0.23/0.55 | ( Phi @ V ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(mdia_s4_type,type,
% 0.23/0.55 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.55
% 0.23/0.55 thf(mdia_s4,definition,
% 0.23/0.55 ( mdia_s4
% 0.23/0.55 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %----We have now two options for stating the B conditions:
% 0.23/0.55 %----We can (i) directly formulate conditions for the accessibility relation
% 0.23/0.55 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.23/0.55 thf(a1,axiom,
% 0.23/0.55 mreflexive @ rel_s4 ).
% 0.23/0.55
% 0.23/0.55 thf(a2,axiom,
% 0.23/0.55 mtransitive @ rel_s4 ).
% 0.23/0.55
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 thf(cumulative_ax,axiom,
% 0.23/0.55 ! [X: mu,V: $i,W: $i] :
% 0.23/0.55 ( ( ( exists_in_world @ X @ V )
% 0.23/0.55 & ( rel_s4 @ V @ W ) )
% 0.23/0.55 => ( exists_in_world @ X @ W ) ) ).
% 0.23/0.55
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 thf(unit_type,type,
% 0.23/0.55 unit: mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_unit_ax,axiom,
% 0.23/0.55 ! [V: $i] : ( exists_in_world @ unit @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(inv_type,type,
% 0.23/0.55 inv: mu > mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_inv_ax,axiom,
% 0.23/0.55 ! [V: $i,V1: mu] : ( exists_in_world @ ( inv @ V1 ) @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(e1_type,type,
% 0.23/0.55 e1: mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_e1_ax,axiom,
% 0.23/0.55 ! [V: $i] : ( exists_in_world @ e1 @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(e2_type,type,
% 0.23/0.55 e2: mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_e2_ax,axiom,
% 0.23/0.55 ! [V: $i] : ( exists_in_world @ e2 @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(e0_type,type,
% 0.23/0.55 e0: mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_e0_ax,axiom,
% 0.23/0.55 ! [V: $i] : ( exists_in_world @ e0 @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(op_type,type,
% 0.23/0.55 op: mu > mu > mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_op_ax,axiom,
% 0.23/0.55 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( op @ V2 @ V1 ) @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(e3_type,type,
% 0.23/0.55 e3: mu ).
% 0.23/0.55
% 0.23/0.55 thf(existence_of_e3_ax,axiom,
% 0.23/0.55 ! [V: $i] : ( exists_in_world @ e3 @ V ) ).
% 0.23/0.55
% 0.23/0.55 thf(reflexivity,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(symmetry,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [X: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(transitivity,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [X: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [Y: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(inv_substitution_1,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [A: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(op_substitution_1,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [A: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [B: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ A @ C ) @ ( op @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(op_substitution_2,axiom,
% 0.23/0.55 ( mvalid
% 0.23/0.55 @ ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [A: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [B: mu] :
% 0.23/0.55 ( mbox_s4
% 0.23/0.55 @ ( mforall_ind
% 0.23/0.55 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ C @ A ) @ ( op @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax1,axiom,
% 0.23/0.55 mvalid @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax2,axiom,
% 0.23/0.55 mvalid @ ( 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 ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax3,axiom,
% 0.23/0.55 mvalid @ ( 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 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ unit @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ unit @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax4,axiom,
% 0.23/0.55 mvalid @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax5,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( inv @ unit ) @ unit ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax6,axiom,
% 0.23/0.55 mvalid @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax7,axiom,
% 0.23/0.55 mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax8,axiom,
% 0.23/0.55 mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e3 ) ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( inv @ e2 ) @ ( inv @ e3 ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax9,axiom,
% 0.23/0.55 mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e1 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ ( op @ e3 @ e2 ) @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax10,axiom,
% 0.23/0.55 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 ) ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax11,axiom,
% 0.23/0.55 mvalid @ ( 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 ) ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax12,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax13,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e3 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax14,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e1 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax15,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e3 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax16,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e1 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax17,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e2 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax18,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e2 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax19,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e3 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax20,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e0 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax21,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e3 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax22,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e0 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax23,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e2 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax24,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e1 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax25,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e3 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax26,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e3 @ e3 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e0 @ e3 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax27,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e3 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax28,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e0 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax29,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e1 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax30,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e1 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax31,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e0 @ ( op @ e2 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax32,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e2 @ e2 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e0 @ e2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax33,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e1 @ ( op @ e2 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax34,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e1 @ e1 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e0 @ e1 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 thf(ax35,axiom,
% 0.23/0.55 mvalid @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ e3 @ ( op @ e0 @ e0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ e2 @ ( op @ e1 @ e0 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.oKU9GHZBsF/cvc5---1.0.5_18023.p...
% 0.23/0.60 (declare-sort $$unsorted 0)
% 0.23/0.60 (declare-sort tptp.mu 0)
% 0.23/0.60 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.60 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.23/0.60 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.23/0.60 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.23/0.60 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.23/0.60 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.23/0.60 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.23/0.60 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.23/0.60 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.60 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.23/0.60 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.23/0.60 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.23/0.60 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.23/0.60 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.23/0.60 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.23/0.60 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.23/0.60 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.23/0.60 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.23/0.60 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.23/0.60 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.23/0.60 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.23/0.60 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.23/0.60 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.60 (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)))))))))
% 0.23/0.60 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.60 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.60 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.60 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.60 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.60 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.23/0.60 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.23/0.60 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.60 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.60 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.23/0.60 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.23/0.60 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.23/0.60 (declare-fun tptp.unit () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.unit) V)))
% 0.23/0.60 (declare-fun tptp.inv (tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inv V1)) V)))
% 0.23/0.60 (declare-fun tptp.e1 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e1) V)))
% 0.23/0.60 (declare-fun tptp.e2 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e2) V)))
% 0.23/0.60 (declare-fun tptp.e0 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e0) V)))
% 0.23/0.60 (declare-fun tptp.op (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.op V2) V1)) V)))
% 0.23/0.60 (declare-fun tptp.e3 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.e3) V)))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.23/0.60 (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))))))
% 0.23/0.60 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op A) C)) (@ (@ tptp.op B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.op tptp.e3))) (let ((_let_2 (@ tptp.qmltpeq (@ _let_1 tptp.e3)))) (let ((_let_3 (@ tptp.qmltpeq (@ _let_1 tptp.e2)))) (let ((_let_4 (@ tptp.qmltpeq (@ _let_1 tptp.e1)))) (let ((_let_5 (@ tptp.qmltpeq (@ _let_1 tptp.e0)))) (let ((_let_6 (@ tptp.op tptp.e2))) (let ((_let_7 (@ tptp.qmltpeq (@ _let_6 tptp.e3)))) (let ((_let_8 (@ tptp.qmltpeq (@ _let_6 tptp.e2)))) (let ((_let_9 (@ tptp.qmltpeq (@ _let_6 tptp.e1)))) (let ((_let_10 (@ tptp.qmltpeq (@ _let_6 tptp.e0)))) (let ((_let_11 (@ tptp.op tptp.e1))) (let ((_let_12 (@ tptp.qmltpeq (@ _let_11 tptp.e3)))) (let ((_let_13 (@ tptp.qmltpeq (@ _let_11 tptp.e2)))) (let ((_let_14 (@ tptp.qmltpeq (@ _let_11 tptp.e1)))) (let ((_let_15 (@ tptp.qmltpeq (@ _let_11 tptp.e0)))) (let ((_let_16 (@ tptp.op tptp.e0))) (let ((_let_17 (@ tptp.qmltpeq (@ _let_16 tptp.e3)))) (let ((_let_18 (@ tptp.qmltpeq (@ _let_16 tptp.e2)))) (let ((_let_19 (@ tptp.qmltpeq (@ _let_16 tptp.e1)))) (let ((_let_20 (@ tptp.qmltpeq (@ _let_16 tptp.e0)))) (@ tptp.mvalid (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_20 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_20 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_20 tptp.e2))) (@ tptp.mbox_s4 (@ _let_20 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_19 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_19 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_19 tptp.e2))) (@ tptp.mbox_s4 (@ _let_19 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_18 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_18 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_18 tptp.e2))) (@ tptp.mbox_s4 (@ _let_18 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_17 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_17 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_17 tptp.e2))) (@ tptp.mbox_s4 (@ _let_17 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_15 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_15 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_15 tptp.e2))) (@ tptp.mbox_s4 (@ _let_15 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_14 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_14 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_14 tptp.e2))) (@ tptp.mbox_s4 (@ _let_14 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.mor (@ tptp.mbox_s4 (@ _let_12 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_12 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_12 tptp.e2))) (@ tptp.mbox_s4 (@ _let_12 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_10 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_10 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_10 tptp.e2))) (@ tptp.mbox_s4 (@ _let_10 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_9 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_9 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_9 tptp.e2))) (@ tptp.mbox_s4 (@ _let_9 tptp.e3)))))) (@ (@ 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_7 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_7 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_7 tptp.e2))) (@ tptp.mbox_s4 (@ _let_7 tptp.e3)))))) (@ (@ tptp.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_5 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_5 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_5 tptp.e2))) (@ tptp.mbox_s4 (@ _let_5 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.mand (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_3 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_3 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_3 tptp.e2))) (@ tptp.mbox_s4 (@ _let_3 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))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.op tptp.e3))) (let ((_let_2 (@ _let_1 tptp.e3))) (let ((_let_3 (@ tptp.op _let_2))) (let ((_let_4 (@ _let_1 tptp.e2))) (let ((_let_5 (@ _let_1 tptp.e1))) (let ((_let_6 (@ _let_1 tptp.e0))) (let ((_let_7 (@ tptp.op tptp.e2))) (let ((_let_8 (@ _let_7 tptp.e3))) (let ((_let_9 (@ tptp.op _let_4))) (let ((_let_10 (@ _let_7 tptp.e2))) (let ((_let_11 (@ _let_7 tptp.e1))) (let ((_let_12 (@ _let_7 tptp.e0))) (let ((_let_13 (@ tptp.op tptp.e1))) (let ((_let_14 (@ _let_13 tptp.e3))) (let ((_let_15 (@ tptp.op _let_5))) (let ((_let_16 (@ _let_13 tptp.e2))) (let ((_let_17 (@ _let_13 tptp.e1))) (let ((_let_18 (@ _let_13 tptp.e0))) (let ((_let_19 (@ tptp.op tptp.e0))) (let ((_let_20 (@ _let_19 tptp.e3))) (let ((_let_21 (@ tptp.op _let_6))) (let ((_let_22 (@ _let_19 tptp.e2))) (let ((_let_23 (@ _let_19 tptp.e1))) (let ((_let_24 (@ _let_19 tptp.e0))) (let ((_let_25 (@ tptp.op _let_8))) (let ((_let_26 (@ tptp.op _let_10))) (let ((_let_27 (@ tptp.op _let_11))) (let ((_let_28 (@ tptp.op _let_12))) (let ((_let_29 (@ tptp.op _let_14))) (let ((_let_30 (@ tptp.op _let_16))) (let ((_let_31 (@ tptp.op _let_17))) (let ((_let_32 (@ tptp.op _let_18))) (let ((_let_33 (@ tptp.op _let_20))) (let ((_let_34 (@ tptp.op _let_22))) (let ((_let_35 (@ tptp.op _let_23))) (let ((_let_36 (@ tptp.op _let_24))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e0)) (@ _let_19 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e1)) (@ _let_19 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e2)) (@ _let_19 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_36 tptp.e3)) (@ _let_19 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e0)) (@ _let_19 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e1)) (@ _let_19 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e2)) (@ _let_19 _let_16)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_35 tptp.e3)) (@ _let_19 _let_14)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_34 tptp.e0)) (@ _let_19 _let_12)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_34 tptp.e1)) (@ _let_19 _let_11)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_34 tptp.e2)) (@ _let_19 _let_10)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_34 tptp.e3)) (@ _let_19 _let_8)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_33 tptp.e0)) (@ _let_19 _let_6)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_33 tptp.e1)) (@ _let_19 _let_5)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_33 tptp.e2)) (@ _let_19 _let_4)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_33 tptp.e3)) (@ _let_19 _let_2)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.e0)) (@ _let_13 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.e1)) (@ _let_13 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.e2)) (@ _let_13 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.e3)) (@ _let_13 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e0)) (@ _let_13 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e1)) (@ _let_13 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e2)) (@ _let_13 _let_16)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_31 tptp.e3)) (@ _let_13 _let_14)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_30 tptp.e0)) (@ _let_13 _let_12)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_30 tptp.e1)) (@ _let_13 _let_11)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_30 tptp.e2)) (@ _let_13 _let_10)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_30 tptp.e3)) (@ _let_13 _let_8)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_29 tptp.e0)) (@ _let_13 _let_6)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_29 tptp.e1)) (@ _let_13 _let_5)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_29 tptp.e2)) (@ _let_13 _let_4)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_29 tptp.e3)) (@ _let_13 _let_2)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_28 tptp.e0)) (@ _let_7 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_28 tptp.e1)) (@ _let_7 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_28 tptp.e2)) (@ _let_7 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_28 tptp.e3)) (@ _let_7 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_27 tptp.e0)) (@ _let_7 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_27 tptp.e1)) (@ _let_7 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_27 tptp.e2)) (@ _let_7 _let_16)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_27 tptp.e3)) (@ _let_7 _let_14)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e0)) (@ _let_7 _let_12)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e1)) (@ _let_7 _let_11)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e2)) (@ _let_7 _let_10)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_26 tptp.e3)) (@ _let_7 _let_8)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.e0)) (@ _let_7 _let_6)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.e1)) (@ _let_7 _let_5)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.e2)) (@ _let_7 _let_4)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.e3)) (@ _let_7 _let_2)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e0)) (@ _let_1 _let_24)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e1)) (@ _let_1 _let_23)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e2)) (@ _let_1 _let_22)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_21 tptp.e3)) (@ _let_1 _let_20)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_15 tptp.e0)) (@ _let_1 _let_18)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_15 tptp.e1)) (@ _let_1 _let_17)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_15 tptp.e2)) (@ _let_1 _let_16)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_15 tptp.e3)) (@ _let_1 _let_14)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 tptp.e0)) (@ _let_1 _let_12)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 tptp.e1)) (@ _let_1 _let_11)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 tptp.e2)) (@ _let_1 _let_10)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_9 tptp.e3)) (@ _let_1 _let_8)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e0)) (@ _let_1 _let_6)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e1)) (@ _let_1 _let_5)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e2)) (@ _let_1 _let_4)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.e3)) (@ _let_1 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.qmltpeq tptp.unit))) (let ((_let_2 (@ tptp.op tptp.unit))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e0)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op tptp.e0) tptp.unit)) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e1)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op tptp.e1) tptp.unit)) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e2)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op tptp.e2) tptp.unit)) tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_2 tptp.e3)) tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op tptp.e3) tptp.unit)) tptp.e3))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.e0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.e1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.e2))) (@ tptp.mbox_s4 (@ _let_1 tptp.e3)))))))))))))))))
% 0.23/0.60 (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))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.op tptp.e0) _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 (@ (@ tptp.op tptp.e1) _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 (@ (@ tptp.op tptp.e2) _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 (@ (@ tptp.op tptp.e3) _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))))))))))))))))))))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv tptp.unit)) tptp.unit))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv (@ tptp.inv tptp.e0))) tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv (@ tptp.inv tptp.e1))) tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv (@ tptp.inv tptp.e2))) tptp.e2))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv (@ tptp.inv tptp.e3))) tptp.e3)))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.qmltpeq (@ tptp.inv tptp.e3)))) (let ((_let_2 (@ tptp.mbox_s4 (@ _let_1 tptp.e3)))) (let ((_let_3 (@ tptp.qmltpeq (@ tptp.inv tptp.e2)))) (let ((_let_4 (@ tptp.mbox_s4 (@ _let_3 tptp.e3)))) (let ((_let_5 (@ tptp.mbox_s4 (@ _let_1 tptp.e2)))) (let ((_let_6 (@ tptp.qmltpeq (@ tptp.inv tptp.e1)))) (let ((_let_7 (@ tptp.mbox_s4 (@ _let_6 tptp.e3)))) (let ((_let_8 (@ tptp.mbox_s4 (@ _let_1 tptp.e1)))) (let ((_let_9 (@ tptp.qmltpeq (@ tptp.inv tptp.e0)))) (let ((_let_10 (@ tptp.mbox_s4 (@ _let_9 tptp.e3)))) (let ((_let_11 (@ tptp.mbox_s4 (@ _let_1 tptp.e0)))) (let ((_let_12 (@ tptp.mbox_s4 (@ _let_3 tptp.e2)))) (let ((_let_13 (@ tptp.mbox_s4 (@ _let_6 tptp.e2)))) (let ((_let_14 (@ tptp.mbox_s4 (@ _let_3 tptp.e1)))) (let ((_let_15 (@ tptp.mbox_s4 (@ _let_9 tptp.e2)))) (let ((_let_16 (@ tptp.mbox_s4 (@ _let_3 tptp.e0)))) (let ((_let_17 (@ tptp.mbox_s4 (@ _let_6 tptp.e1)))) (let ((_let_18 (@ tptp.mbox_s4 (@ _let_9 tptp.e1)))) (let ((_let_19 (@ tptp.mbox_s4 (@ _let_6 tptp.e0)))) (let ((_let_20 (@ tptp.mbox_s4 (@ _let_9 tptp.e0)))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_20) _let_20))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_18) _let_19))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_15) _let_16))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_10) _let_11))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_19) _let_18))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_17) _let_17))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_13) _let_14))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_7) _let_8))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_16) _let_15))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_14) _let_13))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_12) _let_12))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_4) _let_5))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_11) _let_10))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_8) _let_7))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_5) _let_4))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_2)))))))))))))))))))))))))))))))))))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.inv tptp.e3))) (let ((_let_2 (@ tptp.inv tptp.e2))) (let ((_let_3 (@ tptp.inv tptp.e1))) (let ((_let_4 (@ tptp.qmltpeq _let_3))) (let ((_let_5 (@ tptp.qmltpeq (@ tptp.inv tptp.e0)))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_5 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_5 _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_5 _let_1))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_4 _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_4 _let_1))))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_2) _let_1))))))))))))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.op tptp.e3))) (let ((_let_2 (@ _let_1 tptp.e3))) (let ((_let_3 (@ _let_1 tptp.e2))) (let ((_let_4 (@ _let_1 tptp.e1))) (let ((_let_5 (@ tptp.qmltpeq _let_4))) (let ((_let_6 (@ _let_1 tptp.e0))) (let ((_let_7 (@ tptp.qmltpeq _let_6))) (let ((_let_8 (@ tptp.op tptp.e2))) (let ((_let_9 (@ _let_8 tptp.e3))) (let ((_let_10 (@ _let_8 tptp.e2))) (let ((_let_11 (@ tptp.qmltpeq _let_10))) (let ((_let_12 (@ _let_8 tptp.e1))) (let ((_let_13 (@ tptp.qmltpeq _let_12))) (let ((_let_14 (@ _let_8 tptp.e0))) (let ((_let_15 (@ tptp.qmltpeq _let_14))) (let ((_let_16 (@ tptp.op tptp.e1))) (let ((_let_17 (@ _let_16 tptp.e3))) (let ((_let_18 (@ _let_16 tptp.e2))) (let ((_let_19 (@ tptp.qmltpeq _let_18))) (let ((_let_20 (@ _let_16 tptp.e1))) (let ((_let_21 (@ tptp.qmltpeq _let_20))) (let ((_let_22 (@ _let_16 tptp.e0))) (let ((_let_23 (@ tptp.qmltpeq _let_22))) (let ((_let_24 (@ tptp.op tptp.e0))) (let ((_let_25 (@ _let_24 tptp.e3))) (let ((_let_26 (@ _let_24 tptp.e2))) (let ((_let_27 (@ tptp.qmltpeq _let_26))) (let ((_let_28 (@ _let_24 tptp.e1))) (let ((_let_29 (@ tptp.qmltpeq _let_28))) (let ((_let_30 (@ tptp.qmltpeq (@ _let_24 tptp.e0)))) (let ((_let_31 (@ tptp.qmltpeq _let_17))) (let ((_let_32 (@ tptp.qmltpeq _let_25))) (@ tptp.mvalid (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_22))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_14))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_6))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_23 _let_14))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_23 _let_6))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_15 _let_6))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_29 _let_20))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_29 _let_12))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_29 _let_4))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_21 _let_12))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_21 _let_4))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_13 _let_4))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_27 _let_18))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_27 _let_10))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_27 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_19 _let_10))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_19 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_11 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_32 _let_17))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_32 _let_9))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_32 _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_31 _let_9))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_31 _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_9) _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_28))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_26))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_30 _let_25))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_29 _let_26))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_29 _let_25))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_27 _let_25))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_23 _let_20))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_23 _let_18))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_23 _let_17))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_21 _let_18))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_21 _let_17))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_19 _let_17))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_15 _let_12))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_15 _let_10))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_15 _let_9))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_13 _let_10))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_13 _let_9))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_11 _let_9))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_7 _let_4))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_7 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_7 _let_2))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_5 _let_3))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ _let_5 _let_2))))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_3) _let_2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.60 (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)))))))))))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.qmltpeq (@ (@ tptp.op tptp.e3) tptp.e3)))) (let ((_let_2 (@ tptp.qmltpeq (@ (@ tptp.op tptp.e2) tptp.e2)))) (let ((_let_3 (@ tptp.qmltpeq (@ (@ tptp.op tptp.e1) tptp.e1)))) (let ((_let_4 (@ tptp.qmltpeq (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mvalid (@ (@ tptp.mor (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_4 tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_3 tptp.e0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 tptp.e0))) (@ tptp.mbox_s4 (@ _let_1 tptp.e0)))))) (@ (@ tptp.mor (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_4 tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_3 tptp.e1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 tptp.e1))) (@ tptp.mbox_s4 (@ _let_1 tptp.e1)))))) (@ (@ tptp.mor (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_4 tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_3 tptp.e2))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 tptp.e2))) (@ tptp.mbox_s4 (@ _let_1 tptp.e2)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_4 tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_3 tptp.e3))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 tptp.e3))) (@ tptp.mbox_s4 (@ _let_1 tptp.e3))))))))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e2) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e3) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e1) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e3) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e1) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e2) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e2) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e3) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e0) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e3) tptp.e0))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e0) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e2) tptp.e0))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e1) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e3) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e3) tptp.e3)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e0) tptp.e3))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e3) tptp.e0))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e0) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e1) tptp.e0))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e1) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e0) (@ (@ tptp.op tptp.e2) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e2) tptp.e2)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e0) tptp.e2))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e1) (@ (@ tptp.op tptp.e2) tptp.e0))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e1) tptp.e1)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e0) tptp.e1))))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e3) (@ (@ tptp.op tptp.e0) tptp.e0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.e2) (@ (@ tptp.op tptp.e1) tptp.e0))))))))
% 0.23/0.60 (set-info :filename cvc5---1.0.5_18023)
% 0.23/0.60 (check-sat)
% 0.23/0.60 ------- get file name : TPTP file name is ALG023^7
% 0.23/0.60 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18023.smt2...
% 0.23/0.60 --- Run --ho-elim --full-saturate-quant at 10...
% 10.53/10.73 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 20.63/20.85 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 30.75/30.95 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.71/35.98 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.87/41.08 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 50.92/51.22 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 61.04/61.44 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 71.35/71.57 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 81.38/81.69 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.74/300.22 /export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 18236 Alarm clock ( read result; case "$result" in
% 299.74/300.22 unsat)
% 299.74/300.22 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.74/300.22 ;;
% 299.74/300.22 sat)
% 299.74/300.22 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.74/300.22 ;;
% 299.74/300.22 esac; exit 1 )
% 299.74/300.22 % cvc5---1.0.5 exiting
% 299.74/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------