TSTP Solution File: SWV097^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV097^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:49:18 EDT 2023
% Result : Theorem 1.30s 1.56s
% Output : Proof 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : SWV097^7 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.17 % Command : do_cvc5 %s %d
% 0.18/0.38 % Computer : n013.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Tue Aug 29 04:30:46 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 % File : SWV097^7 : TPTP v8.1.2. Released v5.5.0.
% 0.23/0.54 % Domain : Software Verification
% 0.23/0.54 % Problem : Unsimplified proof obligation quaternion_ds1_inuse_0009
% 0.23/0.54 % Version : [Ben12] axioms.
% 0.23/0.54 % English :
% 0.23/0.54
% 0.23/0.54 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.23/0.54 % : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% 0.23/0.54 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.23/0.54 % Source : [Ben12]
% 0.23/0.54 % Names : s4-cumul-GSV097+1 [Ben12]
% 0.23/0.54
% 0.23/0.54 % Status : Theorem
% 0.23/0.54 % Rating : 0.54 v8.1.0, 0.73 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0
% 0.23/0.54 % Syntax : Number of formulae : 292 ( 70 unt; 78 typ; 32 def)
% 0.23/0.54 % Number of atoms : 2301 ( 36 equ; 0 cnn)
% 0.23/0.54 % Maximal formula atoms : 267 ( 10 avg)
% 0.23/0.54 % Number of connectives : 3867 ( 5 ~; 5 |; 9 &;3838 @)
% 0.23/0.54 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.23/0.54 % Maximal formula depth : 52 ( 12 avg)
% 0.23/0.54 % Number of types : 3 ( 1 usr)
% 0.23/0.54 % Number of type conns : 231 ( 231 >; 0 *; 0 +; 0 <<)
% 0.23/0.54 % Number of symbols : 88 ( 86 usr; 29 con; 0-4 aty)
% 0.23/0.54 % Number of variables : 501 ( 385 ^; 109 !; 7 ?; 501 :)
% 0.23/0.54 % SPC : TH0_THM_EQU_NAR
% 0.23/0.54
% 0.23/0.54 % Comments : Goedel translation of SWV097+1
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %----Include axioms for Modal logic S4 under cumulative domains
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %----Declaration of additional base type mu
% 0.23/0.54 thf(mu_type,type,
% 0.23/0.54 mu: $tType ).
% 0.23/0.54
% 0.23/0.54 %----Equality
% 0.23/0.54 thf(qmltpeq_type,type,
% 0.23/0.54 qmltpeq: mu > mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 % originale Definition
% 0.23/0.54 %thf(qmltpeq,definition,
% 0.23/0.54 % ( qmltpeq
% 0.23/0.54 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.23/0.54
% 0.23/0.54 % erweiterte Leibnitz-Definition
% 0.23/0.54 %thf(qmltpeq,definition,
% 0.23/0.54 % ( qmltpeq
% 0.23/0.54 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.23/0.54
% 0.23/0.54 % Leibnitz-Definition
% 0.23/0.54 %thf(qmltpeq,definition,
% 0.23/0.54 % ( qmltpeq
% 0.23/0.54 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.23/0.54
% 0.23/0.54 thf(meq_prop_type,type,
% 0.23/0.54 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(meq_prop,definition,
% 0.23/0.54 ( meq_prop
% 0.23/0.54 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.23/0.54 ( ( X @ W )
% 0.23/0.54 = ( Y @ W ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Modal operators not, or, box, Pi
% 0.23/0.54 thf(mnot_type,type,
% 0.23/0.54 mnot: ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mnot,definition,
% 0.23/0.54 ( mnot
% 0.23/0.54 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.54 ~ ( Phi @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mor_type,type,
% 0.23/0.54 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mor,definition,
% 0.23/0.54 ( mor
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.23/0.54 ( ( Phi @ W )
% 0.23/0.54 | ( Psi @ W ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mbox_type,type,
% 0.23/0.54 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mbox,definition,
% 0.23/0.54 ( mbox
% 0.23/0.54 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.23/0.54 ! [V: $i] :
% 0.23/0.54 ( ~ ( R @ W @ V )
% 0.23/0.54 | ( Phi @ V ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mforall_prop_type,type,
% 0.23/0.54 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mforall_prop,definition,
% 0.23/0.54 ( mforall_prop
% 0.23/0.54 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.23/0.54 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Further modal operators
% 0.23/0.54 thf(mtrue_type,type,
% 0.23/0.54 mtrue: $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mtrue,definition,
% 0.23/0.54 ( mtrue
% 0.23/0.54 = ( ^ [W: $i] : $true ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mfalse_type,type,
% 0.23/0.54 mfalse: $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mfalse,definition,
% 0.23/0.54 ( mfalse
% 0.23/0.54 = ( mnot @ mtrue ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mand_type,type,
% 0.23/0.54 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mand,definition,
% 0.23/0.54 ( mand
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mimplies_type,type,
% 0.23/0.54 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mimplies,definition,
% 0.23/0.54 ( mimplies
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mimplied_type,type,
% 0.23/0.54 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mimplied,definition,
% 0.23/0.54 ( mimplied
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mequiv_type,type,
% 0.23/0.54 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mequiv,definition,
% 0.23/0.54 ( mequiv
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mxor_type,type,
% 0.23/0.54 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mxor,definition,
% 0.23/0.54 ( mxor
% 0.23/0.54 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mdia_type,type,
% 0.23/0.54 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mdia,definition,
% 0.23/0.54 ( mdia
% 0.23/0.54 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %--- (new for cumulative)
% 0.23/0.54 %---Declaration of existence predicate for simulating cumulative domain
% 0.23/0.54 thf(exists_in_world_type,type,
% 0.23/0.54 exists_in_world: mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 %----The domains are non-empty
% 0.23/0.54 thf(nonempty_ax,axiom,
% 0.23/0.54 ! [V: $i] :
% 0.23/0.54 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(mforall_ind_type,type,
% 0.23/0.54 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 %--- (new for cumulative)
% 0.23/0.54 thf(mforall_ind,definition,
% 0.23/0.54 ( mforall_ind
% 0.23/0.54 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.54 ! [X: mu] :
% 0.23/0.54 ( ( exists_in_world @ X @ W )
% 0.23/0.54 => ( Phi @ X @ W ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %thf(mforall_ind,definition,
% 0.23/0.54 % ( mforall_ind
% 0.23/0.54 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.54 % ! [X: mu] :
% 0.23/0.54 % ( Phi @ X @ W ) ) )).
% 0.23/0.54
% 0.23/0.54 thf(mexists_ind_type,type,
% 0.23/0.54 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mexists_ind,definition,
% 0.23/0.54 ( mexists_ind
% 0.23/0.54 = ( ^ [Phi: mu > $i > $o] :
% 0.23/0.54 ( mnot
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mexists_prop_type,type,
% 0.23/0.54 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mexists_prop,definition,
% 0.23/0.54 ( mexists_prop
% 0.23/0.54 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.23/0.54 ( mnot
% 0.23/0.54 @ ( mforall_prop
% 0.23/0.54 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Definition of properties of accessibility relations
% 0.23/0.54 thf(mreflexive_type,type,
% 0.23/0.54 mreflexive: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mreflexive,definition,
% 0.23/0.54 ( mreflexive
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(msymmetric_type,type,
% 0.23/0.54 msymmetric: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(msymmetric,definition,
% 0.23/0.54 ( msymmetric
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i] :
% 0.23/0.54 ( ( R @ S @ T )
% 0.23/0.54 => ( R @ T @ S ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mserial_type,type,
% 0.23/0.54 mserial: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mserial,definition,
% 0.23/0.54 ( mserial
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i] :
% 0.23/0.54 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mtransitive_type,type,
% 0.23/0.54 mtransitive: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mtransitive,definition,
% 0.23/0.54 ( mtransitive
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( ( R @ S @ T )
% 0.23/0.54 & ( R @ T @ U ) )
% 0.23/0.54 => ( R @ S @ U ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(meuclidean_type,type,
% 0.23/0.54 meuclidean: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(meuclidean,definition,
% 0.23/0.54 ( meuclidean
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( ( R @ S @ T )
% 0.23/0.54 & ( R @ S @ U ) )
% 0.23/0.54 => ( R @ T @ U ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mpartially_functional_type,type,
% 0.23/0.54 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mpartially_functional,definition,
% 0.23/0.54 ( mpartially_functional
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( ( R @ S @ T )
% 0.23/0.54 & ( R @ S @ U ) )
% 0.23/0.54 => ( T = U ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mfunctional_type,type,
% 0.23/0.54 mfunctional: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mfunctional,definition,
% 0.23/0.54 ( mfunctional
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i] :
% 0.23/0.54 ? [T: $i] :
% 0.23/0.54 ( ( R @ S @ T )
% 0.23/0.54 & ! [U: $i] :
% 0.23/0.54 ( ( R @ S @ U )
% 0.23/0.54 => ( T = U ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_dense_type,type,
% 0.23/0.54 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_dense,definition,
% 0.23/0.54 ( mweakly_dense
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( R @ S @ T )
% 0.23/0.54 => ? [U: $i] :
% 0.23/0.54 ( ( R @ S @ U )
% 0.23/0.54 & ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_connected_type,type,
% 0.23/0.54 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_connected,definition,
% 0.23/0.54 ( mweakly_connected
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( ( R @ S @ T )
% 0.23/0.54 & ( R @ S @ U ) )
% 0.23/0.54 => ( ( R @ T @ U )
% 0.23/0.54 | ( T = U )
% 0.23/0.54 | ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_directed_type,type,
% 0.23/0.54 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mweakly_directed,definition,
% 0.23/0.54 ( mweakly_directed
% 0.23/0.54 = ( ^ [R: $i > $i > $o] :
% 0.23/0.54 ! [S: $i,T: $i,U: $i] :
% 0.23/0.54 ( ( ( R @ S @ T )
% 0.23/0.54 & ( R @ S @ U ) )
% 0.23/0.54 => ? [V: $i] :
% 0.23/0.54 ( ( R @ T @ V )
% 0.23/0.54 & ( R @ U @ V ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Definition of validity
% 0.23/0.54 thf(mvalid_type,type,
% 0.23/0.54 mvalid: ( $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mvalid,definition,
% 0.23/0.54 ( mvalid
% 0.23/0.54 = ( ^ [Phi: $i > $o] :
% 0.23/0.54 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Definition of satisfiability
% 0.23/0.54 thf(msatisfiable_type,type,
% 0.23/0.54 msatisfiable: ( $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(msatisfiable,definition,
% 0.23/0.54 ( msatisfiable
% 0.23/0.54 = ( ^ [Phi: $i > $o] :
% 0.23/0.54 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Definition of countersatisfiability
% 0.23/0.54 thf(mcountersatisfiable_type,type,
% 0.23/0.54 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mcountersatisfiable,definition,
% 0.23/0.54 ( mcountersatisfiable
% 0.23/0.54 = ( ^ [Phi: $i > $o] :
% 0.23/0.54 ? [W: $i] :
% 0.23/0.54 ~ ( Phi @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----Definition of invalidity
% 0.23/0.54 thf(minvalid_type,type,
% 0.23/0.54 minvalid: ( $i > $o ) > $o ).
% 0.23/0.54
% 0.23/0.54 thf(minvalid,definition,
% 0.23/0.54 ( minvalid
% 0.23/0.54 = ( ^ [Phi: $i > $o] :
% 0.23/0.54 ! [W: $i] :
% 0.23/0.54 ~ ( Phi @ W ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %----We reserve an accessibility relation constant rel_s4
% 0.23/0.54 thf(rel_s4_type,type,
% 0.23/0.54 rel_s4: $i > $i > $o ).
% 0.23/0.54
% 0.23/0.54 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.23/0.54 thf(mbox_s4_type,type,
% 0.23/0.54 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mbox_s4,definition,
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.54 ! [V: $i] :
% 0.23/0.54 ( ~ ( rel_s4 @ W @ V )
% 0.23/0.54 | ( Phi @ V ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(mdia_s4_type,type,
% 0.23/0.54 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(mdia_s4,definition,
% 0.23/0.54 ( mdia_s4
% 0.23/0.54 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %----We have now two options for stating the B conditions:
% 0.23/0.54 %----We can (i) directly formulate conditions for the accessibility relation
% 0.23/0.54 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.23/0.54 thf(a1,axiom,
% 0.23/0.54 mreflexive @ rel_s4 ).
% 0.23/0.54
% 0.23/0.54 thf(a2,axiom,
% 0.23/0.54 mtransitive @ rel_s4 ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 thf(cumulative_ax,axiom,
% 0.23/0.54 ! [X: mu,V: $i,W: $i] :
% 0.23/0.54 ( ( ( exists_in_world @ X @ V )
% 0.23/0.54 & ( rel_s4 @ V @ W ) )
% 0.23/0.54 => ( exists_in_world @ X @ W ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 thf(true_type,type,
% 0.23/0.54 true: $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(lt_type,type,
% 0.23/0.54 lt: mu > mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(geq_type,type,
% 0.23/0.54 geq: mu > mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(gt_type,type,
% 0.23/0.54 gt: mu > mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(leq_type,type,
% 0.23/0.54 leq: mu > mu > $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(uniform_int_rnd_type,type,
% 0.23/0.54 uniform_int_rnd: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_uniform_int_rnd_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( uniform_int_rnd @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array1_type,type,
% 0.23/0.54 tptp_const_array1: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_const_array1_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_const_array1 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(dim_type,type,
% 0.23/0.54 dim: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_dim_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( dim @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array2_type,type,
% 0.23/0.54 tptp_const_array2: mu > mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_const_array2_ax,axiom,
% 0.23/0.54 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_const_array2 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(inv_type,type,
% 0.23/0.54 inv: mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_inv_ax,axiom,
% 0.23/0.54 ! [V: $i,V1: mu] : ( exists_in_world @ ( inv @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_msub_type,type,
% 0.23/0.54 tptp_msub: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_msub_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_msub @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(trans_type,type,
% 0.23/0.54 trans: mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_trans_ax,axiom,
% 0.23/0.54 ! [V: $i,V1: mu] : ( exists_in_world @ ( trans @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_mmul_type,type,
% 0.23/0.54 tptp_mmul: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_mmul_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_mmul @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_madd_type,type,
% 0.23/0.54 tptp_madd: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_madd_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_madd @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_type,type,
% 0.23/0.54 sum: mu > mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_sum_ax,axiom,
% 0.23/0.54 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( sum @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_float_0_0_type,type,
% 0.23/0.54 tptp_float_0_0: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_float_0_0_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ tptp_float_0_0 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(plus_type,type,
% 0.23/0.54 plus: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_plus_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( plus @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(pred_type,type,
% 0.23/0.54 pred: mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_pred_ax,axiom,
% 0.23/0.54 ! [V: $i,V1: mu] : ( exists_in_world @ ( pred @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update3_type,type,
% 0.23/0.54 tptp_update3: mu > mu > mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_update3_ax,axiom,
% 0.23/0.54 ! [V: $i,V4: mu,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_update3 @ V4 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update2_type,type,
% 0.23/0.54 tptp_update2: mu > mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_update2_ax,axiom,
% 0.23/0.54 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_update2 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(def_type,type,
% 0.23/0.54 def: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_def_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ def @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(z_defuse_type,type,
% 0.23/0.54 z_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_z_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ z_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(minus_type,type,
% 0.23/0.54 minus: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_minus_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( minus @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(pv5_type,type,
% 0.23/0.54 pv5: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_pv5_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ pv5 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(xinit_noise_defuse_type,type,
% 0.23/0.54 xinit_noise_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_xinit_noise_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ xinit_noise_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(xinit_mean_defuse_type,type,
% 0.23/0.54 xinit_mean_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_xinit_mean_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ xinit_mean_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(xinit_defuse_type,type,
% 0.23/0.54 xinit_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_xinit_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ xinit_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(u_defuse_type,type,
% 0.23/0.54 u_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_u_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ u_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select3_type,type,
% 0.23/0.54 a_select3: mu > mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_a_select3_ax,axiom,
% 0.23/0.54 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( a_select3 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(sigma_defuse_type,type,
% 0.23/0.54 sigma_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_sigma_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ sigma_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(use_type,type,
% 0.23/0.54 use: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_use_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ use @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(rho_defuse_type,type,
% 0.23/0.54 rho_defuse: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_rho_defuse_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ rho_defuse @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select2_type,type,
% 0.23/0.54 a_select2: mu > mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_a_select2_ax,axiom,
% 0.23/0.54 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( a_select2 @ V2 @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_minus_1_type,type,
% 0.23/0.54 tptp_minus_1: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_tptp_minus_1_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ tptp_minus_1 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n999_type,type,
% 0.23/0.54 n999: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n999_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n999 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n4_type,type,
% 0.23/0.54 n4: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n4_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n4 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n5_type,type,
% 0.23/0.54 n5: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n5_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n5 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n1_type,type,
% 0.23/0.54 n1: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n1_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n1 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n2_type,type,
% 0.23/0.54 n2: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n2_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n2 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n3_type,type,
% 0.23/0.54 n3: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n3_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n3 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(n0_type,type,
% 0.23/0.54 n0: mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_n0_ax,axiom,
% 0.23/0.54 ! [V: $i] : ( exists_in_world @ n0 @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_type,type,
% 0.23/0.54 succ: mu > mu ).
% 0.23/0.54
% 0.23/0.54 thf(existence_of_succ_ax,axiom,
% 0.23/0.54 ! [V: $i,V1: mu] : ( exists_in_world @ ( succ @ V1 ) @ V ) ).
% 0.23/0.54
% 0.23/0.54 thf(reflexivity,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(symmetry,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(transitivity,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select2_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ A @ C ) @ ( a_select2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select2_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ C @ A ) @ ( a_select2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select3_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ C @ D ) @ ( a_select3 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select3_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ C @ A @ D ) @ ( a_select3 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(a_select3_substitution_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ C @ D @ A ) @ ( a_select3 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(dim_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( dim @ A @ C ) @ ( dim @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(dim_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( dim @ C @ A ) @ ( dim @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(inv_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(minus_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( minus @ A @ C ) @ ( minus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(minus_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( minus @ C @ A ) @ ( minus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(plus_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( plus @ A @ C ) @ ( plus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(plus_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( plus @ C @ A ) @ ( plus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(pred_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( pred @ A ) @ ( pred @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( succ @ A ) @ ( succ @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ A @ C @ D ) @ ( sum @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ C @ A @ D ) @ ( sum @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_substitution_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ C @ D @ A ) @ ( sum @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array1_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array1 @ A @ C ) @ ( tptp_const_array1 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array1_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array1 @ C @ A ) @ ( tptp_const_array1 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array2_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array2 @ A @ C @ D ) @ ( tptp_const_array2 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array2_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array2 @ C @ A @ D ) @ ( tptp_const_array2 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_const_array2_substitution_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array2 @ C @ D @ A ) @ ( tptp_const_array2 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_madd_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_madd @ A @ C ) @ ( tptp_madd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_madd_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_madd @ C @ A ) @ ( tptp_madd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_mmul_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_mmul @ A @ C ) @ ( tptp_mmul @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_mmul_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_mmul @ C @ A ) @ ( tptp_mmul @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_msub_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_msub @ A @ C ) @ ( tptp_msub @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_msub_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_msub @ C @ A ) @ ( tptp_msub @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update2_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ A @ C @ D ) @ ( tptp_update2 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update2_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ C @ A @ D ) @ ( tptp_update2 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update2_substitution_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ C @ D @ A ) @ ( tptp_update2 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update3_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [E: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update3 @ A @ C @ D @ E ) @ ( tptp_update3 @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update3_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [E: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update3 @ C @ A @ D @ E ) @ ( tptp_update3 @ C @ B @ D @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update3_substitution_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [E: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update3 @ C @ D @ A @ E ) @ ( tptp_update3 @ C @ D @ B @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tptp_update3_substitution_4,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [E: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update3 @ C @ D @ E @ A ) @ ( tptp_update3 @ C @ D @ E @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(trans_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( trans @ A ) @ ( trans @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(uniform_int_rnd_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( uniform_int_rnd @ A @ C ) @ ( uniform_int_rnd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(uniform_int_rnd_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( uniform_int_rnd @ C @ A ) @ ( uniform_int_rnd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(geq_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( geq @ A @ C ) ) ) @ ( mbox_s4 @ ( geq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(geq_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( geq @ C @ A ) ) ) @ ( mbox_s4 @ ( geq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( gt @ A @ C ) ) ) @ ( mbox_s4 @ ( gt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( gt @ C @ A ) ) ) @ ( mbox_s4 @ ( gt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( leq @ A @ C ) ) ) @ ( mbox_s4 @ ( leq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( leq @ C @ A ) ) ) @ ( mbox_s4 @ ( leq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(lt_substitution_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( lt @ A @ C ) ) ) @ ( mbox_s4 @ ( lt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(lt_substitution_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( lt @ C @ A ) ) ) @ ( mbox_s4 @ ( lt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(totality,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mor @ ( mbox_s4 @ ( gt @ X @ Y ) ) @ ( mor @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(transitivity_gt,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( gt @ X @ Y ) ) @ ( mbox_s4 @ ( gt @ Y @ Z ) ) ) @ ( mbox_s4 @ ( gt @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(irreflexivity_gt,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ X @ X ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(reflexivity_leq,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( leq @ X @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(transitivity_leq,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( leq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(lt_gt,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( lt @ X @ Y ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( lt @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_geq,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( geq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ Y @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ Y @ X ) ) @ ( mbox_s4 @ ( geq @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_gt1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( leq @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_gt2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_gt_pred,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ X @ ( pred @ Y ) ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( leq @ X @ ( pred @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_succ,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( gt @ ( succ @ X ) @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_succ,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ X @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_succ_gt_equiv,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( gt @ ( succ @ Y ) @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ ( succ @ Y ) @ X ) ) @ ( mbox_s4 @ ( leq @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(uniform_int_rand_ranges_hi,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(uniform_int_rand_ranges_lo,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(const_array1_select,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [L: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Val: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ L @ I ) ) @ ( mbox_s4 @ ( leq @ I @ U ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_const_array1 @ ( dim @ L @ U ) @ Val ) @ I ) @ Val ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(const_array2_select,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [L1: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U1: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [L2: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U2: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Val: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ L1 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ U1 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ L2 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ U2 ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_const_array2 @ ( dim @ L1 @ U1 ) @ ( dim @ L2 @ U2 ) @ Val ) @ I @ J ) @ Val ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_trans,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( trans @ A ) @ I @ J ) @ ( a_select3 @ ( trans @ A ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_inv,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( inv @ A ) @ I @ J ) @ ( a_select3 @ ( inv @ A ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_update_diagonal,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [K: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mand @ ( mbox_s4 @ ( leq @ J @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ K ) ) @ ( mbox_s4 @ ( leq @ K @ N ) ) ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ A @ K @ K @ VAL ) @ I @ J ) @ ( a_select3 @ ( tptp_update3 @ A @ K @ K @ VAL ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_add,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_madd @ A @ B ) @ I @ J ) @ ( a_select3 @ ( tptp_madd @ A @ B ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_sub,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_msub @ A @ B ) @ I @ J ) @ ( a_select3 @ ( tptp_msub @ A @ B ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_aba1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_aba2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [M: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ M ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ M ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(matrix_symm_joseph_update,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [E: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [F: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [N: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [M: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ M ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ M ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ D @ I @ J ) @ ( a_select3 @ D @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ F @ I @ J ) @ ( a_select3 @ F @ J @ I ) ) ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ N ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ N ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_plus_base,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Body: mu] : ( mbox_s4 @ ( qmltpeq @ ( sum @ n0 @ tptp_minus_1 @ Body ) @ n0 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sum_plus_base_float,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Body: mu] : ( mbox_s4 @ ( qmltpeq @ tptp_float_0_0 @ ( sum @ n0 @ tptp_minus_1 @ Body ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ tptp_minus_1 ) @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_1_r,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n1 ) @ ( succ @ X ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_1_l,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n1 @ X ) @ ( succ @ X ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_2_r,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n2 ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_2_l,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n2 @ X ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_3_r,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n3 ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_3_l,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n3 @ X ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_4_r,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n4 ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_4_l,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n4 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_5_r,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n5 ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_plus_5_l,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n5 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(pred_minus_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( minus @ X @ n1 ) @ ( pred @ X ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(pred_succ,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( pred @ ( succ @ X ) ) @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(succ_pred,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( succ @ ( pred @ X ) ) @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_succ_succ,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) @ ( mbox_s4 @ ( leq @ X @ Y ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_succ_gt,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ ( succ @ X ) @ Y ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(leq_minus,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ ( minus @ X @ Y ) @ X ) ) @ ( mbox_s4 @ ( leq @ n0 @ Y ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel3_update_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [V: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] : ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ U @ V ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel3_update_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [V: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL2: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ I @ U ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ J @ V ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ X @ U @ V ) @ VAL ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ I @ J @ VAL2 ) @ U @ V ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel3_update_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [V: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I0: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [J0: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I0 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J0 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I0 @ U ) ) @ ( mbox_s4 @ ( leq @ J0 @ V ) ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ X @ I0 @ J0 ) @ VAL ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ U ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ V ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ I @ J ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel2_update_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] : ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U ) @ VAL ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel2_update_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL2: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ I @ U ) ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ X @ U ) @ VAL ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ I @ VAL2 ) @ U ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(sel2_update_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [U: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [VAL: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [I0: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I0 ) ) @ ( mbox_s4 @ ( leq @ I0 @ U ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ X @ I0 ) @ VAL ) ) ) ) ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mbox_s4 @ ( leq @ I @ U ) ) ) )
% 0.23/0.54 @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ttrue,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ true ) ).
% 0.23/0.54
% 0.23/0.54 thf(defuse,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ def @ use ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_4,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n4 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_4,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n4 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_5,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n5 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_4_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n4 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_0_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n0 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_1_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n1 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_2_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n2 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_3_tptp_minus_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n3 @ tptp_minus_1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_4_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_1_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n1 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_2_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n2 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_3_0,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n0 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_4_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_2_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n2 @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_3_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_4_2,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n2 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_2,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n2 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_2,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n2 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_3_2,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n2 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_4_3,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n3 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_5_3,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n3 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(gt_999_3,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( gt @ n999 @ n3 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_4,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n4 ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n2 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n3 ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_5,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n5 ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n2 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n3 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n4 ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n5 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_0,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_1,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n1 ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n1 ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_2,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n2 ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n1 ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n2 ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(finite_domain_3,axiom,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n3 ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ X @ n2 ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n3 ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(successor_4,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) @ n4 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(successor_5,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) @ n5 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(successor_1,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ n0 ) @ n1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(successor_2,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ n0 ) ) @ n2 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(successor_3,axiom,
% 0.23/0.54 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ n0 ) ) ) @ n3 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(quaternion_ds1_inuse_0009,conjecture,
% 0.23/0.54 ( mvalid
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mimplies
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv5 ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( leq @ pv5 @ ( minus @ n999 @ n1 ) ) )
% 0.23/0.54 @ ( mand
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [A: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ A ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ B ) ) @ ( mand @ ( mbox_s4 @ ( leq @ A @ n2 ) ) @ ( mbox_s4 @ ( leq @ B @ pv5 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ A @ B ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ A @ B ) @ use ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [C: mu] :
% 0.23/0.54 ( mbox_s4
% 0.23/0.54 @ ( mforall_ind
% 0.23/0.54 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ C ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ D ) ) @ ( mand @ ( mbox_s4 @ ( leq @ C @ n2 ) ) @ ( mbox_s4 @ ( leq @ D @ ( minus @ pv5 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ C @ D ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ C @ D ) @ use ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use ) )
% 0.23/0.54 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv5 ) )
% 0.23/0.59 @ ( mand @ ( mbox_s4 @ ( leq @ pv5 @ ( minus @ n999 @ n1 ) ) )
% 0.23/0.59 @ ( mand
% 0.23/0.59 @ ( mbox_s4
% 0.23/0.59 @ ( mforall_ind
% 0.23/0.59 @ ^ [E: mu] :
% 0.23/0.59 ( mbox_s4
% 0.23/0.59 @ ( mforall_ind
% 0.23/0.59 @ ^ [F: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ E ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ F ) ) @ ( mand @ ( mbox_s4 @ ( leq @ E @ n2 ) ) @ ( mbox_s4 @ ( leq @ F @ pv5 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ E @ F ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ E @ F ) @ use ) ) ) ) ) ) ) ) )
% 0.23/0.59 @ ( mbox_s4
% 0.23/0.59 @ ( mforall_ind
% 0.23/0.59 @ ^ [G: mu] :
% 0.23/0.59 ( mbox_s4
% 0.23/0.59 @ ( mforall_ind
% 0.23/0.59 @ ^ [H: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ G ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ H ) ) @ ( mand @ ( mbox_s4 @ ( leq @ G @ n2 ) ) @ ( mbox_s4 @ ( leq @ H @ ( minus @ pv5 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ G @ H ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ G @ H ) @ use ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.KgnkhVkhTC/cvc5---1.0.5_28716.p...
% 0.23/0.59 (declare-sort $$unsorted 0)
% 0.23/0.59 (declare-sort tptp.mu 0)
% 0.23/0.59 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.23/0.59 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.23/0.59 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.23/0.59 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.23/0.59 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.23/0.59 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.23/0.59 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.23/0.59 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.59 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.23/0.59 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.23/0.59 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.23/0.59 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.23/0.59 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.23/0.59 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.23/0.59 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.23/0.59 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.23/0.59 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.23/0.59 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.23/0.59 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.23/0.59 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.23/0.59 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.23/0.59 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.23/0.59 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.59 (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)))))))))
% 0.23/0.59 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.59 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.59 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.59 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.59 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.59 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.23/0.59 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.59 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.23/0.59 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.23/0.59 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.23/0.59 (declare-fun tptp.true ($$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.lt (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.geq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.gt (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.leq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.59 (declare-fun tptp.uniform_int_rnd (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.uniform_int_rnd V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_const_array1 (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_const_array1 V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.dim (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.dim V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_const_array2 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_const_array2 V3) V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.inv (tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inv V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_msub (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_msub V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.trans (tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.trans V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_mmul (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_mmul V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_madd (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_madd V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.sum (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.sum V3) V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_float_0_0 () tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_float_0_0) V)))
% 0.23/0.59 (declare-fun tptp.plus (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.plus V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.pred (tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.pred V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_update3 (tptp.mu tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V4 tptp.mu) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ (@ tptp.tptp_update3 V4) V3) V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.tptp_update2 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_update2 V3) V2) V1)) V)))
% 0.23/0.59 (declare-fun tptp.def () tptp.mu)
% 0.23/0.59 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.def) V)))
% 0.23/0.59 (declare-fun tptp.z_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.z_defuse) V)))
% 0.23/0.60 (declare-fun tptp.minus (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.minus V2) V1)) V)))
% 0.23/0.60 (declare-fun tptp.pv5 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.pv5) V)))
% 0.23/0.60 (declare-fun tptp.xinit_noise_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_noise_defuse) V)))
% 0.23/0.60 (declare-fun tptp.xinit_mean_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_mean_defuse) V)))
% 0.23/0.60 (declare-fun tptp.xinit_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_defuse) V)))
% 0.23/0.60 (declare-fun tptp.u_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.u_defuse) V)))
% 0.23/0.60 (declare-fun tptp.a_select3 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.a_select3 V3) V2) V1)) V)))
% 0.23/0.60 (declare-fun tptp.sigma_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.sigma_defuse) V)))
% 0.23/0.60 (declare-fun tptp.use () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.use) V)))
% 0.23/0.60 (declare-fun tptp.rho_defuse () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.rho_defuse) V)))
% 0.23/0.60 (declare-fun tptp.a_select2 (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.a_select2 V2) V1)) V)))
% 0.23/0.60 (declare-fun tptp.tptp_minus_1 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_minus_1) V)))
% 0.23/0.60 (declare-fun tptp.n999 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n999) V)))
% 0.23/0.60 (declare-fun tptp.n4 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n4) V)))
% 0.23/0.60 (declare-fun tptp.n5 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n5) V)))
% 0.23/0.60 (declare-fun tptp.n1 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n1) V)))
% 0.23/0.60 (declare-fun tptp.n2 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n2) V)))
% 0.23/0.60 (declare-fun tptp.n3 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n3) V)))
% 0.23/0.60 (declare-fun tptp.n0 () tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n0) V)))
% 0.23/0.60 (declare-fun tptp.succ (tptp.mu) tptp.mu)
% 0.23/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.succ V1)) V)))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 A) C)) (@ (@ tptp.a_select2 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 $$unsorted)) (let ((_let_1 (@ tptp.a_select2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 A) C) D)) (@ (@ (@ tptp.a_select3 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.a_select3 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.dim A) C)) (@ (@ tptp.dim 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 $$unsorted)) (let ((_let_1 (@ tptp.dim C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.minus A) C)) (@ (@ tptp.minus 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 $$unsorted)) (let ((_let_1 (@ tptp.minus C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.plus A) C)) (@ (@ tptp.plus 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 $$unsorted)) (let ((_let_1 (@ tptp.plus C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.pred A)) (@ tptp.pred B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ A)) (@ tptp.succ B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.sum A) C) D)) (@ (@ (@ tptp.sum B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.sum C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.sum C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.tptp_const_array1 A) C)) (@ (@ tptp.tptp_const_array1 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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_const_array1 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.tptp_const_array2 A) C) D)) (@ (@ (@ tptp.tptp_const_array2 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.tptp_const_array2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.tptp_const_array2 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.tptp_madd A) C)) (@ (@ tptp.tptp_madd 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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_madd C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.tptp_mmul A) C)) (@ (@ tptp.tptp_mmul 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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_mmul C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.tptp_msub A) C)) (@ (@ tptp.tptp_msub 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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_msub C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.tptp_update2 A) C) D)) (@ (@ (@ tptp.tptp_update2 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.tptp_update2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.tptp_update2 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ (@ tptp.tptp_update3 A) C) D) E)) (@ (@ (@ (@ tptp.tptp_update3 B) C) D) E))))) __flatten_var_0)))) __flatten_var_0)))) __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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.tptp_update3 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ _let_1 A) D) E)) (@ (@ (@ _let_1 B) D) E))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.tptp_update3 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) E)) (@ (@ _let_1 B) E))))) __flatten_var_0))))) __flatten_var_0)))) __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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.tptp_update3 C) D) E))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.trans A)) (@ tptp.trans B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.uniform_int_rnd A) C)) (@ (@ tptp.uniform_int_rnd 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 $$unsorted)) (let ((_let_1 (@ tptp.uniform_int_rnd C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.geq A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.geq 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 $$unsorted)) (let ((_let_1 (@ tptp.geq C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.gt A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.gt 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 $$unsorted)) (let ((_let_1 (@ tptp.gt C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.leq A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.leq 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 $$unsorted)) (let ((_let_1 (@ tptp.leq C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.lt A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.lt 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 $$unsorted)) (let ((_let_1 (@ tptp.lt C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 (@ (@ tptp.gt X) Y))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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.gt X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ (@ tptp.gt 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 ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.gt X) X)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.leq 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.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ (@ tptp.leq Y) Z)))) (@ tptp.mbox_s4 (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.lt X) Y)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.geq X) Y)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.leq Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y)))))) (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq X) (@ tptp.pred Y))))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.gt (@ tptp.succ 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)) (let ((_let_1 (@ tptp.leq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ _let_1 (@ tptp.succ Y))))) __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)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.gt (@ tptp.succ Y)) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq (@ (@ tptp.uniform_int_rnd C) X)) 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ _let_1 X))) (@ tptp.mbox_s4 (@ _let_1 (@ (@ tptp.uniform_int_rnd C) X))))) __flatten_var_0))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((L tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Val tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq L) I))) (@ tptp.mbox_s4 (@ (@ tptp.leq I) U)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ tptp.tptp_const_array1 (@ (@ tptp.dim L) U)) Val)) I)) Val)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((L1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U1 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((L2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Val tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq L1) I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) U1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq L2) J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) U2)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ tptp.tptp_const_array2 (@ (@ tptp.dim L1) U1)) (@ (@ tptp.dim L2) U2)) Val)) I) J)) Val)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ tptp.trans A)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ tptp.inv A)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((K tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 A) K) K) VAL)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq J) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 K))) (@ tptp.mbox_s4 (@ (@ tptp.leq K) N)))))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 B))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_madd A) B)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __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 ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 B))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_msub A) B)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 B))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_mmul A) (@ (@ tptp.tptp_mmul B) (@ tptp.trans A)))))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __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 ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((M tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 B))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) M))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) M)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_mmul A) (@ (@ tptp.tptp_mmul B) (@ tptp.trans A)))))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((F tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((N tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((M tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 D))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) M))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) M)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 A))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 F))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0))))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_madd A) (@ (@ tptp.tptp_mmul B) (@ (@ tptp.tptp_mmul (@ (@ tptp.tptp_madd (@ (@ tptp.tptp_mmul C) (@ (@ tptp.tptp_mmul D) (@ tptp.trans C)))) (@ (@ tptp.tptp_mmul E) (@ (@ tptp.tptp_mmul F) (@ tptp.trans E))))) (@ tptp.trans B))))))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body)) tptp.n0)) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.tptp_float_0_0) (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ tptp.tptp_minus_1)) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n1)) (@ tptp.succ X))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n1) X)) (@ tptp.succ X))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n2)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n2) X)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n3)) (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n3) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n4)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n4) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n5)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n5) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.minus X) tptp.n1)) (@ tptp.pred X))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.pred (@ tptp.succ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.pred X))) X)) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) (@ tptp.succ Y))))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) Y))) (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ (@ tptp.minus X) Y)) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) U) V) VAL)) U) V)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq I) U))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq J) V))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 X) U) V)) VAL))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) I) J) VAL2)) U) V)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I0 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J0 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 I0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 J0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I0) U))) (@ tptp.mbox_s4 (@ (@ tptp.leq J0) V)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 X) I0) J0)) VAL)))) __flatten_var_0))))) __flatten_var_0))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) U))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) V))))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) U) V) VAL)) I) J)) VAL)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) U) VAL)) U)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq I) U))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 X) U)) VAL)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) I) VAL2)) U)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I0 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) I0))) (@ tptp.mbox_s4 (@ (@ tptp.leq I0) U)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 X) I0)) VAL)))) __flatten_var_0))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) I))) (@ tptp.mbox_s4 (@ (@ tptp.leq I) U))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) U) VAL)) I)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 tptp.true)))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.def) tptp.use))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n4))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n4))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n5))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n0) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n1) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.tptp_minus_1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n1) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n0))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n2))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n2))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n2))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n2))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n3))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n3))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n999) tptp.n3))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n4)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n3))) (@ tptp.mbox_s4 (@ _let_1 tptp.n4)))))))) __flatten_var_0)))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n5)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n3))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n4))) (@ tptp.mbox_s4 (@ _let_1 tptp.n5))))))))) __flatten_var_0)))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) tptp.n0)))) __flatten_var_0))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n1)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ tptp.mbox_s4 (@ _let_1 tptp.n1))))) __flatten_var_0)))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n2)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ tptp.mbox_s4 (@ _let_1 tptp.n2)))))) __flatten_var_0)))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n3)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ tptp.mbox_s4 (@ _let_1 tptp.n3))))))) __flatten_var_0)))))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0))))) tptp.n4))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0)))))) tptp.n5))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ tptp.n0)) tptp.n1))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ tptp.n0))) tptp.n2))))
% 0.23/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0)))) tptp.n3))))
% 0.23/0.60 (assert (let ((_let_1 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv5) (@ (@ tptp.minus tptp.n999) tptp.n1)))))) (let ((_let_2 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) tptp.pv5))))) (let ((_let_3 (@ tptp.a_select2 tptp.xinit_noise_defuse))) (let ((_let_4 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n5)) tptp.use))))) (let ((_let_5 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n4)) tptp.use))))) (let ((_let_6 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n3)) tptp.use))))) (let ((_let_7 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n2)) tptp.use))))) (let ((_let_8 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n1)) tptp.use))))) (let ((_let_9 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n0)) tptp.use))))) (let ((_let_10 (@ tptp.a_select2 tptp.xinit_mean_defuse))) (let ((_let_11 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n5)) tptp.use))))) (let ((_let_12 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n4)) tptp.use))))) (let ((_let_13 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n3)) tptp.use))))) (let ((_let_14 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n2)) tptp.use))))) (let ((_let_15 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n1)) tptp.use))))) (let ((_let_16 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n0)) tptp.use))))) (let ((_let_17 (@ tptp.a_select2 tptp.xinit_defuse))) (let ((_let_18 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n5)) tptp.use))))) (let ((_let_19 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n4)) tptp.use))))) (let ((_let_20 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n3)) tptp.use))))) (let ((_let_21 (@ tptp.a_select3 tptp.u_defuse))) (let ((_let_22 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n2) tptp.n0)) tptp.use))))) (let ((_let_23 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n1) tptp.n0)) tptp.use))))) (let ((_let_24 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n0) tptp.n0)) tptp.use))))) (let ((_let_25 (@ tptp.a_select2 tptp.sigma_defuse))) (let ((_let_26 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n5)) tptp.use))))) (let ((_let_27 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n4)) tptp.use))))) (let ((_let_28 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n3)) tptp.use))))) (let ((_let_29 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n2)) tptp.use))))) (let ((_let_30 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n1)) tptp.use))))) (let ((_let_31 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n0)) tptp.use))))) (let ((_let_32 (@ tptp.a_select2 tptp.rho_defuse))) (let ((_let_33 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n2)) tptp.use))))) (let ((_let_34 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n1)) tptp.use))))) (let ((_let_35 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n0)) tptp.use))))) (not (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ _let_35 (@ _let_34 (@ _let_33 (@ _let_31 (@ _let_30 (@ _let_29 (@ _let_28 (@ _let_27 (@ _let_26 (@ _let_24 (@ _let_23 (@ _let_22 (@ _let_20 (@ _let_19 (@ _let_18 (@ _let_16 (@ _let_15 (@ _let_14 (@ _let_13 (@ _let_12 (@ _let_11 (@ _let_9 (@ _let_8 (@ _let_7 (@ _let_6 (@ _let_5 (@ _let_4 (@ _let_2 (@ _let_1 (@ (@ tptp.mand (@ 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 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 A))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 B))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq A) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq B) tptp.pv5)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) A) B)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) A) B)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 C))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 D))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq C) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq D) (@ (@ tptp.minus tptp.pv5) tptp.n1))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) C) D)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) C) D)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))))))))))))))))))))))))))))))))) (@ _let_35 (@ _let_34 (@ _let_33 (@ _let_31 (@ _let_30 (@ _let_29 (@ _let_28 (@ _let_27 (@ _let_26 (@ _let_24 (@ _let_23 (@ _let_22 (@ _let_20 (@ _let_19 (@ _let_18 (@ _let_16 (@ _let_15 (@ _let_14 (@ _let_13 (@ _let_12 (@ _let_11 (@ _let_9 (@ _let_8 (@ _let_7 (@ _let_6 (@ _let_5 (@ _let_4 (@ _let_2 (@ _let_1 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((F tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 E))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 F))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq E) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq F) tptp.pv5)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) E) F)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) E) F)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((G tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((H tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 G))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 H))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq G) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq H) (@ (@ tptp.minus tptp.pv5) tptp.n1))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) G) H)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) G) H)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.30/1.56 (set-info :filename cvc5---1.0.5_28716)
% 1.30/1.56 (check-sat-assuming ( true ))
% 1.30/1.56 ------- get file name : TPTP file name is SWV097^7
% 1.30/1.56 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28716.smt2...
% 1.30/1.56 --- Run --ho-elim --full-saturate-quant at 10...
% 1.30/1.56 % SZS status Theorem for SWV097^7
% 1.30/1.56 % SZS output start Proof for SWV097^7
% 1.30/1.56 (
% 1.30/1.56 (let ((_let_1 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv5) (@ (@ tptp.minus tptp.n999) tptp.n1)))))) (let ((_let_2 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) tptp.pv5))))) (let ((_let_3 (@ tptp.a_select2 tptp.xinit_noise_defuse))) (let ((_let_4 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n5)) tptp.use))))) (let ((_let_5 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n4)) tptp.use))))) (let ((_let_6 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n3)) tptp.use))))) (let ((_let_7 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n2)) tptp.use))))) (let ((_let_8 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n1)) tptp.use))))) (let ((_let_9 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_3 tptp.n0)) tptp.use))))) (let ((_let_10 (@ tptp.a_select2 tptp.xinit_mean_defuse))) (let ((_let_11 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n5)) tptp.use))))) (let ((_let_12 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n4)) tptp.use))))) (let ((_let_13 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n3)) tptp.use))))) (let ((_let_14 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n2)) tptp.use))))) (let ((_let_15 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n1)) tptp.use))))) (let ((_let_16 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_10 tptp.n0)) tptp.use))))) (let ((_let_17 (@ tptp.a_select2 tptp.xinit_defuse))) (let ((_let_18 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n5)) tptp.use))))) (let ((_let_19 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n4)) tptp.use))))) (let ((_let_20 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_17 tptp.n3)) tptp.use))))) (let ((_let_21 (@ tptp.a_select3 tptp.u_defuse))) (let ((_let_22 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n2) tptp.n0)) tptp.use))))) (let ((_let_23 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n1) tptp.n0)) tptp.use))))) (let ((_let_24 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_21 tptp.n0) tptp.n0)) tptp.use))))) (let ((_let_25 (@ tptp.a_select2 tptp.sigma_defuse))) (let ((_let_26 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n5)) tptp.use))))) (let ((_let_27 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n4)) tptp.use))))) (let ((_let_28 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n3)) tptp.use))))) (let ((_let_29 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n2)) tptp.use))))) (let ((_let_30 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n1)) tptp.use))))) (let ((_let_31 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_25 tptp.n0)) tptp.use))))) (let ((_let_32 (@ tptp.a_select2 tptp.rho_defuse))) (let ((_let_33 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n2)) tptp.use))))) (let ((_let_34 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n1)) tptp.use))))) (let ((_let_35 (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_32 tptp.n0)) tptp.use))))) (let ((_let_36 (not (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ _let_35 (@ _let_34 (@ _let_33 (@ _let_31 (@ _let_30 (@ _let_29 (@ _let_28 (@ _let_27 (@ _let_26 (@ _let_24 (@ _let_23 (@ _let_22 (@ _let_20 (@ _let_19 (@ _let_18 (@ _let_16 (@ _let_15 (@ _let_14 (@ _let_13 (@ _let_12 (@ _let_11 (@ _let_9 (@ _let_8 (@ _let_7 (@ _let_6 (@ _let_5 (@ _let_4 (@ _let_2 (@ _let_1 (@ (@ tptp.mand (@ 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 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 A))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 B))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq A) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq B) tptp.pv5)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) A) B)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) A) B)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 C))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 D))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq C) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq D) (@ (@ tptp.minus tptp.pv5) tptp.n1))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) C) D)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) C) D)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))))))))))))))))))))))))))))))))) (@ _let_35 (@ _let_34 (@ _let_33 (@ _let_31 (@ _let_30 (@ _let_29 (@ _let_28 (@ _let_27 (@ _let_26 (@ _let_24 (@ _let_23 (@ _let_22 (@ _let_20 (@ _let_19 (@ _let_18 (@ _let_16 (@ _let_15 (@ _let_14 (@ _let_13 (@ _let_12 (@ _let_11 (@ _let_9 (@ _let_8 (@ _let_7 (@ _let_6 (@ _let_5 (@ _let_4 (@ _let_2 (@ _let_1 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((F tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 E))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 F))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq E) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq F) tptp.pv5)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) E) F)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) E) F)) tptp.use))))) __flatten_var_0))))) __flatten_var_0))))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((G tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((H tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 G))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 H))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq G) tptp.n2))) (@ tptp.mbox_s4 (@ (@ tptp.leq H) (@ (@ tptp.minus tptp.pv5) tptp.n1))))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.u_defuse) G) H)) tptp.use))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 tptp.z_defuse) G) H)) tptp.use))))) __flatten_var_0))))) __flatten_var_0)))))))))))))))))))))))))))))))))))))))) (let ((_let_37 (@ tptp.succ tptp.n0))) (let ((_let_38 (@ tptp.succ _let_37))) (let ((_let_39 (@ tptp.succ _let_38))) (let ((_let_40 (@ tptp.succ _let_39))) (let ((_let_41 (@ tptp.gt tptp.n999))) (let ((_let_42 (@ tptp.gt tptp.n5))) (let ((_let_43 (@ tptp.gt tptp.n4))) (let ((_let_44 (@ tptp.gt tptp.n3))) (let ((_let_45 (@ tptp.gt tptp.n2))) (let ((_let_46 (@ tptp.gt tptp.n1))) (let ((_let_47 (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_48 (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))) (let ((_let_49 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_50 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_51 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_52 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_53 (= 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)))))))))) (let ((_let_54 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_55 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_56 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_57 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_58 (= tptp.meuclidean (lambda ((R (-> $$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)))))))) (let ((_let_59 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_60 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_61 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_62 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_63 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_64 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))) (let ((_let_65 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))) (let ((_let_66 (= 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))))) (let ((_let_67 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_68 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_69 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_70 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_71 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_72 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_73 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_74 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_75 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_76 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_77 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_78 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_79 (forall ((BOUND_VARIABLE_75929 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75929) BOUND_VARIABLE_75929)) (ho_4 (ho_3 (ho_30 k_33 tptp.pv5) (ho_9 (ho_8 k_25 tptp.n999) tptp.n1)) BOUND_VARIABLE_75929))))) (let ((_let_80 (forall ((BOUND_VARIABLE_75920 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75920) BOUND_VARIABLE_75920)) (ho_4 (ho_3 (ho_30 k_33 tptp.n0) tptp.pv5) BOUND_VARIABLE_75920))))) (let ((_let_81 (forall ((BOUND_VARIABLE_75911 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75911) BOUND_VARIABLE_75911)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n5)) tptp.use) BOUND_VARIABLE_75911))))) (let ((_let_82 (forall ((BOUND_VARIABLE_75902 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75902) BOUND_VARIABLE_75902)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n4)) tptp.use) BOUND_VARIABLE_75902))))) (let ((_let_83 (forall ((BOUND_VARIABLE_75893 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75893) BOUND_VARIABLE_75893)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n3)) tptp.use) BOUND_VARIABLE_75893))))) (let ((_let_84 (forall ((BOUND_VARIABLE_75884 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75884) BOUND_VARIABLE_75884)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n2)) tptp.use) BOUND_VARIABLE_75884))))) (let ((_let_85 (forall ((BOUND_VARIABLE_75875 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75875) BOUND_VARIABLE_75875)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n1)) tptp.use) BOUND_VARIABLE_75875))))) (let ((_let_86 (forall ((BOUND_VARIABLE_75866 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75866) BOUND_VARIABLE_75866)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_noise_defuse) tptp.n0)) tptp.use) BOUND_VARIABLE_75866))))) (let ((_let_87 (forall ((BOUND_VARIABLE_75857 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75857) BOUND_VARIABLE_75857)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n5)) tptp.use) BOUND_VARIABLE_75857))))) (let ((_let_88 (forall ((BOUND_VARIABLE_75848 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75848) BOUND_VARIABLE_75848)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n4)) tptp.use) BOUND_VARIABLE_75848))))) (let ((_let_89 (forall ((BOUND_VARIABLE_75839 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75839) BOUND_VARIABLE_75839)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n3)) tptp.use) BOUND_VARIABLE_75839))))) (let ((_let_90 (forall ((BOUND_VARIABLE_75830 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75830) BOUND_VARIABLE_75830)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n2)) tptp.use) BOUND_VARIABLE_75830))))) (let ((_let_91 (forall ((BOUND_VARIABLE_75821 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75821) BOUND_VARIABLE_75821)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n1)) tptp.use) BOUND_VARIABLE_75821))))) (let ((_let_92 (forall ((BOUND_VARIABLE_75812 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75812) BOUND_VARIABLE_75812)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_mean_defuse) tptp.n0)) tptp.use) BOUND_VARIABLE_75812))))) (let ((_let_93 (forall ((BOUND_VARIABLE_75803 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75803) BOUND_VARIABLE_75803)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_defuse) tptp.n5)) tptp.use) BOUND_VARIABLE_75803))))) (let ((_let_94 (forall ((BOUND_VARIABLE_75794 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75794) BOUND_VARIABLE_75794)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_defuse) tptp.n4)) tptp.use) BOUND_VARIABLE_75794))))) (let ((_let_95 (forall ((BOUND_VARIABLE_75785 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75785) BOUND_VARIABLE_75785)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.xinit_defuse) tptp.n3)) tptp.use) BOUND_VARIABLE_75785))))) (let ((_let_96 (forall ((BOUND_VARIABLE_75776 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75776) BOUND_VARIABLE_75776)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 (ho_13 k_26 tptp.u_defuse) tptp.n2) tptp.n0)) tptp.use) BOUND_VARIABLE_75776))))) (let ((_let_97 (forall ((BOUND_VARIABLE_75767 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75767) BOUND_VARIABLE_75767)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 (ho_13 k_26 tptp.u_defuse) tptp.n1) tptp.n0)) tptp.use) BOUND_VARIABLE_75767))))) (let ((_let_98 (forall ((BOUND_VARIABLE_75758 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75758) BOUND_VARIABLE_75758)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 (ho_13 k_26 tptp.u_defuse) tptp.n0) tptp.n0)) tptp.use) BOUND_VARIABLE_75758))))) (let ((_let_99 (forall ((BOUND_VARIABLE_75749 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75749) BOUND_VARIABLE_75749)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n5)) tptp.use) BOUND_VARIABLE_75749))))) (let ((_let_100 (forall ((BOUND_VARIABLE_75740 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75740) BOUND_VARIABLE_75740)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n4)) tptp.use) BOUND_VARIABLE_75740))))) (let ((_let_101 (forall ((BOUND_VARIABLE_75731 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75731) BOUND_VARIABLE_75731)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n3)) tptp.use) BOUND_VARIABLE_75731))))) (let ((_let_102 (forall ((BOUND_VARIABLE_75722 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75722) BOUND_VARIABLE_75722)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n2)) tptp.use) BOUND_VARIABLE_75722))))) (let ((_let_103 (forall ((BOUND_VARIABLE_75713 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75713) BOUND_VARIABLE_75713)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n1)) tptp.use) BOUND_VARIABLE_75713))))) (let ((_let_104 (forall ((BOUND_VARIABLE_75704 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75704) BOUND_VARIABLE_75704)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.sigma_defuse) tptp.n0)) tptp.use) BOUND_VARIABLE_75704))))) (let ((_let_105 (forall ((BOUND_VARIABLE_75695 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75695) BOUND_VARIABLE_75695)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.rho_defuse) tptp.n2)) tptp.use) BOUND_VARIABLE_75695))))) (let ((_let_106 (forall ((BOUND_VARIABLE_75686 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75686) BOUND_VARIABLE_75686)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.rho_defuse) tptp.n1)) tptp.use) BOUND_VARIABLE_75686))))) (let ((_let_107 (forall ((BOUND_VARIABLE_75677 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_75677) BOUND_VARIABLE_75677)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 k_27 tptp.rho_defuse) tptp.n0)) tptp.use) BOUND_VARIABLE_75677))))) (let ((_let_108 (forall ((BOUND_VARIABLE_75938 $$unsorted) (BOUND_VARIABLE_74550 $$unsorted) (BOUND_VARIABLE_74548 $$unsorted) (BOUND_VARIABLE_74546 $$unsorted) (BOUND_VARIABLE_74544 tptp.mu) (BOUND_VARIABLE_74542 tptp.mu)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_75938))) (or (not (ho_4 _let_1 BOUND_VARIABLE_75938)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_74542) BOUND_VARIABLE_75938)) (not (forall ((BOUND_VARIABLE_74238 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74238) BOUND_VARIABLE_74238)) (ho_4 (ho_3 (ho_30 k_33 tptp.n0) BOUND_VARIABLE_74542) BOUND_VARIABLE_74238)))) (not (forall ((BOUND_VARIABLE_74258 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74258) BOUND_VARIABLE_74258)) (ho_4 (ho_3 (ho_30 k_33 BOUND_VARIABLE_74542) tptp.n2) BOUND_VARIABLE_74258)))) (not (ho_4 _let_1 BOUND_VARIABLE_74550)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_74544) BOUND_VARIABLE_74550)) (and (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74548) BOUND_VARIABLE_74548)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 (ho_13 k_26 tptp.u_defuse) BOUND_VARIABLE_74542) BOUND_VARIABLE_74544)) tptp.use) BOUND_VARIABLE_74548)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74546) BOUND_VARIABLE_74546)) (ho_4 (ho_3 (ho_30 k_29 (ho_9 (ho_8 (ho_13 k_26 tptp.z_defuse) BOUND_VARIABLE_74542) BOUND_VARIABLE_74544)) tptp.use) BOUND_VARIABLE_74546))) (not (forall ((BOUND_VARIABLE_74248 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74248) BOUND_VARIABLE_74248)) (ho_4 (ho_3 (ho_30 k_33 tptp.n0) BOUND_VARIABLE_74544) BOUND_VARIABLE_74248)))) (not (forall ((BOUND_VARIABLE_74268 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74268) BOUND_VARIABLE_74268)) (ho_4 (ho_3 (ho_30 k_33 BOUND_VARIABLE_74544) tptp.pv5) BOUND_VARIABLE_74268))))))))) (let ((_let_109 (forall ((BOUND_VARIABLE_74366 $$unsorted)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_74366) BOUND_VARIABLE_74366))))) (let ((_let_110 (or _let_109 _let_108))) (let ((_let_111 (forall ((BOUND_VARIABLE_75951 $$unsorted) (BOUND_VARIABLE_75145 $$unsorted) (BOUND_VARIABLE_75143 $$unsorted) (BOUND_VARIABLE_75141 $$unsorted) (BOUND_VARIABLE_75139 tptp.mu) (BOUND_VARIABLE_75137 tptp.mu)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_75951))) (or (not (ho_4 _let_1 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:args (2))))) (let ((_let_240 (NOT_NOT_ELIM (NOT_OR_ELIM _let_211 :args (1))))) (let ((_let_241 (forall ((BOUND_VARIABLE_7730 $$unsorted)) (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_7730) BOUND_VARIABLE_7730))))) (let ((_let_242 (not _let_241))) (let ((_let_243 (REORDERING (NOT_AND (NOT_OR_ELIM _let_211 :args (0))) :args ((or _let_122 _let_123 _let_124 _let_125 _let_126 _let_127 _let_128 _let_129 _let_130 _let_131 _let_132 _let_133 _let_134 _let_135 _let_136 _let_137 _let_138 _let_139 _let_140 _let_141 _let_142 _let_143 _let_144 _let_145 _let_146 _let_147 _let_148 _let_149 _let_150 (not _let_110) (not _let_113)))))) (let ((_let_244 (MACRO_RESOLUTION_TRUST _let_243 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 (CNF_OR_NEG :args (_let_113 0)) (CNF_OR_NEG :args (_let_110 0)) (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_241 (= BOUND_VARIABLE_7730 BOUND_VARIABLE_74961)))) :args ((or _let_112 _let_242))) (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_241 (= BOUND_VARIABLE_7730 BOUND_VARIABLE_74366)))) :args ((or _let_109 _let_242))) :args (_let_242 false _let_107 false _let_106 false _let_105 false _let_104 false _let_103 false _let_102 false _let_101 false _let_100 false _let_99 false _let_98 false _let_97 false _let_96 false _let_95 false _let_94 false _let_93 false _let_92 false _let_91 false _let_90 false _let_89 false _let_88 false _let_87 false _let_86 false _let_85 false _let_84 false _let_83 false _let_82 false _let_81 false _let_80 false _let_79 false _let_113 false _let_110 false _let_112 false _let_109)))) (let ((_let_245 (or))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_243 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_113 1)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (SYMM (ALPHA_EQUIV :args (_let_111 (= BOUND_VARIABLE_75137 BOUND_VARIABLE_73492) (= BOUND_VARIABLE_75139 BOUND_VARIABLE_73494) (= BOUND_VARIABLE_75951 BOUND_VARIABLE_76008) (= BOUND_VARIABLE_75145 BOUND_VARIABLE_73500) (= BOUND_VARIABLE_74833 BOUND_VARIABLE_73187) (= BOUND_VARIABLE_74843 BOUND_VARIABLE_73197) (= BOUND_VARIABLE_74853 BOUND_VARIABLE_73207) (= BOUND_VARIABLE_74863 BOUND_VARIABLE_73217) (= BOUND_VARIABLE_75141 BOUND_VARIABLE_73496) (= BOUND_VARIABLE_75143 BOUND_VARIABLE_73498))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (NOT_OR_ELIM _let_211 :args (31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_117) _let_116))) (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_114))) :args _let_245)) :args ((or _let_114 _let_116))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_241 (= BOUND_VARIABLE_7730 BOUND_VARIABLE_73316)))) _let_244 :args (_let_117 true _let_241)) :args (_let_114 true _let_116)) :args (_let_111 false _let_114)) :args (_let_113 false _let_111)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_110 1)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (SYMM (ALPHA_EQUIV :args (_let_108 (= BOUND_VARIABLE_74542 BOUND_VARIABLE_72896) (= BOUND_VARIABLE_74544 BOUND_VARIABLE_72898) (= BOUND_VARIABLE_75938 BOUND_VARIABLE_75994) (= BOUND_VARIABLE_74550 BOUND_VARIABLE_72904) (= BOUND_VARIABLE_74238 BOUND_VARIABLE_72589) (= BOUND_VARIABLE_74248 BOUND_VARIABLE_72599) (= BOUND_VARIABLE_74258 BOUND_VARIABLE_72609) (= BOUND_VARIABLE_74268 BOUND_VARIABLE_72619) (= BOUND_VARIABLE_74546 BOUND_VARIABLE_72900) (= BOUND_VARIABLE_74548 BOUND_VARIABLE_72902))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (NOT_OR_ELIM _let_211 :args (30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_121) _let_120))) (MACRO_SR_PRED_INTRO :args ((= (not _let_119) _let_118))) :args _let_245)) :args ((or _let_118 _let_120))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_241 (= BOUND_VARIABLE_7730 BOUND_VARIABLE_72718)))) _let_244 :args (_let_121 true _let_241)) :args (_let_118 true _let_120)) :args (_let_108 false _let_118)) :args (_let_110 false _let_108)) _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 :args (false false _let_113 false _let_110 false _let_107 false _let_106 false _let_105 false _let_104 false _let_103 false _let_102 false _let_101 false _let_100 false _let_99 false _let_98 false _let_97 false _let_96 false _let_95 false _let_94 false _let_93 false _let_92 false _let_91 false _let_90 false _let_89 false _let_88 false _let_87 false _let_86 false _let_85 false _let_84 false _let_83 false _let_82 false _let_81 false _let_80 false _let_79)) :args (_let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))) _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 (@ tptp.mreflexive tptp.rel_s4) (@ tptp.mtransitive tptp.rel_s4) (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.uniform_int_rnd V2) V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_const_array1 V2) V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.dim V2) V1)) V)) (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_const_array2 V3) V2) V1)) V)) (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inv V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_msub V2) V1)) V)) (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.trans V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_mmul V2) V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_madd V2) V1)) V)) (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.sum V3) V2) V1)) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_float_0_0) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.plus V2) V1)) V)) (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.pred V1)) V)) (forall ((V $$unsorted) (V4 tptp.mu) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ (@ tptp.tptp_update3 V4) V3) V2) V1)) V)) (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_update2 V3) V2) V1)) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.def) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.z_defuse) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.minus V2) V1)) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.pv5) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_noise_defuse) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_mean_defuse) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.xinit_defuse) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.u_defuse) V)) (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.a_select3 V3) V2) V1)) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.sigma_defuse) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.use) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.rho_defuse) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.a_select2 V2) V1)) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_minus_1) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n999) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n4) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n5) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n1) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n2) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n3) V)) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n0) V)) (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.succ V1)) V)) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 A) C)) (@ (@ tptp.a_select2 B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.a_select2 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))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 A) C) D)) (@ (@ (@ tptp.a_select3 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.a_select3 C) D))) (@ (@ 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)))) __flatten_var_0))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.dim A) C)) (@ (@ tptp.dim B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.dim 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))))) (@ 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))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.minus A) C)) (@ (@ tptp.minus B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.minus 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))))) (@ 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus A) C)) (@ (@ tptp.plus B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 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tptp.qmltpeq (@ (@ tptp.plus tptp.n5) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.minus X) tptp.n1)) (@ tptp.pred X))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.pred (@ tptp.succ X))) X)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.pred X))) X)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) (@ tptp.succ Y))))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) Y))) (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ (@ tptp.minus X) Y)) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) Y)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) U) V) VAL)) U) V)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq I) U))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq J) V))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 X) U) V)) VAL))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) I) J) VAL2)) U) V)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I0 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((J0 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 I0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 J0))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I0) U))) (@ tptp.mbox_s4 (@ (@ tptp.leq J0) V)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 X) I0) J0)) VAL)))) __flatten_var_0))))) __flatten_var_0))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) U))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) V))))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) U) V) VAL)) I) J)) VAL)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) U) VAL)) U)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL2 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq I) U))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 X) U)) VAL)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) I) VAL2)) U)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((VAL tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I0 tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) I0))) (@ tptp.mbox_s4 (@ (@ tptp.leq I0) U)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 X) I0)) VAL)))) __flatten_var_0))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) I))) (@ tptp.mbox_s4 (@ (@ tptp.leq I) U))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) U) VAL)) I)) VAL)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 tptp.true)) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.def) tptp.use))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.n4))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n4))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n5))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_43 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n0) tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_46 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_45 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_44 tptp.tptp_minus_1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_43 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_46 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_45 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_44 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_43 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_45 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_44 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_43 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_44 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_43 tptp.n3))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_42 tptp.n3))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_41 tptp.n3))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n4)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n3))) (@ tptp.mbox_s4 (@ _let_1 tptp.n4)))))))) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n5)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n3))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n4))) (@ tptp.mbox_s4 (@ _let_1 tptp.n5))))))))) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n0)))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) tptp.n0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n1)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ tptp.mbox_s4 (@ _let_1 tptp.n1))))) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n2)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ tptp.mbox_s4 (@ _let_1 tptp.n2)))))) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n3)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ tptp.mbox_s4 (@ _let_1 tptp.n3))))))) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_40) tptp.n4))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ _let_40)) tptp.n5))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_37) tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_38) tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_39) tptp.n3))) _let_36 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.39/1.56 )
% 1.39/1.56 % SZS output end Proof for SWV097^7
% 1.39/1.56 % cvc5---1.0.5 exiting
% 1.39/1.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------