TSTP Solution File: SWV073^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV073^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 21:49:11 EDT 2023
% Result : Theorem 1.82s 2.02s
% Output : Proof 1.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.15 % Problem : SWV073^7 : TPTP v8.1.2. Released v5.5.0.
% 0.15/0.16 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n024.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Aug 29 07:54:23 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 % File : SWV073^7 : TPTP v8.1.2. Released v5.5.0.
% 0.22/0.53 % Domain : Software Verification
% 0.22/0.53 % Problem : Unsimplified proof obligation cl5_nebula_array_0014
% 0.22/0.53 % Version : [Ben12] axioms.
% 0.22/0.53 % English :
% 0.22/0.53
% 0.22/0.53 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.22/0.53 % : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% 0.22/0.53 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.22/0.53 % Source : [Ben12]
% 0.22/0.53 % Names : s4-cumul-GSV073+1 [Ben12]
% 0.22/0.53
% 0.22/0.53 % Status : Theorem
% 0.22/0.53 % Rating : 0.31 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.22 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0
% 0.22/0.53 % Syntax : Number of formulae : 280 ( 64 unt; 72 typ; 32 def)
% 0.22/0.53 % Number of atoms : 2053 ( 36 equ; 0 cnn)
% 0.22/0.53 % Maximal formula atoms : 97 ( 9 avg)
% 0.22/0.53 % Number of connectives : 3327 ( 5 ~; 5 |; 9 &;3298 @)
% 0.22/0.53 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.22/0.53 % Maximal formula depth : 51 ( 12 avg)
% 0.22/0.53 % Number of types : 3 ( 1 usr)
% 0.22/0.53 % Number of type conns : 231 ( 231 >; 0 *; 0 +; 0 <<)
% 0.22/0.53 % Number of symbols : 82 ( 80 usr; 23 con; 0-4 aty)
% 0.22/0.53 % Number of variables : 487 ( 377 ^; 103 !; 7 ?; 487 :)
% 0.22/0.53 % SPC : TH0_THM_EQU_NAR
% 0.22/0.53
% 0.22/0.53 % Comments : Goedel translation of SWV073+1
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %----Include axioms for Modal logic S4 under cumulative domains
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %----Declaration of additional base type mu
% 0.22/0.53 thf(mu_type,type,
% 0.22/0.53 mu: $tType ).
% 0.22/0.53
% 0.22/0.53 %----Equality
% 0.22/0.53 thf(qmltpeq_type,type,
% 0.22/0.53 qmltpeq: mu > mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 % originale Definition
% 0.22/0.53 %thf(qmltpeq,definition,
% 0.22/0.53 % ( qmltpeq
% 0.22/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.22/0.53
% 0.22/0.53 % erweiterte Leibnitz-Definition
% 0.22/0.53 %thf(qmltpeq,definition,
% 0.22/0.53 % ( qmltpeq
% 0.22/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.22/0.53
% 0.22/0.53 % Leibnitz-Definition
% 0.22/0.53 %thf(qmltpeq,definition,
% 0.22/0.53 % ( qmltpeq
% 0.22/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.22/0.53
% 0.22/0.53 thf(meq_prop_type,type,
% 0.22/0.53 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(meq_prop,definition,
% 0.22/0.53 ( meq_prop
% 0.22/0.53 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.22/0.53 ( ( X @ W )
% 0.22/0.53 = ( Y @ W ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Modal operators not, or, box, Pi
% 0.22/0.53 thf(mnot_type,type,
% 0.22/0.53 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mnot,definition,
% 0.22/0.53 ( mnot
% 0.22/0.53 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.53 ~ ( Phi @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mor_type,type,
% 0.22/0.53 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mor,definition,
% 0.22/0.53 ( mor
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.22/0.53 ( ( Phi @ W )
% 0.22/0.53 | ( Psi @ W ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mbox_type,type,
% 0.22/0.53 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mbox,definition,
% 0.22/0.53 ( mbox
% 0.22/0.53 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.22/0.53 ! [V: $i] :
% 0.22/0.53 ( ~ ( R @ W @ V )
% 0.22/0.53 | ( Phi @ V ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mforall_prop_type,type,
% 0.22/0.53 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mforall_prop,definition,
% 0.22/0.53 ( mforall_prop
% 0.22/0.53 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.22/0.53 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Further modal operators
% 0.22/0.53 thf(mtrue_type,type,
% 0.22/0.53 mtrue: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mtrue,definition,
% 0.22/0.53 ( mtrue
% 0.22/0.53 = ( ^ [W: $i] : $true ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mfalse_type,type,
% 0.22/0.53 mfalse: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mfalse,definition,
% 0.22/0.53 ( mfalse
% 0.22/0.53 = ( mnot @ mtrue ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mand_type,type,
% 0.22/0.53 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mand,definition,
% 0.22/0.53 ( mand
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mimplies_type,type,
% 0.22/0.53 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mimplies,definition,
% 0.22/0.53 ( mimplies
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mimplied_type,type,
% 0.22/0.53 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mimplied,definition,
% 0.22/0.53 ( mimplied
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mequiv_type,type,
% 0.22/0.53 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mequiv,definition,
% 0.22/0.53 ( mequiv
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mxor_type,type,
% 0.22/0.53 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mxor,definition,
% 0.22/0.53 ( mxor
% 0.22/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mdia_type,type,
% 0.22/0.53 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mdia,definition,
% 0.22/0.53 ( mdia
% 0.22/0.53 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %--- (new for cumulative)
% 0.22/0.53 %---Declaration of existence predicate for simulating cumulative domain
% 0.22/0.53 thf(exists_in_world_type,type,
% 0.22/0.53 exists_in_world: mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 %----The domains are non-empty
% 0.22/0.53 thf(nonempty_ax,axiom,
% 0.22/0.53 ! [V: $i] :
% 0.22/0.53 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(mforall_ind_type,type,
% 0.22/0.53 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 %--- (new for cumulative)
% 0.22/0.53 thf(mforall_ind,definition,
% 0.22/0.53 ( mforall_ind
% 0.22/0.53 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.53 ! [X: mu] :
% 0.22/0.53 ( ( exists_in_world @ X @ W )
% 0.22/0.53 => ( Phi @ X @ W ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %thf(mforall_ind,definition,
% 0.22/0.53 % ( mforall_ind
% 0.22/0.53 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.53 % ! [X: mu] :
% 0.22/0.53 % ( Phi @ X @ W ) ) )).
% 0.22/0.53
% 0.22/0.53 thf(mexists_ind_type,type,
% 0.22/0.53 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mexists_ind,definition,
% 0.22/0.53 ( mexists_ind
% 0.22/0.53 = ( ^ [Phi: mu > $i > $o] :
% 0.22/0.53 ( mnot
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mexists_prop_type,type,
% 0.22/0.53 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mexists_prop,definition,
% 0.22/0.53 ( mexists_prop
% 0.22/0.53 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.22/0.53 ( mnot
% 0.22/0.53 @ ( mforall_prop
% 0.22/0.53 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Definition of properties of accessibility relations
% 0.22/0.53 thf(mreflexive_type,type,
% 0.22/0.53 mreflexive: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mreflexive,definition,
% 0.22/0.53 ( mreflexive
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(msymmetric_type,type,
% 0.22/0.53 msymmetric: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(msymmetric,definition,
% 0.22/0.53 ( msymmetric
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i] :
% 0.22/0.53 ( ( R @ S @ T )
% 0.22/0.53 => ( R @ T @ S ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mserial_type,type,
% 0.22/0.53 mserial: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mserial,definition,
% 0.22/0.53 ( mserial
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i] :
% 0.22/0.53 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mtransitive_type,type,
% 0.22/0.53 mtransitive: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mtransitive,definition,
% 0.22/0.53 ( mtransitive
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( ( R @ S @ T )
% 0.22/0.53 & ( R @ T @ U ) )
% 0.22/0.53 => ( R @ S @ U ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(meuclidean_type,type,
% 0.22/0.53 meuclidean: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(meuclidean,definition,
% 0.22/0.53 ( meuclidean
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( ( R @ S @ T )
% 0.22/0.53 & ( R @ S @ U ) )
% 0.22/0.53 => ( R @ T @ U ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mpartially_functional_type,type,
% 0.22/0.53 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mpartially_functional,definition,
% 0.22/0.53 ( mpartially_functional
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( ( R @ S @ T )
% 0.22/0.53 & ( R @ S @ U ) )
% 0.22/0.53 => ( T = U ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mfunctional_type,type,
% 0.22/0.53 mfunctional: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mfunctional,definition,
% 0.22/0.53 ( mfunctional
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i] :
% 0.22/0.53 ? [T: $i] :
% 0.22/0.53 ( ( R @ S @ T )
% 0.22/0.53 & ! [U: $i] :
% 0.22/0.53 ( ( R @ S @ U )
% 0.22/0.53 => ( T = U ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_dense_type,type,
% 0.22/0.53 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_dense,definition,
% 0.22/0.53 ( mweakly_dense
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( R @ S @ T )
% 0.22/0.53 => ? [U: $i] :
% 0.22/0.53 ( ( R @ S @ U )
% 0.22/0.53 & ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_connected_type,type,
% 0.22/0.53 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_connected,definition,
% 0.22/0.53 ( mweakly_connected
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( ( R @ S @ T )
% 0.22/0.53 & ( R @ S @ U ) )
% 0.22/0.53 => ( ( R @ T @ U )
% 0.22/0.53 | ( T = U )
% 0.22/0.53 | ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_directed_type,type,
% 0.22/0.53 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mweakly_directed,definition,
% 0.22/0.53 ( mweakly_directed
% 0.22/0.53 = ( ^ [R: $i > $i > $o] :
% 0.22/0.53 ! [S: $i,T: $i,U: $i] :
% 0.22/0.53 ( ( ( R @ S @ T )
% 0.22/0.53 & ( R @ S @ U ) )
% 0.22/0.53 => ? [V: $i] :
% 0.22/0.53 ( ( R @ T @ V )
% 0.22/0.53 & ( R @ U @ V ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Definition of validity
% 0.22/0.53 thf(mvalid_type,type,
% 0.22/0.53 mvalid: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mvalid,definition,
% 0.22/0.53 ( mvalid
% 0.22/0.53 = ( ^ [Phi: $i > $o] :
% 0.22/0.53 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Definition of satisfiability
% 0.22/0.53 thf(msatisfiable_type,type,
% 0.22/0.53 msatisfiable: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(msatisfiable,definition,
% 0.22/0.53 ( msatisfiable
% 0.22/0.53 = ( ^ [Phi: $i > $o] :
% 0.22/0.53 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Definition of countersatisfiability
% 0.22/0.53 thf(mcountersatisfiable_type,type,
% 0.22/0.53 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mcountersatisfiable,definition,
% 0.22/0.53 ( mcountersatisfiable
% 0.22/0.53 = ( ^ [Phi: $i > $o] :
% 0.22/0.53 ? [W: $i] :
% 0.22/0.53 ~ ( Phi @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----Definition of invalidity
% 0.22/0.53 thf(minvalid_type,type,
% 0.22/0.53 minvalid: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(minvalid,definition,
% 0.22/0.53 ( minvalid
% 0.22/0.53 = ( ^ [Phi: $i > $o] :
% 0.22/0.53 ! [W: $i] :
% 0.22/0.53 ~ ( Phi @ W ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %----We reserve an accessibility relation constant rel_s4
% 0.22/0.53 thf(rel_s4_type,type,
% 0.22/0.53 rel_s4: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.22/0.53 thf(mbox_s4_type,type,
% 0.22/0.53 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mbox_s4,definition,
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.53 ! [V: $i] :
% 0.22/0.53 ( ~ ( rel_s4 @ W @ V )
% 0.22/0.53 | ( Phi @ V ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(mdia_s4_type,type,
% 0.22/0.53 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(mdia_s4,definition,
% 0.22/0.53 ( mdia_s4
% 0.22/0.53 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %----We have now two options for stating the B conditions:
% 0.22/0.53 %----We can (i) directly formulate conditions for the accessibility relation
% 0.22/0.53 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.22/0.53 thf(a1,axiom,
% 0.22/0.53 mreflexive @ rel_s4 ).
% 0.22/0.53
% 0.22/0.53 thf(a2,axiom,
% 0.22/0.53 mtransitive @ rel_s4 ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(cumulative_ax,axiom,
% 0.22/0.53 ! [X: mu,V: $i,W: $i] :
% 0.22/0.53 ( ( ( exists_in_world @ X @ V )
% 0.22/0.53 & ( rel_s4 @ V @ W ) )
% 0.22/0.53 => ( exists_in_world @ X @ W ) ) ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(true_type,type,
% 0.22/0.53 true: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(lt_type,type,
% 0.22/0.53 lt: mu > mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(geq_type,type,
% 0.22/0.53 geq: mu > mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(gt_type,type,
% 0.22/0.53 gt: mu > mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(leq_type,type,
% 0.22/0.53 leq: mu > mu > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(uniform_int_rnd_type,type,
% 0.22/0.53 uniform_int_rnd: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_uniform_int_rnd_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( uniform_int_rnd @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array1_type,type,
% 0.22/0.53 tptp_const_array1: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_const_array1_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_const_array1 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(dim_type,type,
% 0.22/0.53 dim: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_dim_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( dim @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array2_type,type,
% 0.22/0.53 tptp_const_array2: mu > mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_const_array2_ax,axiom,
% 0.22/0.53 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_const_array2 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(inv_type,type,
% 0.22/0.53 inv: mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_inv_ax,axiom,
% 0.22/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( inv @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_msub_type,type,
% 0.22/0.53 tptp_msub: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_msub_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_msub @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(trans_type,type,
% 0.22/0.53 trans: mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_trans_ax,axiom,
% 0.22/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( trans @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_mmul_type,type,
% 0.22/0.53 tptp_mmul: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_mmul_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_mmul @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_madd_type,type,
% 0.22/0.53 tptp_madd: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_madd_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_madd @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_type,type,
% 0.22/0.53 sum: mu > mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_sum_ax,axiom,
% 0.22/0.53 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( sum @ V3 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_float_0_0_type,type,
% 0.22/0.53 tptp_float_0_0: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_float_0_0_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ tptp_float_0_0 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(plus_type,type,
% 0.22/0.53 plus: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_plus_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( plus @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(pred_type,type,
% 0.22/0.53 pred: mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_pred_ax,axiom,
% 0.22/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( pred @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update3_type,type,
% 0.22/0.53 tptp_update3: mu > mu > mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_update3_ax,axiom,
% 0.22/0.53 ! [V: $i,V4: mu,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_update3 @ V4 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select3_type,type,
% 0.22/0.53 a_select3: mu > mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_a_select3_ax,axiom,
% 0.22/0.53 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( a_select3 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update2_type,type,
% 0.22/0.53 tptp_update2: mu > mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_update2_ax,axiom,
% 0.22/0.53 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( tptp_update2 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select2_type,type,
% 0.22/0.53 a_select2: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_a_select2_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( a_select2 @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(use_type,type,
% 0.22/0.53 use: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_use_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ use @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(def_type,type,
% 0.22/0.53 def: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_def_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ def @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(minus_type,type,
% 0.22/0.53 minus: mu > mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_minus_ax,axiom,
% 0.22/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( minus @ V2 @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(pv35_type,type,
% 0.22/0.53 pv35: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_pv35_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ pv35 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(pv31_type,type,
% 0.22/0.53 pv31: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_pv31_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ pv31 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_minus_1_type,type,
% 0.22/0.53 tptp_minus_1: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_tptp_minus_1_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ tptp_minus_1 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n135300_type,type,
% 0.22/0.53 n135300: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n135300_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n135300 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n4_type,type,
% 0.22/0.53 n4: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n4_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n4 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n5_type,type,
% 0.22/0.53 n5: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n5_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n5 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n1_type,type,
% 0.22/0.53 n1: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n1_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n1 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n2_type,type,
% 0.22/0.53 n2: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n2_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n2 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n3_type,type,
% 0.22/0.53 n3: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n3_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n3 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(n0_type,type,
% 0.22/0.53 n0: mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_n0_ax,axiom,
% 0.22/0.53 ! [V: $i] : ( exists_in_world @ n0 @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_type,type,
% 0.22/0.53 succ: mu > mu ).
% 0.22/0.53
% 0.22/0.53 thf(existence_of_succ_ax,axiom,
% 0.22/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( succ @ V1 ) @ V ) ).
% 0.22/0.53
% 0.22/0.53 thf(reflexivity,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(symmetry,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(transitivity,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select2_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ A @ C ) @ ( a_select2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select2_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ C @ A ) @ ( a_select2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select3_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ A @ C @ D ) @ ( a_select3 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select3_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ C @ A @ D ) @ ( a_select3 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(a_select3_substitution_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ C @ D @ A ) @ ( a_select3 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(dim_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( dim @ A @ C ) @ ( dim @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(dim_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( dim @ C @ A ) @ ( dim @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(inv_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(minus_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( minus @ A @ C ) @ ( minus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(minus_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( minus @ C @ A ) @ ( minus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(plus_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( plus @ A @ C ) @ ( plus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(plus_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( plus @ C @ A ) @ ( plus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pred_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( pred @ A ) @ ( pred @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( succ @ A ) @ ( succ @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ A @ C @ D ) @ ( sum @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ C @ A @ D ) @ ( sum @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_substitution_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( sum @ C @ D @ A ) @ ( sum @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array1_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array1 @ A @ C ) @ ( tptp_const_array1 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array1_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_const_array1 @ C @ A ) @ ( tptp_const_array1 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array2_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array2_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_const_array2_substitution_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_madd_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_madd @ A @ C ) @ ( tptp_madd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_madd_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_madd @ C @ A ) @ ( tptp_madd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_mmul_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_mmul @ A @ C ) @ ( tptp_mmul @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_mmul_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_mmul @ C @ A ) @ ( tptp_mmul @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_msub_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_msub @ A @ C ) @ ( tptp_msub @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_msub_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_msub @ C @ A ) @ ( tptp_msub @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update2_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ A @ C @ D ) @ ( tptp_update2 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update2_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ C @ A @ D ) @ ( tptp_update2 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update2_substitution_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( tptp_update2 @ C @ D @ A ) @ ( tptp_update2 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update3_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update3_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update3_substitution_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(tptp_update3_substitution_4,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(trans_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( trans @ A ) @ ( trans @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(uniform_int_rnd_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( uniform_int_rnd @ A @ C ) @ ( uniform_int_rnd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(uniform_int_rnd_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( uniform_int_rnd @ C @ A ) @ ( uniform_int_rnd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(geq_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( geq @ A @ C ) ) ) @ ( mbox_s4 @ ( geq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(geq_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( geq @ C @ A ) ) ) @ ( mbox_s4 @ ( geq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( gt @ A @ C ) ) ) @ ( mbox_s4 @ ( gt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( gt @ C @ A ) ) ) @ ( mbox_s4 @ ( gt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( leq @ A @ C ) ) ) @ ( mbox_s4 @ ( leq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( leq @ C @ A ) ) ) @ ( mbox_s4 @ ( leq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(lt_substitution_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( lt @ A @ C ) ) ) @ ( mbox_s4 @ ( lt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(lt_substitution_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( lt @ C @ A ) ) ) @ ( mbox_s4 @ ( lt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(totality,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mor @ ( mbox_s4 @ ( gt @ X @ Y ) ) @ ( mor @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(transitivity_gt,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( gt @ X @ Y ) ) @ ( mbox_s4 @ ( gt @ Y @ Z ) ) ) @ ( mbox_s4 @ ( gt @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(irreflexivity_gt,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( gt @ X @ X ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(reflexivity_leq,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( leq @ X @ X ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(transitivity_leq,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( leq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(lt_gt,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_geq,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_gt1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( gt @ Y @ X ) ) @ ( mbox_s4 @ ( leq @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_gt2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) ) ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_gt_pred,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_succ,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( gt @ ( succ @ X ) @ X ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_succ,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ X @ Y ) ) @ ( mbox_s4 @ ( leq @ X @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_succ_gt_equiv,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(uniform_int_rand_ranges_hi,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(uniform_int_rand_ranges_lo,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(const_array1_select,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [L: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(const_array2_select,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [L1: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U1: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [J: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [L2: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U2: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_trans,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_inv,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_update_diagonal,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [J: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [K: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_add,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_sub,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_aba1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_aba2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [M: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(matrix_symm_joseph_update,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [A: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [B: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [C: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [D: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [E: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [F: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [N: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [M: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_plus_base,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Body: mu] : ( mbox_s4 @ ( qmltpeq @ ( sum @ n0 @ tptp_minus_1 @ Body ) @ n0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sum_plus_base_float,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Body: mu] : ( mbox_s4 @ ( qmltpeq @ tptp_float_0_0 @ ( sum @ n0 @ tptp_minus_1 @ Body ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ tptp_minus_1 ) @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_1_r,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n1 ) @ ( succ @ X ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_1_l,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n1 @ X ) @ ( succ @ X ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_2_r,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n2 ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_2_l,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n2 @ X ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_3_r,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n3 ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_3_l,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n3 @ X ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_4_r,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n4 ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_4_l,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n4 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_5_r,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ X @ n5 ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_plus_5_l,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( plus @ n5 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pred_minus_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( minus @ X @ n1 ) @ ( pred @ X ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pred_succ,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( pred @ ( succ @ X ) ) @ X ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(succ_pred,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ ( succ @ ( pred @ X ) ) @ X ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_succ_succ,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_succ_gt,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ ( succ @ X ) @ Y ) ) @ ( mbox_s4 @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(leq_minus,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( leq @ ( minus @ X @ Y ) @ X ) ) @ ( mbox_s4 @ ( leq @ n0 @ Y ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel3_update_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [V: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] : ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ U @ V ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel3_update_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [J: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [V: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel3_update_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [J: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [V: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I0: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) )
% 0.22/0.53 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox_s4 @ ( leq @ I @ U ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ J ) ) @ ( mbox_s4 @ ( leq @ J @ V ) ) ) ) ) )
% 0.22/0.53 @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ I @ J ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel2_update_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] : ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U ) @ VAL ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel2_update_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(sel2_update_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [U: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [VAL: mu] :
% 0.22/0.53 ( mbox_s4
% 0.22/0.53 @ ( mimplies
% 0.22/0.53 @ ( mand
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [I0: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I0 ) ) @ ( mbox_s4 @ ( leq @ I0 @ U ) ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ X @ I0 ) @ VAL ) ) ) ) ) )
% 0.22/0.53 @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ I ) ) @ ( mbox_s4 @ ( leq @ I @ U ) ) ) )
% 0.22/0.53 @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ttrue,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ true ) ).
% 0.22/0.53
% 0.22/0.53 thf(defuse,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ def @ use ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_4,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n4 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_4,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n4 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_5,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n5 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_4_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n4 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_0_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n0 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_1_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n1 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_2_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n2 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_3_tptp_minus_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n3 @ tptp_minus_1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_4_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_1_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n1 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_2_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n2 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_3_0,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_4_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_2_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n2 @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_3_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_4_2,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_2,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_2,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_3_2,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n3 @ n2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_4_3,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n4 @ n3 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_5_3,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n5 @ n3 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(gt_135300_3,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( gt @ n135300 @ n3 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_4,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_5,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_0,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [X: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ X ) ) @ ( mbox_s4 @ ( leq @ X @ n0 ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ n0 ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_1,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_2,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(finite_domain_3,axiom,
% 0.22/0.53 ( mvalid
% 0.22/0.53 @ ( mbox_s4
% 0.22/0.53 @ ( mforall_ind
% 0.22/0.53 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(successor_4,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) @ n4 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(successor_5,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) @ n5 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(successor_1,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ n0 ) @ n1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(successor_2,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ n0 ) ) @ n2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(successor_3,axiom,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( qmltpeq @ ( succ @ ( succ @ ( succ @ n0 ) ) ) @ n3 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(cl5_nebula_array_0014,conjecture,
% 0.22/0.53 mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) ) ) ).
% 0.22/0.60
% 0.22/0.60 %------------------------------------------------------------------------------
% 0.22/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cHLUhO1nLT/cvc5---1.0.5_3870.p...
% 0.22/0.60 (declare-sort $$unsorted 0)
% 0.22/0.60 (declare-sort tptp.mu 0)
% 0.22/0.60 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.22/0.60 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.22/0.60 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.22/0.60 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.22/0.60 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.22/0.60 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.22/0.60 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.22/0.60 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.22/0.60 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.22/0.60 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.60 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.22/0.60 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.22/0.60 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.22/0.60 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.22/0.60 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.22/0.60 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.22/0.60 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.22/0.60 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.22/0.60 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.22/0.60 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.22/0.60 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.60 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.60 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.60 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.60 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.60 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.22/0.60 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.60 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.60 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.22/0.60 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.22/0.60 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.22/0.60 (declare-fun tptp.true ($$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.lt (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.geq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.gt (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.leq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.60 (declare-fun tptp.uniform_int_rnd (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.uniform_int_rnd V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_const_array1 (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_const_array1 V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.dim (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.dim V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_const_array2 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_const_array2 V3) V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.inv (tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inv V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_msub (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_msub V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.trans (tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.trans V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_mmul (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_mmul V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_madd (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.tptp_madd V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.sum (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.sum V3) V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_float_0_0 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_float_0_0) V)))
% 0.22/0.60 (declare-fun tptp.plus (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.plus V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.pred (tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.pred V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_update3 (tptp.mu tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$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)))
% 0.22/0.60 (declare-fun tptp.a_select3 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.a_select3 V3) V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.tptp_update2 (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.tptp_update2 V3) V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.a_select2 (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.a_select2 V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.use () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.use) V)))
% 0.22/0.60 (declare-fun tptp.def () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.def) V)))
% 0.22/0.60 (declare-fun tptp.minus (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.minus V2) V1)) V)))
% 0.22/0.60 (declare-fun tptp.pv35 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.pv35) V)))
% 0.22/0.60 (declare-fun tptp.pv31 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.pv31) V)))
% 0.22/0.60 (declare-fun tptp.tptp_minus_1 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.tptp_minus_1) V)))
% 0.22/0.60 (declare-fun tptp.n135300 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n135300) V)))
% 0.22/0.60 (declare-fun tptp.n4 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n4) V)))
% 0.22/0.60 (declare-fun tptp.n5 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n5) V)))
% 0.22/0.60 (declare-fun tptp.n1 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n1) V)))
% 0.22/0.60 (declare-fun tptp.n2 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n2) V)))
% 0.22/0.60 (declare-fun tptp.n3 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n3) V)))
% 0.22/0.60 (declare-fun tptp.n0 () tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.n0) V)))
% 0.22/0.60 (declare-fun tptp.succ (tptp.mu) tptp.mu)
% 0.22/0.60 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.succ V1)) V)))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) Z)))) (@ tptp.mbox_s4 (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.a_select2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 A) C) D)) (@ (@ (@ tptp.a_select3 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ (@ tptp.a_select3 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.dim C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.inv A)) (@ tptp.inv B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.minus C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.plus C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.pred A)) (@ tptp.pred B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ A)) (@ tptp.succ B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.sum A) C) D)) (@ (@ (@ tptp.sum B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.sum C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ (@ tptp.sum C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_const_array1 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.tptp_const_array2 A) C) D)) (@ (@ (@ tptp.tptp_const_array2 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_const_array2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ (@ tptp.tptp_const_array2 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_madd C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_mmul C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_msub C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.tptp_update2 A) C) D)) (@ (@ (@ tptp.tptp_update2 B) C) D))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_update2 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ (@ tptp.tptp_update2 C) D))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.tptp_update3 C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ _let_1 A) D) E)) (@ (@ (@ _let_1 B) D) E))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ (@ (@ tptp.tptp_update3 C) D) E))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.trans A)) (@ tptp.trans B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.uniform_int_rnd C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.geq C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.gt C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.leq C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.lt C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ _let_1 A)))) (@ tptp.mbox_s4 (@ _let_1 B)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 (@ (@ tptp.gt X) Y))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.gt X) X)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.leq X) X)) __flatten_var_0))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.leq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 Y))) (@ tptp.mbox_s4 (@ (@ tptp.leq Y) Z)))) (@ tptp.mbox_s4 (@ _let_1 Z)))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.lt X) Y)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.geq X) Y)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.leq Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y)))))) (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq X) (@ tptp.pred Y))))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.gt (@ tptp.succ X)) X)) __flatten_var_0))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq L1) I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) U1))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq L2) J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) U2)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ tptp.tptp_const_array2 (@ (@ tptp.dim L1) U1)) (@ (@ tptp.dim L2) U2)) Val)) I) J)) Val)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ tptp.trans A)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ tptp.inv A)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 A) K) K) VAL)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq J) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 K))) (@ tptp.mbox_s4 (@ (@ tptp.leq K) N)))))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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 $$unsorted)) (let ((_let_1 (@ tptp.a_select3 (@ (@ tptp.tptp_msub A) B)))) (let ((_let_2 (@ tptp.leq tptp.n0))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 I))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq I) N))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_2 J))) (@ tptp.mbox_s4 (@ (@ tptp.leq J) N)))))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ _let_1 I) J)) (@ (@ _let_1 J) I))))) __flatten_var_0)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body)) tptp.n0)) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.tptp_float_0_0) (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ tptp.tptp_minus_1)) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n1)) (@ tptp.succ X))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n1) X)) (@ tptp.succ X))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n2)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n2) X)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n3)) (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n3) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n4)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n4) X)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n5)) (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ X))))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.minus X) tptp.n1)) (@ tptp.pred X))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.pred (@ tptp.succ X))) X)) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.pred X))) X)) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) (@ tptp.succ Y))))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.leq X) Y)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_2))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_1))) __flatten_var_0)))))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ tptp.succ X)) Y))) (@ tptp.mbox_s4 (@ (@ tptp.gt Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.leq (@ (@ tptp.minus X) Y)) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) Y)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.a_select3 (@ (@ (@ (@ tptp.tptp_update3 X) U) V) VAL)) U) V)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.a_select2 (@ (@ (@ tptp.tptp_update2 X) U) VAL)) U)) VAL)) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((I tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (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))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 tptp.true)))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.def) tptp.use))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n4))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n4))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n5))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n0) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n1) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.tptp_minus_1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n1) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n0))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n2) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n2))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n2))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n2))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n3) tptp.n2))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n4) tptp.n3))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n5) tptp.n3))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.gt tptp.n135300) tptp.n3))))
% 0.22/0.60 (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)))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n5)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n1))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n2))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n3))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n4))) (@ tptp.mbox_s4 (@ _let_1 tptp.n5))))))))) __flatten_var_0)))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.n0) X))) (@ tptp.mbox_s4 (@ (@ tptp.leq X) tptp.n1)))) (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_1 tptp.n0))) (@ tptp.mbox_s4 (@ _let_1 tptp.n1))))) __flatten_var_0)))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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)))))))
% 0.22/0.60 (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)))))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0))))) tptp.n4))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0)))))) tptp.n5))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ tptp.n0)) tptp.n1))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ tptp.n0))) tptp.n2))))
% 0.22/0.60 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ (@ tptp.succ (@ tptp.succ tptp.n0)))) tptp.n3))))
% 0.22/0.60 (assert (let ((_let_1 (@ tptp.leq tptp.n0))) (let ((_let_2 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 tptp.pv31))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 tptp.pv35))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv31) (@ (@ tptp.minus tptp.n5) tptp.n1)))) (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv35) (@ (@ tptp.minus tptp.n135300) tptp.n1)))))))) (not (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_2)))))))
% 1.82/2.02 (set-info :filename cvc5---1.0.5_3870)
% 1.82/2.02 (check-sat-assuming ( true ))
% 1.82/2.02 ------- get file name : TPTP file name is SWV073^7
% 1.82/2.02 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3870.smt2...
% 1.82/2.02 --- Run --ho-elim --full-saturate-quant at 10...
% 1.82/2.02 % SZS status Theorem for SWV073^7
% 1.82/2.02 % SZS output start Proof for SWV073^7
% 1.82/2.02 (
% 1.82/2.02 (let ((_let_1 (@ tptp.leq tptp.n0))) (let ((_let_2 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 tptp.pv31))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 tptp.pv35))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv31) (@ (@ tptp.minus tptp.n5) tptp.n1)))) (@ tptp.mbox_s4 (@ (@ tptp.leq tptp.pv35) (@ (@ tptp.minus tptp.n135300) tptp.n1)))))))) (let ((_let_3 (not (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_2)))))) (let ((_let_4 (@ tptp.succ tptp.n0))) (let ((_let_5 (@ tptp.succ _let_4))) (let ((_let_6 (@ tptp.succ _let_5))) (let ((_let_7 (@ tptp.succ _let_6))) (let ((_let_8 (@ tptp.gt tptp.n135300))) (let ((_let_9 (@ tptp.gt tptp.n5))) (let ((_let_10 (@ tptp.gt tptp.n4))) (let ((_let_11 (@ tptp.gt tptp.n3))) (let ((_let_12 (@ tptp.gt tptp.n2))) (let ((_let_13 (@ tptp.gt tptp.n1))) (let ((_let_14 (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_15 (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))) (let ((_let_16 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_17 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_18 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_19 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_20 (= 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_21 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_22 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_23 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_24 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_25 (= tptp.meuclidean (lambda ((R (-> $$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_26 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_27 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_28 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_29 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_30 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_31 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_32 (= 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_33 (= 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_34 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_35 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_36 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_37 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_38 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_39 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_40 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_41 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_42 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_43 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_44 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_45 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_46 (forall ((BOUND_VARIABLE_71445 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_71445) BOUND_VARIABLE_71445)) (ho_4 (ho_3 (ho_30 k_33 tptp.pv35) (ho_9 (ho_8 k_27 tptp.n135300) tptp.n1)) BOUND_VARIABLE_71445))))) (let ((_let_47 (forall ((BOUND_VARIABLE_71418 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_71418) BOUND_VARIABLE_71418)) (ho_4 (ho_3 (ho_30 k_33 tptp.n0) tptp.pv31) BOUND_VARIABLE_71418))))) (let ((_let_48 (forall ((BOUND_VARIABLE_71427 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_71427) BOUND_VARIABLE_71427)) (ho_4 (ho_3 (ho_30 k_33 tptp.n0) tptp.pv35) BOUND_VARIABLE_71427))))) (let ((_let_49 (forall ((BOUND_VARIABLE_71436 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_71436) BOUND_VARIABLE_71436)) (ho_4 (ho_3 (ho_30 k_33 tptp.pv31) (ho_9 (ho_8 k_27 tptp.n5) tptp.n1)) BOUND_VARIABLE_71436))))) (let ((_let_50 (not _let_46))) (let ((_let_51 (not _let_49))) (let ((_let_52 (not _let_48))) (let ((_let_53 (not _let_47))) (let ((_let_54 (forall ((BOUND_VARIABLE_71445 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_71445) BOUND_VARIABLE_71445)) (@ (@ (@ tptp.leq tptp.pv35) (@ (@ tptp.minus tptp.n135300) tptp.n1)) BOUND_VARIABLE_71445))))) (let ((_let_55 (forall ((BOUND_VARIABLE_71436 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_71436) BOUND_VARIABLE_71436)) (@ (@ (@ tptp.leq tptp.pv31) (@ (@ tptp.minus tptp.n5) tptp.n1)) BOUND_VARIABLE_71436))))) (let ((_let_56 (forall ((BOUND_VARIABLE_71427 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_71427) BOUND_VARIABLE_71427)) (@ (@ (@ tptp.leq tptp.n0) tptp.pv35) BOUND_VARIABLE_71427))))) (let ((_let_57 (forall ((BOUND_VARIABLE_71418 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_71418) BOUND_VARIABLE_71418)) (@ (@ (@ tptp.leq tptp.n0) tptp.pv31) BOUND_VARIABLE_71418))))) (let ((_let_58 (ASSUME :args (_let_45)))) (let ((_let_59 (ASSUME :args (_let_44)))) (let ((_let_60 (ASSUME :args (_let_43)))) (let ((_let_61 (ASSUME :args (_let_42)))) (let ((_let_62 (ASSUME :args (_let_41)))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (ASSUME :args (_let_29)))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (ASSUME :args (_let_19)))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (ASSUME :args (_let_16)))) (let ((_let_88 (ASSUME :args (_let_15)))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _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 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _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 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (and _let_57 _let_56 _let_55 _let_54) (not _let_57) (not _let_56) (not _let_55) (not _let_54) (forall ((W $$unsorted) (V $$unsorted)) (not (@ (@ tptp.rel_s4 W) V))))) (not (or (and _let_47 _let_48 _let_49 _let_46) _let_53 _let_52 _let_51 _let_50 (forall ((W $$unsorted) (V $$unsorted)) (not (ho_4 (ho_6 k_5 W) V)))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_NOT_ELIM (NOT_OR_ELIM _let_89 :args (4))) (MACRO_RESOLUTION_TRUST (REORDERING (NOT_AND (NOT_OR_ELIM _let_89 :args (0))) :args ((or _let_50 _let_51 _let_52 _let_53))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_89 :args (3))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_89 :args (2))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_89 :args (1))) :args (_let_50 false _let_49 false _let_48 false _let_47)) :args (false true _let_46)) :args (_let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))) _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 (@ 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 (@ (@ 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$$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.succ V1)) V)) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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) 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((_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))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body)) tptp.n0)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Body tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq tptp.tptp_float_0_0) (@ (@ (@ tptp.sum tptp.n0) tptp.tptp_minus_1) Body))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ tptp.tptp_minus_1)) tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n1)) (@ tptp.succ X))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n1) X)) (@ tptp.succ X))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus X) tptp.n2)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.plus tptp.n2) X)) (@ tptp.succ (@ tptp.succ X)))) __flatten_var_0))))) (@ tptp.mvalid (@ 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tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_8 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_13 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_12 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_11 tptp.n0))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_10 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_9 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_8 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_12 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_11 tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_10 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_9 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_8 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_11 tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_10 tptp.n3))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_9 tptp.n3))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ _let_8 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_7) tptp.n4))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.succ _let_7)) tptp.n5))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_4) tptp.n1))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_5) tptp.n2))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq _let_6) tptp.n3))) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.85/2.03 )
% 1.85/2.03 % SZS output end Proof for SWV073^7
% 1.85/2.03 % cvc5---1.0.5 exiting
% 1.85/2.03 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------