TSTP Solution File: SWV010^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV010^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 21:48:56 EDT 2023
% Result : Timeout 299.84s 300.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SWV010^7 : TPTP v8.1.2. Released v5.5.0.
% 0.15/0.16 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Tue Aug 29 08:21:37 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.24/0.52 %----Proving TH0
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 % File : SWV010^7 : TPTP v8.1.2. Released v5.5.0.
% 0.24/0.52 % Domain : Software Verification
% 0.24/0.52 % Problem : Fact 1 of the Neumann-Stubblebine analysis
% 0.24/0.52 % Version : [Ben12] axioms.
% 0.24/0.52 % English :
% 0.24/0.52
% 0.24/0.52 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.24/0.52 % : [Wei99] Weidenbach (1999), Towards and Automatic Analysis of S
% 0.24/0.52 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.24/0.52 % Source : [Ben12]
% 0.24/0.52 % Names : s4-cumul-GSV010+1 [Ben12]
% 0.24/0.52
% 0.24/0.52 % Status : Satisfiable
% 0.24/0.52 % Rating : 0.67 v6.1.0, 0.50 v5.5.0
% 0.24/0.52 % Syntax : Number of formulae : 124 ( 48 unt; 59 typ; 32 def)
% 0.24/0.52 % Number of atoms : 236 ( 36 equ; 0 cnn)
% 0.24/0.52 % Maximal formula atoms : 27 ( 3 avg)
% 0.24/0.52 % Number of connectives : 431 ( 5 ~; 5 |; 9 &; 402 @)
% 0.24/0.52 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.24/0.52 % Maximal formula depth : 37 ( 5 avg)
% 0.24/0.52 % Number of types : 3 ( 1 usr)
% 0.24/0.52 % Number of type conns : 215 ( 215 >; 0 *; 0 +; 0 <<)
% 0.24/0.52 % Number of symbols : 66 ( 64 usr; 13 con; 0-4 aty)
% 0.24/0.52 % Number of variables : 142 ( 67 ^; 68 !; 7 ?; 142 :)
% 0.24/0.52 % SPC : TH0_SAT_EQU_NAR
% 0.24/0.52
% 0.24/0.52 % Comments : Goedel translation of SWV010+1
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %----Include axioms for Modal logic S4 under cumulative domains
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %----Declaration of additional base type mu
% 0.24/0.52 thf(mu_type,type,
% 0.24/0.52 mu: $tType ).
% 0.24/0.52
% 0.24/0.52 %----Equality
% 0.24/0.52 thf(qmltpeq_type,type,
% 0.24/0.52 qmltpeq: mu > mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 % originale Definition
% 0.24/0.52 %thf(qmltpeq,definition,
% 0.24/0.52 % ( qmltpeq
% 0.24/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.24/0.52
% 0.24/0.52 % erweiterte Leibnitz-Definition
% 0.24/0.52 %thf(qmltpeq,definition,
% 0.24/0.52 % ( qmltpeq
% 0.24/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.24/0.52
% 0.24/0.52 % Leibnitz-Definition
% 0.24/0.52 %thf(qmltpeq,definition,
% 0.24/0.52 % ( qmltpeq
% 0.24/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.24/0.52
% 0.24/0.52 thf(meq_prop_type,type,
% 0.24/0.52 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(meq_prop,definition,
% 0.24/0.52 ( meq_prop
% 0.24/0.52 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.24/0.52 ( ( X @ W )
% 0.24/0.52 = ( Y @ W ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Modal operators not, or, box, Pi
% 0.24/0.52 thf(mnot_type,type,
% 0.24/0.52 mnot: ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mnot,definition,
% 0.24/0.52 ( mnot
% 0.24/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.24/0.52 ~ ( Phi @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mor_type,type,
% 0.24/0.52 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mor,definition,
% 0.24/0.52 ( mor
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.24/0.52 ( ( Phi @ W )
% 0.24/0.52 | ( Psi @ W ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mbox_type,type,
% 0.24/0.52 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mbox,definition,
% 0.24/0.52 ( mbox
% 0.24/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.24/0.52 ! [V: $i] :
% 0.24/0.52 ( ~ ( R @ W @ V )
% 0.24/0.52 | ( Phi @ V ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mforall_prop_type,type,
% 0.24/0.52 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mforall_prop,definition,
% 0.24/0.52 ( mforall_prop
% 0.24/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.24/0.52 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Further modal operators
% 0.24/0.52 thf(mtrue_type,type,
% 0.24/0.52 mtrue: $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mtrue,definition,
% 0.24/0.52 ( mtrue
% 0.24/0.52 = ( ^ [W: $i] : $true ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mfalse_type,type,
% 0.24/0.52 mfalse: $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mfalse,definition,
% 0.24/0.52 ( mfalse
% 0.24/0.52 = ( mnot @ mtrue ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mand_type,type,
% 0.24/0.52 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mand,definition,
% 0.24/0.52 ( mand
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mimplies_type,type,
% 0.24/0.52 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mimplies,definition,
% 0.24/0.52 ( mimplies
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mimplied_type,type,
% 0.24/0.52 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mimplied,definition,
% 0.24/0.52 ( mimplied
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mequiv_type,type,
% 0.24/0.52 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mequiv,definition,
% 0.24/0.52 ( mequiv
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mxor_type,type,
% 0.24/0.52 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mxor,definition,
% 0.24/0.52 ( mxor
% 0.24/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mdia_type,type,
% 0.24/0.52 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mdia,definition,
% 0.24/0.52 ( mdia
% 0.24/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %--- (new for cumulative)
% 0.24/0.52 %---Declaration of existence predicate for simulating cumulative domain
% 0.24/0.52 thf(exists_in_world_type,type,
% 0.24/0.52 exists_in_world: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 %----The domains are non-empty
% 0.24/0.52 thf(nonempty_ax,axiom,
% 0.24/0.52 ! [V: $i] :
% 0.24/0.52 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(mforall_ind_type,type,
% 0.24/0.52 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 %--- (new for cumulative)
% 0.24/0.52 thf(mforall_ind,definition,
% 0.24/0.52 ( mforall_ind
% 0.24/0.52 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.24/0.52 ! [X: mu] :
% 0.24/0.52 ( ( exists_in_world @ X @ W )
% 0.24/0.52 => ( Phi @ X @ W ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %thf(mforall_ind,definition,
% 0.24/0.52 % ( mforall_ind
% 0.24/0.52 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.24/0.52 % ! [X: mu] :
% 0.24/0.52 % ( Phi @ X @ W ) ) )).
% 0.24/0.52
% 0.24/0.52 thf(mexists_ind_type,type,
% 0.24/0.52 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mexists_ind,definition,
% 0.24/0.52 ( mexists_ind
% 0.24/0.52 = ( ^ [Phi: mu > $i > $o] :
% 0.24/0.52 ( mnot
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mexists_prop_type,type,
% 0.24/0.52 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mexists_prop,definition,
% 0.24/0.52 ( mexists_prop
% 0.24/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.24/0.52 ( mnot
% 0.24/0.52 @ ( mforall_prop
% 0.24/0.52 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Definition of properties of accessibility relations
% 0.24/0.52 thf(mreflexive_type,type,
% 0.24/0.52 mreflexive: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mreflexive,definition,
% 0.24/0.52 ( mreflexive
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(msymmetric_type,type,
% 0.24/0.52 msymmetric: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(msymmetric,definition,
% 0.24/0.52 ( msymmetric
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i] :
% 0.24/0.52 ( ( R @ S @ T )
% 0.24/0.52 => ( R @ T @ S ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mserial_type,type,
% 0.24/0.52 mserial: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mserial,definition,
% 0.24/0.52 ( mserial
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i] :
% 0.24/0.52 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mtransitive_type,type,
% 0.24/0.52 mtransitive: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mtransitive,definition,
% 0.24/0.52 ( mtransitive
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( ( R @ S @ T )
% 0.24/0.52 & ( R @ T @ U ) )
% 0.24/0.52 => ( R @ S @ U ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(meuclidean_type,type,
% 0.24/0.52 meuclidean: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(meuclidean,definition,
% 0.24/0.52 ( meuclidean
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( ( R @ S @ T )
% 0.24/0.52 & ( R @ S @ U ) )
% 0.24/0.52 => ( R @ T @ U ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mpartially_functional_type,type,
% 0.24/0.52 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mpartially_functional,definition,
% 0.24/0.52 ( mpartially_functional
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( ( R @ S @ T )
% 0.24/0.52 & ( R @ S @ U ) )
% 0.24/0.52 => ( T = U ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mfunctional_type,type,
% 0.24/0.52 mfunctional: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mfunctional,definition,
% 0.24/0.52 ( mfunctional
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i] :
% 0.24/0.52 ? [T: $i] :
% 0.24/0.52 ( ( R @ S @ T )
% 0.24/0.52 & ! [U: $i] :
% 0.24/0.52 ( ( R @ S @ U )
% 0.24/0.52 => ( T = U ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_dense_type,type,
% 0.24/0.52 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_dense,definition,
% 0.24/0.52 ( mweakly_dense
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( R @ S @ T )
% 0.24/0.52 => ? [U: $i] :
% 0.24/0.52 ( ( R @ S @ U )
% 0.24/0.52 & ( R @ U @ T ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_connected_type,type,
% 0.24/0.52 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_connected,definition,
% 0.24/0.52 ( mweakly_connected
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( ( R @ S @ T )
% 0.24/0.52 & ( R @ S @ U ) )
% 0.24/0.52 => ( ( R @ T @ U )
% 0.24/0.52 | ( T = U )
% 0.24/0.52 | ( R @ U @ T ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_directed_type,type,
% 0.24/0.52 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mweakly_directed,definition,
% 0.24/0.52 ( mweakly_directed
% 0.24/0.52 = ( ^ [R: $i > $i > $o] :
% 0.24/0.52 ! [S: $i,T: $i,U: $i] :
% 0.24/0.52 ( ( ( R @ S @ T )
% 0.24/0.52 & ( R @ S @ U ) )
% 0.24/0.52 => ? [V: $i] :
% 0.24/0.52 ( ( R @ T @ V )
% 0.24/0.52 & ( R @ U @ V ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Definition of validity
% 0.24/0.52 thf(mvalid_type,type,
% 0.24/0.52 mvalid: ( $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mvalid,definition,
% 0.24/0.52 ( mvalid
% 0.24/0.52 = ( ^ [Phi: $i > $o] :
% 0.24/0.52 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Definition of satisfiability
% 0.24/0.52 thf(msatisfiable_type,type,
% 0.24/0.52 msatisfiable: ( $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(msatisfiable,definition,
% 0.24/0.52 ( msatisfiable
% 0.24/0.52 = ( ^ [Phi: $i > $o] :
% 0.24/0.52 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Definition of countersatisfiability
% 0.24/0.52 thf(mcountersatisfiable_type,type,
% 0.24/0.52 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mcountersatisfiable,definition,
% 0.24/0.52 ( mcountersatisfiable
% 0.24/0.52 = ( ^ [Phi: $i > $o] :
% 0.24/0.52 ? [W: $i] :
% 0.24/0.52 ~ ( Phi @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----Definition of invalidity
% 0.24/0.52 thf(minvalid_type,type,
% 0.24/0.52 minvalid: ( $i > $o ) > $o ).
% 0.24/0.52
% 0.24/0.52 thf(minvalid,definition,
% 0.24/0.52 ( minvalid
% 0.24/0.52 = ( ^ [Phi: $i > $o] :
% 0.24/0.52 ! [W: $i] :
% 0.24/0.52 ~ ( Phi @ W ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %----We reserve an accessibility relation constant rel_s4
% 0.24/0.52 thf(rel_s4_type,type,
% 0.24/0.52 rel_s4: $i > $i > $o ).
% 0.24/0.52
% 0.24/0.52 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.24/0.52 thf(mbox_s4_type,type,
% 0.24/0.52 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mbox_s4,definition,
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.24/0.52 ! [V: $i] :
% 0.24/0.52 ( ~ ( rel_s4 @ W @ V )
% 0.24/0.52 | ( Phi @ V ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(mdia_s4_type,type,
% 0.24/0.52 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mdia_s4,definition,
% 0.24/0.52 ( mdia_s4
% 0.24/0.52 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %----We have now two options for stating the B conditions:
% 0.24/0.52 %----We can (i) directly formulate conditions for the accessibility relation
% 0.24/0.52 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.24/0.52 thf(a1,axiom,
% 0.24/0.52 mreflexive @ rel_s4 ).
% 0.24/0.52
% 0.24/0.52 thf(a2,axiom,
% 0.24/0.52 mtransitive @ rel_s4 ).
% 0.24/0.52
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 thf(cumulative_ax,axiom,
% 0.24/0.52 ! [X: mu,V: $i,W: $i] :
% 0.24/0.52 ( ( ( exists_in_world @ X @ V )
% 0.24/0.52 & ( rel_s4 @ V @ W ) )
% 0.24/0.52 => ( exists_in_world @ X @ W ) ) ).
% 0.24/0.52
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 thf(a_holds_type,type,
% 0.24/0.52 a_holds: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(a_stored_type,type,
% 0.24/0.52 a_stored: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(fresh_to_b_type,type,
% 0.24/0.52 fresh_to_b: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(b_holds_type,type,
% 0.24/0.52 b_holds: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(b_stored_type,type,
% 0.24/0.52 b_stored: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(party_of_protocol_type,type,
% 0.24/0.52 party_of_protocol: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(t_holds_type,type,
% 0.24/0.52 t_holds: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(message_type,type,
% 0.24/0.52 message: mu > $i > $o ).
% 0.24/0.52
% 0.24/0.52 thf(an_a_nonce_type,type,
% 0.24/0.52 an_a_nonce: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_an_a_nonce_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ an_a_nonce @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(generate_b_nonce_type,type,
% 0.24/0.52 generate_b_nonce: mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_generate_b_nonce_ax,axiom,
% 0.24/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( generate_b_nonce @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(generate_expiration_time_type,type,
% 0.24/0.52 generate_expiration_time: mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_generate_expiration_time_ax,axiom,
% 0.24/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( generate_expiration_time @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(pair_type,type,
% 0.24/0.52 pair: mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_pair_ax,axiom,
% 0.24/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( pair @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_type,type,
% 0.24/0.52 a: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_a_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ a @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(at_type,type,
% 0.24/0.52 at: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_at_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ at @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(b_type,type,
% 0.24/0.52 b: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_b_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ b @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(bt_type,type,
% 0.24/0.52 bt: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_bt_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ bt @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(generate_key_type,type,
% 0.24/0.52 generate_key: mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_generate_key_ax,axiom,
% 0.24/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( generate_key @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(quadruple_type,type,
% 0.24/0.52 quadruple: mu > mu > mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_quadruple_ax,axiom,
% 0.24/0.52 ! [V: $i,V4: mu,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( quadruple @ V4 @ V3 @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(key_type,type,
% 0.24/0.52 key: mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_key_ax,axiom,
% 0.24/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( key @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(encrypt_type,type,
% 0.24/0.52 encrypt: mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_encrypt_ax,axiom,
% 0.24/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( encrypt @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(triple_type,type,
% 0.24/0.52 triple: mu > mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_triple_ax,axiom,
% 0.24/0.52 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( triple @ V3 @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(t_type,type,
% 0.24/0.52 t: mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_t_ax,axiom,
% 0.24/0.52 ! [V: $i] : ( exists_in_world @ t @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(sent_type,type,
% 0.24/0.52 sent: mu > mu > mu > mu ).
% 0.24/0.52
% 0.24/0.52 thf(existence_of_sent_ax,axiom,
% 0.24/0.52 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( sent @ V3 @ V2 @ V1 ) @ V ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_holds_key_at_for_t,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( a_holds @ ( key @ at @ t ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_is_party_of_protocol,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( party_of_protocol @ a ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_sent_message_i_to_b,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( message @ ( sent @ a @ b @ ( pair @ a @ an_a_nonce ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_stored_message_i,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( a_stored @ ( pair @ b @ an_a_nonce ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(a_forwards_secure,axiom,
% 0.24/0.52 ( mvalid
% 0.24/0.52 @ ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [U: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [V: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [W: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [X: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [Y: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ Y @ Z @ W @ V ) @ at ) @ X @ U ) ) ) ) @ ( mbox_s4 @ ( a_stored @ ( pair @ Y @ Z ) ) ) ) @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ a @ Y @ ( pair @ X @ ( encrypt @ U @ W ) ) ) ) ) @ ( mbox_s4 @ ( a_holds @ ( key @ W @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(b_hold_key_bt_for_t,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( b_holds @ ( key @ bt @ t ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(b_is_party_of_protocol,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( party_of_protocol @ b ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(nonce_a_is_fresh_to_b,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( fresh_to_b @ an_a_nonce ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(b_creates_freash_nonces_in_time,axiom,
% 0.24/0.52 ( mvalid
% 0.24/0.52 @ ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [U: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [V: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ U @ b @ ( pair @ U @ V ) ) ) ) @ ( mbox_s4 @ ( fresh_to_b @ V ) ) ) @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ V ) @ ( encrypt @ ( triple @ U @ V @ ( generate_expiration_time @ V ) ) @ bt ) ) ) ) ) @ ( mbox_s4 @ ( b_stored @ ( pair @ U @ V ) ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(b_accepts_secure_session_key,axiom,
% 0.24/0.52 ( mvalid
% 0.24/0.52 @ ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [V: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [X: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ X @ b @ ( pair @ ( encrypt @ ( triple @ X @ V @ ( generate_expiration_time @ Y ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ Y ) @ V ) ) ) ) ) @ ( mbox_s4 @ ( b_stored @ ( pair @ X @ Y ) ) ) ) @ ( mbox_s4 @ ( b_holds @ ( key @ V @ X ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(t_holds_key_at_for_a,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( t_holds @ ( key @ at @ a ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(t_holds_key_bt_for_b,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( t_holds @ ( key @ bt @ b ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(t_is_party_of_protocol,axiom,
% 0.24/0.52 mvalid @ ( mbox_s4 @ ( party_of_protocol @ t ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(server_t_generates_key,axiom,
% 0.24/0.52 ( mvalid
% 0.24/0.52 @ ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [U: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [V: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [W: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [X: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [Y: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [Z: mu] :
% 0.24/0.52 ( mbox_s4
% 0.24/0.52 @ ( mforall_ind
% 0.24/0.52 @ ^ [X1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ U @ t @ ( triple @ U @ V @ ( encrypt @ ( triple @ W @ X @ Y ) @ Z ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( t_holds @ ( key @ Z @ U ) ) ) @ ( mbox_s4 @ ( t_holds @ ( key @ X1 @ W ) ) ) ) ) @ ( mbox_s4 @ ( message @ ( sent @ t @ W @ ( triple @ ( encrypt @ ( quadruple @ U @ X @ ( generate_key @ X ) @ Y ) @ X1 ) @ ( encrypt @ ( triple @ W @ ( generate_key @ X ) @ Y ) @ Z ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Aud0DDAxB4/cvc5---1.0.5_3893.p...
% 0.24/0.54 (declare-sort $$unsorted 0)
% 0.24/0.54 (declare-sort tptp.mu 0)
% 0.24/0.54 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.24/0.54 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.24/0.54 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.24/0.54 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.24/0.54 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.24/0.54 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.24/0.54 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.24/0.54 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.24/0.54 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.24/0.54 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.24/0.54 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.24/0.54 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.24/0.54 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.24/0.54 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.24/0.54 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.24/0.54 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.24/0.54 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.24/0.54 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.24/0.54 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.24/0.54 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.24/0.54 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.24/0.54 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.24/0.54 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.24/0.54 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.24/0.54 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.24/0.54 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.24/0.54 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.24/0.54 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.24/0.54 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.24/0.54 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.24/0.54 (declare-fun tptp.a_holds (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.a_stored (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.fresh_to_b (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.b_holds (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.b_stored (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.party_of_protocol (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.t_holds (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.message (tptp.mu $$unsorted) Bool)
% 0.24/0.54 (declare-fun tptp.an_a_nonce () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.an_a_nonce) V)))
% 0.24/0.54 (declare-fun tptp.generate_b_nonce (tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.generate_b_nonce V1)) V)))
% 0.24/0.54 (declare-fun tptp.generate_expiration_time (tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.generate_expiration_time V1)) V)))
% 0.24/0.54 (declare-fun tptp.pair (tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.pair V2) V1)) V)))
% 0.24/0.54 (declare-fun tptp.a () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.a) V)))
% 0.24/0.54 (declare-fun tptp.at () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.at) V)))
% 0.24/0.54 (declare-fun tptp.b () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.b) V)))
% 0.24/0.54 (declare-fun tptp.bt () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.bt) V)))
% 0.24/0.54 (declare-fun tptp.generate_key (tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.generate_key V1)) V)))
% 0.24/0.54 (declare-fun tptp.quadruple (tptp.mu tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V4 tptp.mu) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ (@ tptp.quadruple V4) V3) V2) V1)) V)))
% 0.24/0.54 (declare-fun tptp.key (tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.key V2) V1)) V)))
% 0.24/0.54 (declare-fun tptp.encrypt (tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.encrypt V2) V1)) V)))
% 0.24/0.54 (declare-fun tptp.triple (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.triple V3) V2) V1)) V)))
% 0.24/0.54 (declare-fun tptp.t () tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.t) V)))
% 0.24/0.54 (declare-fun tptp.sent (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.24/0.54 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.sent V3) V2) V1)) V)))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.a_holds (@ (@ tptp.key tptp.at) tptp.t)))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.party_of_protocol tptp.a))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent tptp.a) tptp.b) (@ (@ tptp.pair tptp.a) tptp.an_a_nonce))))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.a_stored (@ (@ tptp.pair tptp.b) tptp.an_a_nonce)))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ 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 ((W 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 ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent tptp.t) tptp.a) (@ (@ (@ tptp.triple (@ (@ tptp.encrypt (@ (@ (@ (@ tptp.quadruple Y) Z) W) V)) tptp.at)) X) U))))) (@ tptp.mbox_s4 (@ tptp.a_stored (@ (@ tptp.pair Y) Z))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent tptp.a) Y) (@ (@ tptp.pair X) (@ (@ tptp.encrypt U) W)))))) (@ tptp.mbox_s4 (@ tptp.a_holds (@ (@ tptp.key W) Y)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.b_holds (@ (@ tptp.key tptp.bt) tptp.t)))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.party_of_protocol tptp.b))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.fresh_to_b tptp.an_a_nonce))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ 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)) (let ((_let_1 (@ (@ tptp.pair U) V))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent U) tptp.b) _let_1)))) (@ tptp.mbox_s4 (@ tptp.fresh_to_b V)))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent tptp.b) tptp.t) (@ (@ (@ tptp.triple tptp.b) (@ tptp.generate_b_nonce V)) (@ (@ tptp.encrypt (@ (@ (@ tptp.triple U) V) (@ tptp.generate_expiration_time V))) tptp.bt)))))) (@ tptp.mbox_s4 (@ tptp.b_stored _let_1))))) __flatten_var_0))))) __flatten_var_0))))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ 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 ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent X) tptp.b) (@ (@ tptp.pair (@ (@ tptp.encrypt (@ (@ (@ tptp.triple X) V) (@ tptp.generate_expiration_time Y))) tptp.bt)) (@ (@ tptp.encrypt (@ tptp.generate_b_nonce Y)) V)))))) (@ tptp.mbox_s4 (@ tptp.b_stored (@ (@ tptp.pair X) Y))))) (@ tptp.mbox_s4 (@ tptp.b_holds (@ (@ tptp.key V) X))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.t_holds (@ (@ tptp.key tptp.at) tptp.a)))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.t_holds (@ (@ tptp.key tptp.bt) tptp.b)))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.party_of_protocol tptp.t))))
% 0.24/0.54 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X1 tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.generate_key X))) (let ((_let_2 (@ tptp.triple W))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent U) tptp.t) (@ (@ (@ tptp.triple U) V) (@ (@ tptp.encrypt (@ (@ _let_2 X) Y)) Z)))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.t_holds (@ (@ tptp.key Z) U)))) (@ tptp.mbox_s4 (@ tptp.t_holds (@ (@ tptp.key X1) W)))))) (@ tptp.mbox_s4 (@ tptp.message (@ (@ (@ tptp.sent tptp.t) W) (@ (@ (@ tptp.triple (@ (@ tptp.encrypt (@ (@ (@ (@ tptp.quadruple U) X) _let_1) Y)) X1)) (@ (@ tptp.encrypt (@ (@ _let_2 _let_1) Y)) Z)) V)))))) __flatten_var_0)))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.24/0.54 (set-info :filename cvc5---1.0.5_3893)
% 0.24/0.54 (check-sat)
% 0.24/0.54 ------- get file name : TPTP file name is SWV010^7
% 0.24/0.54 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3893.smt2...
% 0.24/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 10.31/10.55 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 20.36/20.57 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 30.33/30.58 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.38/35.60 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.43/40.70 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 50.56/50.76 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 60.58/60.86 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 70.53/70.88 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 80.68/80.94 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.84/300.16 /export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 6139 Alarm clock ( read result; case "$result" in
% 299.84/300.16 unsat)
% 299.84/300.16 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.84/300.16 ;;
% 299.84/300.16 sat)
% 299.84/300.16 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.84/300.16 ;;
% 299.84/300.16 esac; exit 1 )
% 299.84/300.17 % cvc5---1.0.5 exiting
% 299.84/300.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------