TSTP Solution File: SET925^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET925^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 14:41:02 EDT 2023
% Result : Theorem 0.19s 0.65s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET925^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 09:17:15 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.50 %----Proving TH0
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 % File : SET925^7 : TPTP v8.1.2. Released v5.5.0.
% 0.19/0.50 % Domain : Set Theory
% 0.19/0.50 % Problem : difference(singleton(A),B) = empty_set <=> in(A,B)
% 0.19/0.50 % Version : [Ben12] axioms.
% 0.19/0.50 % English :
% 0.19/0.50
% 0.19/0.50 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.19/0.50 % : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.50 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.19/0.50 % Source : [Ben12]
% 0.19/0.50 % Names : s4-cumul-GSE925+1 [Ben12]
% 0.19/0.50
% 0.19/0.50 % Status : Theorem
% 0.19/0.50 % Rating : 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0
% 0.19/0.50 % Syntax : Number of formulae : 95 ( 36 unt; 41 typ; 32 def)
% 0.19/0.50 % Number of atoms : 286 ( 36 equ; 0 cnn)
% 0.19/0.50 % Maximal formula atoms : 18 ( 5 avg)
% 0.19/0.50 % Number of connectives : 402 ( 5 ~; 5 |; 9 &; 373 @)
% 0.19/0.50 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.19/0.50 % Maximal formula depth : 19 ( 5 avg)
% 0.19/0.50 % Number of types : 3 ( 1 usr)
% 0.19/0.50 % Number of type conns : 188 ( 188 >; 0 *; 0 +; 0 <<)
% 0.19/0.50 % Number of symbols : 51 ( 49 usr; 11 con; 0-3 aty)
% 0.19/0.50 % Number of variables : 126 ( 79 ^; 40 !; 7 ?; 126 :)
% 0.19/0.50 % SPC : TH0_THM_EQU_NAR
% 0.19/0.50
% 0.19/0.50 % Comments : Goedel translation of SET925+1
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %----Include axioms for Modal logic S4 under cumulative domains
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %----Declaration of additional base type mu
% 0.19/0.50 thf(mu_type,type,
% 0.19/0.50 mu: $tType ).
% 0.19/0.50
% 0.19/0.50 %----Equality
% 0.19/0.50 thf(qmltpeq_type,type,
% 0.19/0.50 qmltpeq: mu > mu > $i > $o ).
% 0.19/0.50
% 0.19/0.50 % originale Definition
% 0.19/0.50 %thf(qmltpeq,definition,
% 0.19/0.50 % ( qmltpeq
% 0.19/0.50 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.19/0.50
% 0.19/0.50 % erweiterte Leibnitz-Definition
% 0.19/0.50 %thf(qmltpeq,definition,
% 0.19/0.50 % ( qmltpeq
% 0.19/0.50 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.19/0.50
% 0.19/0.50 % Leibnitz-Definition
% 0.19/0.50 %thf(qmltpeq,definition,
% 0.19/0.50 % ( qmltpeq
% 0.19/0.50 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.19/0.50
% 0.19/0.50 thf(meq_prop_type,type,
% 0.19/0.50 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(meq_prop,definition,
% 0.19/0.50 ( meq_prop
% 0.19/0.50 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.19/0.50 ( ( X @ W )
% 0.19/0.50 = ( Y @ W ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Modal operators not, or, box, Pi
% 0.19/0.50 thf(mnot_type,type,
% 0.19/0.50 mnot: ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mnot,definition,
% 0.19/0.50 ( mnot
% 0.19/0.50 = ( ^ [Phi: $i > $o,W: $i] :
% 0.19/0.50 ~ ( Phi @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mor_type,type,
% 0.19/0.50 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mor,definition,
% 0.19/0.50 ( mor
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.19/0.50 ( ( Phi @ W )
% 0.19/0.50 | ( Psi @ W ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mbox_type,type,
% 0.19/0.50 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mbox,definition,
% 0.19/0.50 ( mbox
% 0.19/0.50 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.19/0.50 ! [V: $i] :
% 0.19/0.50 ( ~ ( R @ W @ V )
% 0.19/0.50 | ( Phi @ V ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mforall_prop_type,type,
% 0.19/0.50 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mforall_prop,definition,
% 0.19/0.50 ( mforall_prop
% 0.19/0.50 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.19/0.50 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Further modal operators
% 0.19/0.50 thf(mtrue_type,type,
% 0.19/0.50 mtrue: $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mtrue,definition,
% 0.19/0.50 ( mtrue
% 0.19/0.50 = ( ^ [W: $i] : $true ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mfalse_type,type,
% 0.19/0.50 mfalse: $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mfalse,definition,
% 0.19/0.50 ( mfalse
% 0.19/0.50 = ( mnot @ mtrue ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mand_type,type,
% 0.19/0.50 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mand,definition,
% 0.19/0.50 ( mand
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mimplies_type,type,
% 0.19/0.50 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mimplies,definition,
% 0.19/0.50 ( mimplies
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mimplied_type,type,
% 0.19/0.50 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mimplied,definition,
% 0.19/0.50 ( mimplied
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mequiv_type,type,
% 0.19/0.50 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mequiv,definition,
% 0.19/0.50 ( mequiv
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mxor_type,type,
% 0.19/0.50 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mxor,definition,
% 0.19/0.50 ( mxor
% 0.19/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mdia_type,type,
% 0.19/0.50 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mdia,definition,
% 0.19/0.50 ( mdia
% 0.19/0.50 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %--- (new for cumulative)
% 0.19/0.50 %---Declaration of existence predicate for simulating cumulative domain
% 0.19/0.50 thf(exists_in_world_type,type,
% 0.19/0.50 exists_in_world: mu > $i > $o ).
% 0.19/0.50
% 0.19/0.50 %----The domains are non-empty
% 0.19/0.50 thf(nonempty_ax,axiom,
% 0.19/0.50 ! [V: $i] :
% 0.19/0.50 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.19/0.50
% 0.19/0.50 thf(mforall_ind_type,type,
% 0.19/0.50 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 %--- (new for cumulative)
% 0.19/0.50 thf(mforall_ind,definition,
% 0.19/0.50 ( mforall_ind
% 0.19/0.50 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.19/0.50 ! [X: mu] :
% 0.19/0.50 ( ( exists_in_world @ X @ W )
% 0.19/0.50 => ( Phi @ X @ W ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %thf(mforall_ind,definition,
% 0.19/0.50 % ( mforall_ind
% 0.19/0.50 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.19/0.50 % ! [X: mu] :
% 0.19/0.50 % ( Phi @ X @ W ) ) )).
% 0.19/0.50
% 0.19/0.50 thf(mexists_ind_type,type,
% 0.19/0.50 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mexists_ind,definition,
% 0.19/0.50 ( mexists_ind
% 0.19/0.50 = ( ^ [Phi: mu > $i > $o] :
% 0.19/0.50 ( mnot
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mexists_prop_type,type,
% 0.19/0.50 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mexists_prop,definition,
% 0.19/0.50 ( mexists_prop
% 0.19/0.50 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.19/0.50 ( mnot
% 0.19/0.50 @ ( mforall_prop
% 0.19/0.50 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Definition of properties of accessibility relations
% 0.19/0.50 thf(mreflexive_type,type,
% 0.19/0.50 mreflexive: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mreflexive,definition,
% 0.19/0.50 ( mreflexive
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(msymmetric_type,type,
% 0.19/0.50 msymmetric: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(msymmetric,definition,
% 0.19/0.50 ( msymmetric
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i] :
% 0.19/0.50 ( ( R @ S @ T )
% 0.19/0.50 => ( R @ T @ S ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mserial_type,type,
% 0.19/0.50 mserial: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mserial,definition,
% 0.19/0.50 ( mserial
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i] :
% 0.19/0.50 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mtransitive_type,type,
% 0.19/0.50 mtransitive: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mtransitive,definition,
% 0.19/0.50 ( mtransitive
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( ( R @ S @ T )
% 0.19/0.50 & ( R @ T @ U ) )
% 0.19/0.50 => ( R @ S @ U ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(meuclidean_type,type,
% 0.19/0.50 meuclidean: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(meuclidean,definition,
% 0.19/0.50 ( meuclidean
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( ( R @ S @ T )
% 0.19/0.50 & ( R @ S @ U ) )
% 0.19/0.50 => ( R @ T @ U ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mpartially_functional_type,type,
% 0.19/0.50 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mpartially_functional,definition,
% 0.19/0.50 ( mpartially_functional
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( ( R @ S @ T )
% 0.19/0.50 & ( R @ S @ U ) )
% 0.19/0.50 => ( T = U ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mfunctional_type,type,
% 0.19/0.50 mfunctional: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mfunctional,definition,
% 0.19/0.50 ( mfunctional
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i] :
% 0.19/0.50 ? [T: $i] :
% 0.19/0.50 ( ( R @ S @ T )
% 0.19/0.50 & ! [U: $i] :
% 0.19/0.50 ( ( R @ S @ U )
% 0.19/0.50 => ( T = U ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_dense_type,type,
% 0.19/0.50 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_dense,definition,
% 0.19/0.50 ( mweakly_dense
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( R @ S @ T )
% 0.19/0.50 => ? [U: $i] :
% 0.19/0.50 ( ( R @ S @ U )
% 0.19/0.50 & ( R @ U @ T ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_connected_type,type,
% 0.19/0.50 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_connected,definition,
% 0.19/0.50 ( mweakly_connected
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( ( R @ S @ T )
% 0.19/0.50 & ( R @ S @ U ) )
% 0.19/0.50 => ( ( R @ T @ U )
% 0.19/0.50 | ( T = U )
% 0.19/0.50 | ( R @ U @ T ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_directed_type,type,
% 0.19/0.50 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mweakly_directed,definition,
% 0.19/0.50 ( mweakly_directed
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [S: $i,T: $i,U: $i] :
% 0.19/0.50 ( ( ( R @ S @ T )
% 0.19/0.50 & ( R @ S @ U ) )
% 0.19/0.50 => ? [V: $i] :
% 0.19/0.50 ( ( R @ T @ V )
% 0.19/0.50 & ( R @ U @ V ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Definition of validity
% 0.19/0.50 thf(mvalid_type,type,
% 0.19/0.50 mvalid: ( $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mvalid,definition,
% 0.19/0.50 ( mvalid
% 0.19/0.50 = ( ^ [Phi: $i > $o] :
% 0.19/0.50 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Definition of satisfiability
% 0.19/0.50 thf(msatisfiable_type,type,
% 0.19/0.50 msatisfiable: ( $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(msatisfiable,definition,
% 0.19/0.50 ( msatisfiable
% 0.19/0.50 = ( ^ [Phi: $i > $o] :
% 0.19/0.50 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Definition of countersatisfiability
% 0.19/0.50 thf(mcountersatisfiable_type,type,
% 0.19/0.50 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mcountersatisfiable,definition,
% 0.19/0.50 ( mcountersatisfiable
% 0.19/0.50 = ( ^ [Phi: $i > $o] :
% 0.19/0.50 ? [W: $i] :
% 0.19/0.50 ~ ( Phi @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----Definition of invalidity
% 0.19/0.50 thf(minvalid_type,type,
% 0.19/0.50 minvalid: ( $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(minvalid,definition,
% 0.19/0.50 ( minvalid
% 0.19/0.50 = ( ^ [Phi: $i > $o] :
% 0.19/0.50 ! [W: $i] :
% 0.19/0.50 ~ ( Phi @ W ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %----We reserve an accessibility relation constant rel_s4
% 0.19/0.50 thf(rel_s4_type,type,
% 0.19/0.50 rel_s4: $i > $i > $o ).
% 0.19/0.50
% 0.19/0.50 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.19/0.50 thf(mbox_s4_type,type,
% 0.19/0.50 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mbox_s4,definition,
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 = ( ^ [Phi: $i > $o,W: $i] :
% 0.19/0.50 ! [V: $i] :
% 0.19/0.50 ( ~ ( rel_s4 @ W @ V )
% 0.19/0.50 | ( Phi @ V ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(mdia_s4_type,type,
% 0.19/0.50 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(mdia_s4,definition,
% 0.19/0.50 ( mdia_s4
% 0.19/0.50 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %----We have now two options for stating the B conditions:
% 0.19/0.50 %----We can (i) directly formulate conditions for the accessibility relation
% 0.19/0.50 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.19/0.50 thf(a1,axiom,
% 0.19/0.50 mreflexive @ rel_s4 ).
% 0.19/0.50
% 0.19/0.50 thf(a2,axiom,
% 0.19/0.50 mtransitive @ rel_s4 ).
% 0.19/0.50
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 thf(cumulative_ax,axiom,
% 0.19/0.50 ! [X: mu,V: $i,W: $i] :
% 0.19/0.50 ( ( ( exists_in_world @ X @ V )
% 0.19/0.50 & ( rel_s4 @ V @ W ) )
% 0.19/0.50 => ( exists_in_world @ X @ W ) ) ).
% 0.19/0.50
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 thf(empty_type,type,
% 0.19/0.50 empty: mu > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(in_type,type,
% 0.19/0.50 in: mu > mu > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(empty_set_type,type,
% 0.19/0.50 empty_set: mu ).
% 0.19/0.50
% 0.19/0.50 thf(existence_of_empty_set_ax,axiom,
% 0.19/0.50 ! [V: $i] : ( exists_in_world @ empty_set @ V ) ).
% 0.19/0.50
% 0.19/0.50 thf(singleton_type,type,
% 0.19/0.50 singleton: mu > mu ).
% 0.19/0.50
% 0.19/0.50 thf(existence_of_singleton_ax,axiom,
% 0.19/0.50 ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) ).
% 0.19/0.50
% 0.19/0.50 thf(set_difference_type,type,
% 0.19/0.50 set_difference: mu > mu > mu ).
% 0.19/0.50
% 0.19/0.50 thf(existence_of_set_difference_ax,axiom,
% 0.19/0.50 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) ).
% 0.19/0.50
% 0.19/0.50 thf(reflexivity,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(symmetry,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [X: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(transitivity,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [X: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [Y: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(set_difference_substitution_1,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(set_difference_substitution_2,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(singleton_substitution_1,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(empty_substitution_1,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( empty @ A ) ) ) @ ( mbox_s4 @ ( empty @ B ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(in_substitution_1,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ A @ C ) ) ) @ ( mbox_s4 @ ( in @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(in_substitution_2,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ C @ A ) ) ) @ ( mbox_s4 @ ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(antisymmetry_r2_hidden,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(fc1_xboole_0,axiom,
% 0.19/0.50 mvalid @ ( mbox_s4 @ ( empty @ empty_set ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(rc1_xboole_0,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mexists_ind
% 0.19/0.50 @ ^ [A: mu] : ( mbox_s4 @ ( empty @ A ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(rc2_xboole_0,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mexists_ind
% 0.19/0.50 @ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( empty @ A ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(l36_zfmisc_1,axiom,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(t68_zfmisc_1,conjecture,
% 0.19/0.50 ( mvalid
% 0.19/0.50 @ ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.50 @ ^ [A: mu] :
% 0.19/0.50 ( mbox_s4
% 0.19/0.50 @ ( mforall_ind
% 0.19/0.52 @ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.52
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.SOh5DyxB6D/cvc5---1.0.5_12710.p...
% 0.19/0.52 (declare-sort $$unsorted 0)
% 0.19/0.52 (declare-sort tptp.mu 0)
% 0.19/0.52 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.19/0.52 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.19/0.52 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.19/0.52 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.19/0.52 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.19/0.52 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.19/0.52 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.19/0.52 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.19/0.52 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.19/0.52 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.19/0.52 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.19/0.52 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.19/0.52 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.19/0.52 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.19/0.52 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.19/0.52 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.19/0.52 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.19/0.52 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.19/0.52 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.19/0.52 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.19/0.52 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.19/0.52 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.19/0.52 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.19/0.52 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.52 (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)))))))))
% 0.19/0.52 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.19/0.52 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.19/0.52 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.19/0.52 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.19/0.52 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.19/0.52 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.19/0.52 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.19/0.52 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.19/0.52 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.19/0.52 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.19/0.52 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.19/0.52 (declare-fun tptp.empty (tptp.mu $$unsorted) Bool)
% 0.19/0.52 (declare-fun tptp.in (tptp.mu tptp.mu $$unsorted) Bool)
% 0.19/0.52 (declare-fun tptp.empty_set () tptp.mu)
% 0.19/0.52 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.empty_set) V)))
% 0.19/0.52 (declare-fun tptp.singleton (tptp.mu) tptp.mu)
% 0.19/0.52 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.singleton V1)) V)))
% 0.19/0.52 (declare-fun tptp.set_difference (tptp.mu tptp.mu) tptp.mu)
% 0.19/0.52 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.set_difference V2) V1)) V)))
% 0.19/0.52 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))))
% 0.19/0.52 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.52 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.19/0.52 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference A) C)) (@ (@ tptp.set_difference B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.52 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.set_difference 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))))))
% 0.19/0.52 (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.singleton A)) (@ tptp.singleton B))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.52 (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.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ tptp.empty A)))) (@ tptp.mbox_s4 (@ tptp.empty B)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.65 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.in A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.in B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.65 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.in 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))))))
% 0.19/0.65 (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.in A) B))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.in B) A)))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.19/0.65 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.empty tptp.empty_set))))
% 0.19/0.65 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.empty A)) __flatten_var_0)))))
% 0.19/0.65 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.empty A)))) __flatten_var_0)))))
% 0.19/0.65 (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)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.in A) B)))) (@ (@ (@ 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))))))
% 0.19/0.65 (assert (not (@ 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)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.in A) B)))) (@ (@ (@ 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)))))))
% 0.19/0.65 (set-info :filename cvc5---1.0.5_12710)
% 0.19/0.65 (check-sat-assuming ( true ))
% 0.19/0.65 ------- get file name : TPTP file name is SET925^7
% 0.19/0.65 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12710.smt2...
% 0.19/0.65 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.65 % SZS status Theorem for SET925^7
% 0.19/0.65 % SZS output start Proof for SET925^7
% 0.19/0.65 (
% 0.19/0.65 (let ((_let_1 (not (@ 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)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.in A) B)))) (@ (@ (@ 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)))))))) (let ((_let_2 (@ 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)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton A)) B)) tptp.empty_set)))) (let ((_let_2 (@ tptp.mbox_s4 (@ (@ tptp.in A) B)))) (@ (@ (@ 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))))))) (let ((_let_3 (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_4 (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))) (let ((_let_5 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_6 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_7 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_8 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_9 (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))) (let ((_let_10 (= tptp.mweakly_connected (lambda ((R (-> $$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_11 (= 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_12 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_13 (= tptp.mpartially_functional (lambda ((R (-> $$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_14 (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))) (let ((_let_15 (= tptp.mtransitive (lambda ((R (-> $$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_16 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_17 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_18 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_19 (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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_20 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_21 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))) (let ((_let_22 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_23 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_24 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_25 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_26 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_27 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_28 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_29 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_30 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_31 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_32 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_33 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_34 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_35 (forall ((W $$unsorted) (V $$unsorted) (BOUND_VARIABLE_7106 $$unsorted) (BOUND_VARIABLE_7104 $$unsorted) (BOUND_VARIABLE_7102 $$unsorted) (BOUND_VARIABLE_7100 $$unsorted) (BOUND_VARIABLE_7098 tptp.mu) (BOUND_VARIABLE_7096 tptp.mu)) (let ((_let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_7106) BOUND_VARIABLE_7102)))) (or (not (ho_4 (ho_6 k_5 W) V)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_7096) V)) (not (ho_4 (ho_6 k_5 V) BOUND_VARIABLE_7106)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_7098) BOUND_VARIABLE_7106)) (and (or (not (forall ((BOUND_VARIABLE_6761 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6761) BOUND_VARIABLE_6761)) (ho_4 (ho_3 (ho_12 k_11 (ho_8 (ho_10 k_9 (ho_8 k_7 BOUND_VARIABLE_7096)) BOUND_VARIABLE_7098)) tptp.empty_set) BOUND_VARIABLE_6761)))) _let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_7104) BOUND_VARIABLE_7104)) (ho_4 (ho_3 (ho_12 k_14 BOUND_VARIABLE_7096) BOUND_VARIABLE_7098) BOUND_VARIABLE_7104)) (or (not (forall ((BOUND_VARIABLE_6819 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6819) BOUND_VARIABLE_6819)) (ho_4 (ho_3 (ho_12 k_14 BOUND_VARIABLE_7096) BOUND_VARIABLE_7098) BOUND_VARIABLE_6819)))) _let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_7100) BOUND_VARIABLE_7100)) (ho_4 (ho_3 (ho_12 k_11 (ho_8 (ho_10 k_9 (ho_8 k_7 BOUND_VARIABLE_7096)) BOUND_VARIABLE_7098)) tptp.empty_set) BOUND_VARIABLE_7100)))))))) (let ((_let_36 (forall ((W $$unsorted) (V $$unsorted) (BOUND_VARIABLE_6645 $$unsorted) (BOUND_VARIABLE_6643 $$unsorted) (BOUND_VARIABLE_6641 $$unsorted) (BOUND_VARIABLE_6639 $$unsorted) (BOUND_VARIABLE_6637 tptp.mu) (BOUND_VARIABLE_6635 tptp.mu)) (let ((_let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6645) BOUND_VARIABLE_6641)))) (or (not (ho_4 (ho_6 k_5 W) V)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_6635) V)) (not (ho_4 (ho_6 k_5 V) BOUND_VARIABLE_6645)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_6637) BOUND_VARIABLE_6645)) (and (or (not (forall ((BOUND_VARIABLE_6298 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6298) BOUND_VARIABLE_6298)) (ho_4 (ho_3 (ho_12 k_11 (ho_8 (ho_10 k_9 (ho_8 k_7 BOUND_VARIABLE_6635)) BOUND_VARIABLE_6637)) tptp.empty_set) BOUND_VARIABLE_6298)))) _let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6643) BOUND_VARIABLE_6643)) (ho_4 (ho_3 (ho_12 k_14 BOUND_VARIABLE_6635) BOUND_VARIABLE_6637) BOUND_VARIABLE_6643)) (or (not (forall ((BOUND_VARIABLE_6357 $$unsorted)) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6357) BOUND_VARIABLE_6357)) (ho_4 (ho_3 (ho_12 k_14 BOUND_VARIABLE_6635) BOUND_VARIABLE_6637) BOUND_VARIABLE_6357)))) _let_1 (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_6639) BOUND_VARIABLE_6639)) (ho_4 (ho_3 (ho_12 k_11 (ho_8 (ho_10 k_9 (ho_8 k_7 BOUND_VARIABLE_6635)) BOUND_VARIABLE_6637)) tptp.empty_set) BOUND_VARIABLE_6639)))))))) (let ((_let_37 (ASSUME :args (_let_34)))) (let ((_let_38 (ASSUME :args (_let_33)))) (let ((_let_39 (ASSUME :args (_let_32)))) (let ((_let_40 (ASSUME :args (_let_31)))) (let ((_let_41 (ASSUME :args (_let_30)))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (ASSUME :args (_let_18)))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (ASSUME :args (_let_8)))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_5)))) (let ((_let_67 (ASSUME :args (_let_4)))) (let ((_let_68 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (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 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_68 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((W $$unsorted) (V $$unsorted) (BOUND_VARIABLE_7106 $$unsorted) (BOUND_VARIABLE_7104 $$unsorted) (BOUND_VARIABLE_7102 $$unsorted) (BOUND_VARIABLE_7100 $$unsorted) (BOUND_VARIABLE_7098 tptp.mu) (BOUND_VARIABLE_7096 tptp.mu)) (let ((_let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_7106) BOUND_VARIABLE_7102)))) (or (not (@ (@ tptp.rel_s4 W) V)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_7096) V)) (not (@ (@ tptp.rel_s4 V) BOUND_VARIABLE_7106)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_7098) BOUND_VARIABLE_7106)) (and (or (not (forall ((BOUND_VARIABLE_6761 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6761) BOUND_VARIABLE_6761)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton BOUND_VARIABLE_7096)) BOUND_VARIABLE_7098)) tptp.empty_set) BOUND_VARIABLE_6761)))) _let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_7104) BOUND_VARIABLE_7104)) (@ (@ (@ tptp.in BOUND_VARIABLE_7096) BOUND_VARIABLE_7098) BOUND_VARIABLE_7104)) (or (not (forall ((BOUND_VARIABLE_6819 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6819) BOUND_VARIABLE_6819)) (@ (@ (@ tptp.in BOUND_VARIABLE_7096) BOUND_VARIABLE_7098) BOUND_VARIABLE_6819)))) _let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_7100) BOUND_VARIABLE_7100)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton BOUND_VARIABLE_7096)) BOUND_VARIABLE_7098)) tptp.empty_set) BOUND_VARIABLE_7100))))))) (not _let_35)))))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_36 (= BOUND_VARIABLE_6635 BOUND_VARIABLE_7096) (= BOUND_VARIABLE_6637 BOUND_VARIABLE_7098) (= W W) (= V V) (= BOUND_VARIABLE_6645 BOUND_VARIABLE_7106) (= BOUND_VARIABLE_6643 BOUND_VARIABLE_7104) (= BOUND_VARIABLE_6641 BOUND_VARIABLE_7102) (= BOUND_VARIABLE_6298 BOUND_VARIABLE_6761) (= BOUND_VARIABLE_6639 BOUND_VARIABLE_7100) (= BOUND_VARIABLE_6357 BOUND_VARIABLE_6819)))) :args ((or _let_35 (not _let_36)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_68 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (V $$unsorted) (BOUND_VARIABLE_6645 $$unsorted) (BOUND_VARIABLE_6643 $$unsorted) (BOUND_VARIABLE_6641 $$unsorted) (BOUND_VARIABLE_6639 $$unsorted) (BOUND_VARIABLE_6637 tptp.mu) (BOUND_VARIABLE_6635 tptp.mu)) (let ((_let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6645) BOUND_VARIABLE_6641)))) (or (not (@ (@ tptp.rel_s4 W) V)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_6635) V)) (not (@ (@ tptp.rel_s4 V) BOUND_VARIABLE_6645)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_6637) BOUND_VARIABLE_6645)) (and (or (not (forall ((BOUND_VARIABLE_6298 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6298) BOUND_VARIABLE_6298)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton BOUND_VARIABLE_6635)) BOUND_VARIABLE_6637)) tptp.empty_set) BOUND_VARIABLE_6298)))) _let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6643) BOUND_VARIABLE_6643)) (@ (@ (@ tptp.in BOUND_VARIABLE_6635) BOUND_VARIABLE_6637) BOUND_VARIABLE_6643)) (or (not (forall ((BOUND_VARIABLE_6357 $$unsorted)) (or (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6357) BOUND_VARIABLE_6357)) (@ (@ (@ tptp.in BOUND_VARIABLE_6635) BOUND_VARIABLE_6637) BOUND_VARIABLE_6357)))) _let_1 (not (@ (@ tptp.rel_s4 BOUND_VARIABLE_6639) BOUND_VARIABLE_6639)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference (@ tptp.singleton BOUND_VARIABLE_6635)) BOUND_VARIABLE_6637)) tptp.empty_set) BOUND_VARIABLE_6639)))))) _let_36))))) :args (_let_35 false _let_36)) :args (false false _let_35)) :args (_let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))) _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (@ tptp.mreflexive tptp.rel_s4) (@ tptp.mtransitive tptp.rel_s4) (forall ((X tptp.mu) (V $$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)) (@ (@ tptp.exists_in_world tptp.empty_set) V)) (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.singleton V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.set_difference V2) 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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_difference A) C)) (@ (@ tptp.set_difference B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.set_difference C))) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ tptp.empty A)))) (@ tptp.mbox_s4 (@ tptp.empty B)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.in A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.in B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.in 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))))) (@ 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.in A) B))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.in B) A)))))) __flatten_var_0)))) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.empty tptp.empty_set))) (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.empty A)) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.empty A)))) __flatten_var_0)))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.66 )
% 0.19/0.66 % SZS output end Proof for SET925^7
% 0.19/0.66 % cvc5---1.0.5 exiting
% 0.19/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------