TSTP Solution File: SET013^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 14:36:43 EDT 2023
% Result : Theorem 10.42s 10.91s
% Output : Proof 10.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat Aug 26 13:10:53 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% 0.22/0.52 % Domain : Set Theory
% 0.22/0.52 % Problem : Commutativity of intersection
% 0.22/0.52 % Version : [Ben12] axioms.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 0.22/0.52 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.22/0.52 % Source : [Ben12]
% 0.22/0.52 % Names : s4-cumul-SET013+4 [Ben12]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.77 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.89 v7.3.0, 1.00 v5.5.0
% 0.22/0.52 % Syntax : Number of formulae : 126 ( 42 unt; 48 typ; 32 def)
% 0.22/0.52 % Number of atoms : 359 ( 36 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 10 ( 4 avg)
% 0.22/0.52 % Number of connectives : 599 ( 5 ~; 5 |; 9 &; 570 @)
% 0.22/0.52 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 14 ( 6 avg)
% 0.22/0.52 % Number of types : 3 ( 1 usr)
% 0.22/0.52 % Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 59 ( 57 usr; 12 con; 0-3 aty)
% 0.22/0.52 % Number of variables : 197 ( 135 ^; 55 !; 7 ?; 197 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments :
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----Include axioms for Modal logic S4 under cumulative domains
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----Declaration of additional base type mu
% 0.22/0.52 thf(mu_type,type,
% 0.22/0.52 mu: $tType ).
% 0.22/0.52
% 0.22/0.52 %----Equality
% 0.22/0.52 thf(qmltpeq_type,type,
% 0.22/0.52 qmltpeq: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 % originale Definition
% 0.22/0.52 %thf(qmltpeq,definition,
% 0.22/0.52 % ( qmltpeq
% 0.22/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.22/0.52
% 0.22/0.52 % erweiterte Leibnitz-Definition
% 0.22/0.52 %thf(qmltpeq,definition,
% 0.22/0.52 % ( qmltpeq
% 0.22/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.22/0.52
% 0.22/0.52 % Leibnitz-Definition
% 0.22/0.52 %thf(qmltpeq,definition,
% 0.22/0.52 % ( qmltpeq
% 0.22/0.52 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.22/0.52
% 0.22/0.52 thf(meq_prop_type,type,
% 0.22/0.52 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(meq_prop,definition,
% 0.22/0.52 ( meq_prop
% 0.22/0.52 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.22/0.52 ( ( X @ W )
% 0.22/0.52 = ( Y @ W ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Modal operators not, or, box, Pi
% 0.22/0.52 thf(mnot_type,type,
% 0.22/0.52 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mnot,definition,
% 0.22/0.52 ( mnot
% 0.22/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.52 ~ ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mor_type,type,
% 0.22/0.52 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mor,definition,
% 0.22/0.52 ( mor
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.22/0.52 ( ( Phi @ W )
% 0.22/0.52 | ( Psi @ W ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mbox_type,type,
% 0.22/0.52 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mbox,definition,
% 0.22/0.52 ( mbox
% 0.22/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.22/0.52 ! [V: $i] :
% 0.22/0.52 ( ~ ( R @ W @ V )
% 0.22/0.52 | ( Phi @ V ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_prop_type,type,
% 0.22/0.52 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_prop,definition,
% 0.22/0.52 ( mforall_prop
% 0.22/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.22/0.52 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Further modal operators
% 0.22/0.52 thf(mtrue_type,type,
% 0.22/0.52 mtrue: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mtrue,definition,
% 0.22/0.52 ( mtrue
% 0.22/0.52 = ( ^ [W: $i] : $true ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mfalse_type,type,
% 0.22/0.52 mfalse: $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mfalse,definition,
% 0.22/0.52 ( mfalse
% 0.22/0.52 = ( mnot @ mtrue ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mand_type,type,
% 0.22/0.52 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mand,definition,
% 0.22/0.52 ( mand
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mimplies_type,type,
% 0.22/0.52 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mimplies,definition,
% 0.22/0.52 ( mimplies
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mimplied_type,type,
% 0.22/0.52 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mimplied,definition,
% 0.22/0.52 ( mimplied
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mequiv_type,type,
% 0.22/0.52 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mequiv,definition,
% 0.22/0.52 ( mequiv
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mxor_type,type,
% 0.22/0.52 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mxor,definition,
% 0.22/0.52 ( mxor
% 0.22/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mdia_type,type,
% 0.22/0.52 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mdia,definition,
% 0.22/0.52 ( mdia
% 0.22/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %--- (new for cumulative)
% 0.22/0.52 %---Declaration of existence predicate for simulating cumulative domain
% 0.22/0.52 thf(exists_in_world_type,type,
% 0.22/0.52 exists_in_world: mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 %----The domains are non-empty
% 0.22/0.52 thf(nonempty_ax,axiom,
% 0.22/0.52 ! [V: $i] :
% 0.22/0.52 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(mforall_ind_type,type,
% 0.22/0.52 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 %--- (new for cumulative)
% 0.22/0.52 thf(mforall_ind,definition,
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.52 ! [X: mu] :
% 0.22/0.52 ( ( exists_in_world @ X @ W )
% 0.22/0.52 => ( Phi @ X @ W ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %thf(mforall_ind,definition,
% 0.22/0.52 % ( mforall_ind
% 0.22/0.52 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.52 % ! [X: mu] :
% 0.22/0.52 % ( Phi @ X @ W ) ) )).
% 0.22/0.52
% 0.22/0.52 thf(mexists_ind_type,type,
% 0.22/0.52 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_ind,definition,
% 0.22/0.52 ( mexists_ind
% 0.22/0.52 = ( ^ [Phi: mu > $i > $o] :
% 0.22/0.52 ( mnot
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_prop_type,type,
% 0.22/0.52 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mexists_prop,definition,
% 0.22/0.52 ( mexists_prop
% 0.22/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.22/0.52 ( mnot
% 0.22/0.52 @ ( mforall_prop
% 0.22/0.52 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of properties of accessibility relations
% 0.22/0.52 thf(mreflexive_type,type,
% 0.22/0.52 mreflexive: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mreflexive,definition,
% 0.22/0.52 ( mreflexive
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(msymmetric_type,type,
% 0.22/0.52 msymmetric: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(msymmetric,definition,
% 0.22/0.52 ( msymmetric
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 => ( R @ T @ S ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mserial_type,type,
% 0.22/0.52 mserial: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mserial,definition,
% 0.22/0.52 ( mserial
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] :
% 0.22/0.52 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mtransitive_type,type,
% 0.22/0.52 mtransitive: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mtransitive,definition,
% 0.22/0.52 ( mtransitive
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ T @ U ) )
% 0.22/0.52 => ( R @ S @ U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(meuclidean_type,type,
% 0.22/0.52 meuclidean: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(meuclidean,definition,
% 0.22/0.52 ( meuclidean
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( R @ T @ U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mpartially_functional_type,type,
% 0.22/0.52 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mpartially_functional,definition,
% 0.22/0.52 ( mpartially_functional
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( T = U ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mfunctional_type,type,
% 0.22/0.52 mfunctional: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mfunctional,definition,
% 0.22/0.52 ( mfunctional
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i] :
% 0.22/0.52 ? [T: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 & ! [U: $i] :
% 0.22/0.52 ( ( R @ S @ U )
% 0.22/0.52 => ( T = U ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_dense_type,type,
% 0.22/0.52 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_dense,definition,
% 0.22/0.52 ( mweakly_dense
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( R @ S @ T )
% 0.22/0.52 => ? [U: $i] :
% 0.22/0.52 ( ( R @ S @ U )
% 0.22/0.52 & ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_connected_type,type,
% 0.22/0.52 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_connected,definition,
% 0.22/0.52 ( mweakly_connected
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ( ( R @ T @ U )
% 0.22/0.52 | ( T = U )
% 0.22/0.52 | ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_directed_type,type,
% 0.22/0.52 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mweakly_directed,definition,
% 0.22/0.52 ( mweakly_directed
% 0.22/0.52 = ( ^ [R: $i > $i > $o] :
% 0.22/0.52 ! [S: $i,T: $i,U: $i] :
% 0.22/0.52 ( ( ( R @ S @ T )
% 0.22/0.52 & ( R @ S @ U ) )
% 0.22/0.52 => ? [V: $i] :
% 0.22/0.52 ( ( R @ T @ V )
% 0.22/0.52 & ( R @ U @ V ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of validity
% 0.22/0.52 thf(mvalid_type,type,
% 0.22/0.52 mvalid: ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mvalid,definition,
% 0.22/0.52 ( mvalid
% 0.22/0.52 = ( ^ [Phi: $i > $o] :
% 0.22/0.52 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of satisfiability
% 0.22/0.52 thf(msatisfiable_type,type,
% 0.22/0.52 msatisfiable: ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(msatisfiable,definition,
% 0.22/0.52 ( msatisfiable
% 0.22/0.52 = ( ^ [Phi: $i > $o] :
% 0.22/0.52 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of countersatisfiability
% 0.22/0.52 thf(mcountersatisfiable_type,type,
% 0.22/0.52 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mcountersatisfiable,definition,
% 0.22/0.52 ( mcountersatisfiable
% 0.22/0.52 = ( ^ [Phi: $i > $o] :
% 0.22/0.52 ? [W: $i] :
% 0.22/0.52 ~ ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----Definition of invalidity
% 0.22/0.52 thf(minvalid_type,type,
% 0.22/0.52 minvalid: ( $i > $o ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(minvalid,definition,
% 0.22/0.52 ( minvalid
% 0.22/0.52 = ( ^ [Phi: $i > $o] :
% 0.22/0.52 ! [W: $i] :
% 0.22/0.52 ~ ( Phi @ W ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %----We reserve an accessibility relation constant rel_s4
% 0.22/0.52 thf(rel_s4_type,type,
% 0.22/0.52 rel_s4: $i > $i > $o ).
% 0.22/0.52
% 0.22/0.52 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.22/0.52 thf(mbox_s4_type,type,
% 0.22/0.52 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mbox_s4,definition,
% 0.22/0.52 ( mbox_s4
% 0.22/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.52 ! [V: $i] :
% 0.22/0.52 ( ~ ( rel_s4 @ W @ V )
% 0.22/0.52 | ( Phi @ V ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(mdia_s4_type,type,
% 0.22/0.52 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mdia_s4,definition,
% 0.22/0.52 ( mdia_s4
% 0.22/0.52 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 %----We have now two options for stating the B conditions:
% 0.22/0.52 %----We can (i) directly formulate conditions for the accessibility relation
% 0.22/0.52 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.22/0.52 thf(a1,axiom,
% 0.22/0.52 mreflexive @ rel_s4 ).
% 0.22/0.52
% 0.22/0.52 thf(a2,axiom,
% 0.22/0.52 mtransitive @ rel_s4 ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(cumulative_ax,axiom,
% 0.22/0.52 ! [X: mu,V: $i,W: $i] :
% 0.22/0.52 ( ( ( exists_in_world @ X @ V )
% 0.22/0.52 & ( rel_s4 @ V @ W ) )
% 0.22/0.52 => ( exists_in_world @ X @ W ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(subset_type,type,
% 0.22/0.52 subset: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(member_type,type,
% 0.22/0.52 member: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(equal_set_type,type,
% 0.22/0.52 equal_set: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(power_set_type,type,
% 0.22/0.52 power_set: mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_power_set_ax,axiom,
% 0.22/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( power_set @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(union_type,type,
% 0.22/0.52 union: mu > mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_union_ax,axiom,
% 0.22/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(empty_set_type,type,
% 0.22/0.52 empty_set: mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_empty_set_ax,axiom,
% 0.22/0.52 ! [V: $i] : ( exists_in_world @ empty_set @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(difference_type,type,
% 0.22/0.52 difference: mu > mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_difference_ax,axiom,
% 0.22/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( difference @ V2 @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(singleton_type,type,
% 0.22/0.52 singleton: mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_singleton_ax,axiom,
% 0.22/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(unordered_pair_type,type,
% 0.22/0.52 unordered_pair: mu > mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_unordered_pair_ax,axiom,
% 0.22/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(sum_type,type,
% 0.22/0.52 sum: mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_sum_ax,axiom,
% 0.22/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( sum @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(product_type,type,
% 0.22/0.52 product: mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_product_ax,axiom,
% 0.22/0.52 ! [V: $i,V1: mu] : ( exists_in_world @ ( product @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(intersection_type,type,
% 0.22/0.52 intersection: mu > mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_intersection_ax,axiom,
% 0.22/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( intersection @ V2 @ V1 ) @ V ) ).
% 0.22/0.52
% 0.22/0.52 thf(reflexivity,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(symmetry,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(transitivity,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [Y: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(difference_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(difference_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(intersection_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(intersection_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(power_set_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(product_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(singleton_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(sum_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(union_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(union_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(unordered_pair_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(unordered_pair_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(equal_set_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(equal_set_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(member_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(member_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(subset_substitution_1,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(subset_substitution_2,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(subset,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mequiv @ ( subset @ A @ B )
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(equal_set,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(power_set,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(intersection,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(union,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(empty_set,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(difference,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [E: mu] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(singleton,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(unordered_pair,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [X: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(sum,axiom,
% 0.22/0.55 ( mvalid
% 0.22/0.55 @ ( mforall_ind
% 0.22/0.55 @ ^ [X: mu] :
% 0.22/0.55 ( mforall_ind
% 0.22/0.55 @ ^ [A: mu] :
% 0.22/0.55 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.22/0.55 @ ( mexists_ind
% 0.22/0.55 @ ^ [Y: mu] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(product,axiom,
% 0.22/0.55 ( mvalid
% 0.22/0.55 @ ( mforall_ind
% 0.22/0.55 @ ^ [X: mu] :
% 0.22/0.55 ( mforall_ind
% 0.22/0.55 @ ^ [A: mu] :
% 0.22/0.55 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.22/0.55 @ ( mforall_ind
% 0.22/0.55 @ ^ [Y: mu] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.22/0.55
% 0.22/0.55 thf(thI06,conjecture,
% 0.22/0.55 ( mvalid
% 0.22/0.55 @ ( mforall_ind
% 0.22/0.55 @ ^ [A: mu] :
% 0.22/0.55 ( mforall_ind
% 0.22/0.55 @ ^ [B: mu] : ( equal_set @ ( intersection @ A @ B ) @ ( intersection @ B @ A ) ) ) ) ) ).
% 0.22/0.55
% 0.22/0.55 %------------------------------------------------------------------------------
% 0.22/0.55 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DgX4pwdDBt/cvc5---1.0.5_15322.p...
% 0.22/0.55 (declare-sort $$unsorted 0)
% 0.22/0.55 (declare-sort tptp.mu 0)
% 0.22/0.55 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.55 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.22/0.55 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.22/0.55 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.22/0.55 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.22/0.55 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.22/0.55 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.22/0.55 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.22/0.55 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.22/0.55 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.22/0.55 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.22/0.55 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.55 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.22/0.55 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.22/0.55 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.22/0.55 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.22/0.55 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.22/0.55 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.22/0.55 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.22/0.55 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.22/0.55 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.22/0.55 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.22/0.55 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.55 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.55 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.55 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.55 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.55 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.22/0.55 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.22/0.55 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.55 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.55 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.22/0.55 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.22/0.55 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.22/0.55 (declare-fun tptp.subset (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.55 (declare-fun tptp.member (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.55 (declare-fun tptp.equal_set (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.55 (declare-fun tptp.power_set (tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.power_set V1)) V)))
% 0.22/0.55 (declare-fun tptp.union (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.union V2) V1)) V)))
% 0.22/0.55 (declare-fun tptp.empty_set () tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.empty_set) V)))
% 0.22/0.55 (declare-fun tptp.difference (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.difference V2) V1)) V)))
% 0.22/0.55 (declare-fun tptp.singleton (tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.singleton V1)) V)))
% 0.22/0.55 (declare-fun tptp.unordered_pair (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.unordered_pair V2) V1)) V)))
% 0.22/0.55 (declare-fun tptp.sum (tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.sum V1)) V)))
% 0.22/0.55 (declare-fun tptp.product (tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.product V1)) V)))
% 0.22/0.55 (declare-fun tptp.intersection (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.55 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.intersection V2) V1)) V)))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ _let_1 Y)) (@ (@ tptp.qmltpeq Y) Z))) (@ _let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.difference A) C)) (@ (@ tptp.difference B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.difference C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.intersection A) C)) (@ (@ tptp.intersection B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.intersection C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.power_set A)) (@ tptp.power_set B))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.product A)) (@ tptp.product B))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.sum A)) (@ tptp.sum B))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.union A) C)) (@ (@ tptp.union B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.union C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.unordered_pair C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.equal_set A) C))) (@ (@ tptp.equal_set B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.equal_set C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.member A) C))) (@ (@ tptp.member B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.subset A) C))) (@ (@ tptp.subset B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.subset A) B)) (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mimplies (@ _let_1 A)) (@ _let_1 B)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.equal_set A) B)) (@ (@ tptp.mand (@ (@ tptp.subset A) B)) (@ (@ tptp.subset B) A))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.power_set A))) (@ (@ tptp.subset X) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.55 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.intersection A) B))) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.union A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.member X) tptp.empty_set)) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member B))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.difference E) A))) (@ (@ tptp.mand (@ _let_1 E)) (@ tptp.mnot (@ _let_1 A)))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.singleton A))) (@ (@ tptp.qmltpeq X) A)) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ (@ tptp.unordered_pair A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.sum A))) (@ tptp.mexists_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.product A))) (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 10.42/10.91 (assert (not (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.equal_set (@ (@ tptp.intersection A) B)) (@ (@ tptp.intersection B) A)) __flatten_var_0))) __flatten_var_0))))))
% 10.42/10.91 (set-info :filename cvc5---1.0.5_15322)
% 10.42/10.91 (check-sat-assuming ( true ))
% 10.42/10.91 ------- get file name : TPTP file name is SET013^7
% 10.42/10.91 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15322.smt2...
% 10.42/10.91 --- Run --ho-elim --full-saturate-quant at 10...
% 10.42/10.91 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 10.42/10.91 % SZS status Theorem for SET013^7
% 10.42/10.91 % SZS output start Proof for SET013^7
% 10.42/10.91 (
% 10.42/10.91 (let ((_let_1 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.member X) tptp.empty_set)) __flatten_var_0)))))) (let ((_let_2 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.power_set A))) (@ (@ tptp.subset X) A)) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_3 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.subset A) B)) (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mimplies (@ _let_1 A)) (@ _let_1 B)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_4 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_5 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))) (let ((_let_6 (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.empty_set) V)))) (let ((_let_7 (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.power_set V1)) V)))) (let ((_let_8 (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_9 (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))) (let ((_let_10 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_11 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_12 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_13 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_14 (= 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_15 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_16 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_17 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_18 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_19 (= tptp.meuclidean (lambda ((R (-> $$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_20 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_21 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_22 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_23 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_24 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_25 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_26 (= 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_27 (= 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_28 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_29 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_30 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_31 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_32 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_33 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_34 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_35 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_36 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_37 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_38 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_39 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_40 (forall ((W $$unsorted) (BOUND_VARIABLE_6633 tptp.mu) (BOUND_VARIABLE_6631 tptp.mu) (BOUND_VARIABLE_6621 tptp.mu)) (let ((_let_1 (ho_18 k_20 BOUND_VARIABLE_6633))) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_6621) W)) (not (ho_4 (ho_3 (ho_18 k_17 BOUND_VARIABLE_6621) BOUND_VARIABLE_6621) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_6631) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_6633) W)) (ho_4 (ho_3 _let_1 BOUND_VARIABLE_6633) W) (not (ho_4 (ho_3 _let_1 BOUND_VARIABLE_6631) W))))))) (let ((_let_41 (ho_18 k_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_108))) (let ((_let_42 (ho_4 (ho_3 _let_41 tptp.empty_set) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_43 (not _let_42))) (let ((_let_44 (ho_4 (ho_3 _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_108) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_45 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_108) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_46 (not _let_45))) (let ((_let_47 (ho_4 (ho_3 k_2 tptp.empty_set) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_48 (not _let_47))) (let ((_let_49 (ho_4 (ho_3 (ho_18 k_17 tptp.empty_set) tptp.empty_set) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_48 _let_50 _let_48 _let_46 _let_44 _let_43))) (let ((_let_52 (ASSUME :args (_let_39)))) (let ((_let_53 (ASSUME :args (_let_38)))) (let ((_let_54 (ASSUME :args (_let_37)))) (let ((_let_55 (ASSUME :args (_let_36)))) (let ((_let_56 (ASSUME :args (_let_35)))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (ASSUME :args (_let_23)))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_13)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (ASSUME :args (_let_10)))) (let ((_let_82 (ASSUME :args (_let_9)))) (let ((_let_83 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52))) (let ((_let_84 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(__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.intersection C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.power_set A)) (@ tptp.power_set B))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.product A)) (@ tptp.product B))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.sum A)) (@ tptp.sum B))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.union A) C)) (@ (@ tptp.union B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.union C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.unordered_pair C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.equal_set A) C))) (@ (@ tptp.equal_set B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.equal_set C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.member A) C))) (@ (@ tptp.member B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) _let_4 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.subset A) C))) (@ (@ tptp.subset B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) _let_3 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.equal_set A) B)) (@ (@ tptp.mand (@ (@ tptp.subset A) B)) (@ (@ tptp.subset B) A))) __flatten_var_0))) __flatten_var_0)))) _let_2 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.intersection A) B))) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member X))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.union A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) _let_1 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((E tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member B))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.difference E) A))) (@ (@ tptp.mand (@ _let_1 E)) (@ tptp.mnot (@ _let_1 A)))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.singleton A))) (@ (@ tptp.qmltpeq X) A)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ (@ tptp.unordered_pair A) B))) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.sum A))) (@ tptp.mexists_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member X) (@ tptp.product A))) (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) A)) (@ (@ tptp.member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (not (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.equal_set (@ (@ tptp.intersection A) B)) (@ (@ tptp.intersection B) A)) __flatten_var_0))) __flatten_var_0))))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.42/10.91 )
% 10.42/10.91 % SZS output end Proof for SET013^7
% 10.42/10.91 % cvc5---1.0.5 exiting
% 10.42/10.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------