TSTP Solution File: SET916^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET916^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 14:40:59 EDT 2023
% Result : Timeout 299.60s 300.15s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET916^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 15:36:14 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.41 %----Proving TH0
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SET916^7 : TPTP v8.1.2. Released v5.5.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : ~ ( ~ in(A,B) & ~ in(C,B) & ~ disjoint(unordered_pair(A,C),B) )
% 0.16/0.42 % Version : [Ben12] axioms.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.16/0.42 % : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.16/0.42 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Ben12]
% 0.16/0.42 % Names : s4-cumul-GSE916+1 [Ben12]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 1.00 v5.5.0
% 0.16/0.42 % Syntax : Number of formulae : 102 ( 35 unt; 41 typ; 32 def)
% 0.16/0.42 % Number of atoms : 491 ( 36 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 58 ( 8 avg)
% 0.16/0.42 % Number of connectives : 696 ( 5 ~; 5 |; 9 &; 667 @)
% 0.16/0.42 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 27 ( 7 avg)
% 0.16/0.42 % Number of types : 3 ( 1 usr)
% 0.16/0.42 % Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 52 ( 50 usr; 11 con; 0-3 aty)
% 0.16/0.42 % Number of variables : 157 ( 110 ^; 40 !; 7 ?; 157 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : Goedel translation of SET916+1
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %----Include axioms for Modal logic S4 under cumulative domains
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %----Declaration of additional base type mu
% 0.16/0.42 thf(mu_type,type,
% 0.16/0.42 mu: $tType ).
% 0.16/0.42
% 0.16/0.42 %----Equality
% 0.16/0.42 thf(qmltpeq_type,type,
% 0.16/0.42 qmltpeq: mu > mu > $i > $o ).
% 0.16/0.42
% 0.16/0.42 % originale Definition
% 0.16/0.42 %thf(qmltpeq,definition,
% 0.16/0.42 % ( qmltpeq
% 0.16/0.42 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.16/0.42
% 0.16/0.42 % erweiterte Leibnitz-Definition
% 0.16/0.42 %thf(qmltpeq,definition,
% 0.16/0.42 % ( qmltpeq
% 0.16/0.42 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.16/0.42
% 0.16/0.42 % Leibnitz-Definition
% 0.16/0.42 %thf(qmltpeq,definition,
% 0.16/0.42 % ( qmltpeq
% 0.16/0.42 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.16/0.42
% 0.16/0.42 thf(meq_prop_type,type,
% 0.16/0.42 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(meq_prop,definition,
% 0.16/0.42 ( meq_prop
% 0.16/0.42 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.16/0.42 ( ( X @ W )
% 0.16/0.42 = ( Y @ W ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Modal operators not, or, box, Pi
% 0.16/0.42 thf(mnot_type,type,
% 0.16/0.42 mnot: ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mnot,definition,
% 0.16/0.42 ( mnot
% 0.16/0.42 = ( ^ [Phi: $i > $o,W: $i] :
% 0.16/0.42 ~ ( Phi @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mor_type,type,
% 0.16/0.42 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mor,definition,
% 0.16/0.42 ( mor
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.16/0.42 ( ( Phi @ W )
% 0.16/0.42 | ( Psi @ W ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mbox_type,type,
% 0.16/0.42 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mbox,definition,
% 0.16/0.42 ( mbox
% 0.16/0.42 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.16/0.42 ! [V: $i] :
% 0.16/0.42 ( ~ ( R @ W @ V )
% 0.16/0.42 | ( Phi @ V ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mforall_prop_type,type,
% 0.16/0.42 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mforall_prop,definition,
% 0.16/0.42 ( mforall_prop
% 0.16/0.42 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.16/0.42 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Further modal operators
% 0.16/0.42 thf(mtrue_type,type,
% 0.16/0.42 mtrue: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mtrue,definition,
% 0.16/0.42 ( mtrue
% 0.16/0.42 = ( ^ [W: $i] : $true ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mfalse_type,type,
% 0.16/0.42 mfalse: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mfalse,definition,
% 0.16/0.42 ( mfalse
% 0.16/0.42 = ( mnot @ mtrue ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mand_type,type,
% 0.16/0.42 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mand,definition,
% 0.16/0.42 ( mand
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mimplies_type,type,
% 0.16/0.42 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mimplies,definition,
% 0.16/0.42 ( mimplies
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mimplied_type,type,
% 0.16/0.42 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mimplied,definition,
% 0.16/0.42 ( mimplied
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mequiv_type,type,
% 0.16/0.42 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mequiv,definition,
% 0.16/0.42 ( mequiv
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mxor_type,type,
% 0.16/0.42 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mxor,definition,
% 0.16/0.42 ( mxor
% 0.16/0.42 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mdia_type,type,
% 0.16/0.42 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mdia,definition,
% 0.16/0.42 ( mdia
% 0.16/0.42 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %--- (new for cumulative)
% 0.16/0.42 %---Declaration of existence predicate for simulating cumulative domain
% 0.16/0.42 thf(exists_in_world_type,type,
% 0.16/0.42 exists_in_world: mu > $i > $o ).
% 0.16/0.42
% 0.16/0.42 %----The domains are non-empty
% 0.16/0.42 thf(nonempty_ax,axiom,
% 0.16/0.42 ! [V: $i] :
% 0.16/0.42 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.16/0.42
% 0.16/0.42 thf(mforall_ind_type,type,
% 0.16/0.42 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 %--- (new for cumulative)
% 0.16/0.42 thf(mforall_ind,definition,
% 0.16/0.42 ( mforall_ind
% 0.16/0.42 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.16/0.42 ! [X: mu] :
% 0.16/0.42 ( ( exists_in_world @ X @ W )
% 0.16/0.42 => ( Phi @ X @ W ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %thf(mforall_ind,definition,
% 0.16/0.42 % ( mforall_ind
% 0.16/0.42 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.16/0.42 % ! [X: mu] :
% 0.16/0.42 % ( Phi @ X @ W ) ) )).
% 0.16/0.42
% 0.16/0.42 thf(mexists_ind_type,type,
% 0.16/0.42 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mexists_ind,definition,
% 0.16/0.42 ( mexists_ind
% 0.16/0.42 = ( ^ [Phi: mu > $i > $o] :
% 0.16/0.42 ( mnot
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mexists_prop_type,type,
% 0.16/0.42 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mexists_prop,definition,
% 0.16/0.42 ( mexists_prop
% 0.16/0.42 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.16/0.42 ( mnot
% 0.16/0.42 @ ( mforall_prop
% 0.16/0.42 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Definition of properties of accessibility relations
% 0.16/0.42 thf(mreflexive_type,type,
% 0.16/0.42 mreflexive: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mreflexive,definition,
% 0.16/0.42 ( mreflexive
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(msymmetric_type,type,
% 0.16/0.42 msymmetric: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(msymmetric,definition,
% 0.16/0.42 ( msymmetric
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i] :
% 0.16/0.42 ( ( R @ S @ T )
% 0.16/0.42 => ( R @ T @ S ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mserial_type,type,
% 0.16/0.42 mserial: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mserial,definition,
% 0.16/0.42 ( mserial
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i] :
% 0.16/0.42 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mtransitive_type,type,
% 0.16/0.42 mtransitive: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mtransitive,definition,
% 0.16/0.42 ( mtransitive
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( ( R @ S @ T )
% 0.16/0.42 & ( R @ T @ U ) )
% 0.16/0.42 => ( R @ S @ U ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(meuclidean_type,type,
% 0.16/0.42 meuclidean: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(meuclidean,definition,
% 0.16/0.42 ( meuclidean
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( ( R @ S @ T )
% 0.16/0.42 & ( R @ S @ U ) )
% 0.16/0.42 => ( R @ T @ U ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mpartially_functional_type,type,
% 0.16/0.42 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mpartially_functional,definition,
% 0.16/0.42 ( mpartially_functional
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( ( R @ S @ T )
% 0.16/0.42 & ( R @ S @ U ) )
% 0.16/0.42 => ( T = U ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mfunctional_type,type,
% 0.16/0.42 mfunctional: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mfunctional,definition,
% 0.16/0.42 ( mfunctional
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i] :
% 0.16/0.42 ? [T: $i] :
% 0.16/0.42 ( ( R @ S @ T )
% 0.16/0.42 & ! [U: $i] :
% 0.16/0.42 ( ( R @ S @ U )
% 0.16/0.42 => ( T = U ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_dense_type,type,
% 0.16/0.42 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_dense,definition,
% 0.16/0.42 ( mweakly_dense
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( R @ S @ T )
% 0.16/0.42 => ? [U: $i] :
% 0.16/0.42 ( ( R @ S @ U )
% 0.16/0.42 & ( R @ U @ T ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_connected_type,type,
% 0.16/0.42 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_connected,definition,
% 0.16/0.42 ( mweakly_connected
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( ( R @ S @ T )
% 0.16/0.42 & ( R @ S @ U ) )
% 0.16/0.42 => ( ( R @ T @ U )
% 0.16/0.42 | ( T = U )
% 0.16/0.42 | ( R @ U @ T ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_directed_type,type,
% 0.16/0.42 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mweakly_directed,definition,
% 0.16/0.42 ( mweakly_directed
% 0.16/0.42 = ( ^ [R: $i > $i > $o] :
% 0.16/0.42 ! [S: $i,T: $i,U: $i] :
% 0.16/0.42 ( ( ( R @ S @ T )
% 0.16/0.42 & ( R @ S @ U ) )
% 0.16/0.42 => ? [V: $i] :
% 0.16/0.42 ( ( R @ T @ V )
% 0.16/0.42 & ( R @ U @ V ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Definition of validity
% 0.16/0.42 thf(mvalid_type,type,
% 0.16/0.42 mvalid: ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mvalid,definition,
% 0.16/0.42 ( mvalid
% 0.16/0.42 = ( ^ [Phi: $i > $o] :
% 0.16/0.42 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Definition of satisfiability
% 0.16/0.42 thf(msatisfiable_type,type,
% 0.16/0.42 msatisfiable: ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(msatisfiable,definition,
% 0.16/0.42 ( msatisfiable
% 0.16/0.42 = ( ^ [Phi: $i > $o] :
% 0.16/0.42 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Definition of countersatisfiability
% 0.16/0.42 thf(mcountersatisfiable_type,type,
% 0.16/0.42 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mcountersatisfiable,definition,
% 0.16/0.42 ( mcountersatisfiable
% 0.16/0.42 = ( ^ [Phi: $i > $o] :
% 0.16/0.42 ? [W: $i] :
% 0.16/0.42 ~ ( Phi @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----Definition of invalidity
% 0.16/0.42 thf(minvalid_type,type,
% 0.16/0.42 minvalid: ( $i > $o ) > $o ).
% 0.16/0.42
% 0.16/0.42 thf(minvalid,definition,
% 0.16/0.42 ( minvalid
% 0.16/0.42 = ( ^ [Phi: $i > $o] :
% 0.16/0.42 ! [W: $i] :
% 0.16/0.42 ~ ( Phi @ W ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %----We reserve an accessibility relation constant rel_s4
% 0.16/0.42 thf(rel_s4_type,type,
% 0.16/0.42 rel_s4: $i > $i > $o ).
% 0.16/0.42
% 0.16/0.42 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.16/0.42 thf(mbox_s4_type,type,
% 0.16/0.42 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mbox_s4,definition,
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 = ( ^ [Phi: $i > $o,W: $i] :
% 0.16/0.42 ! [V: $i] :
% 0.16/0.42 ( ~ ( rel_s4 @ W @ V )
% 0.16/0.42 | ( Phi @ V ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(mdia_s4_type,type,
% 0.16/0.42 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(mdia_s4,definition,
% 0.16/0.42 ( mdia_s4
% 0.16/0.42 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %----We have now two options for stating the B conditions:
% 0.16/0.42 %----We can (i) directly formulate conditions for the accessibility relation
% 0.16/0.42 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.16/0.42 thf(a1,axiom,
% 0.16/0.42 mreflexive @ rel_s4 ).
% 0.16/0.42
% 0.16/0.42 thf(a2,axiom,
% 0.16/0.42 mtransitive @ rel_s4 ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(cumulative_ax,axiom,
% 0.16/0.42 ! [X: mu,V: $i,W: $i] :
% 0.16/0.42 ( ( ( exists_in_world @ X @ V )
% 0.16/0.42 & ( rel_s4 @ V @ W ) )
% 0.16/0.42 => ( exists_in_world @ X @ W ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(empty_type,type,
% 0.16/0.42 empty: mu > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(disjoint_type,type,
% 0.16/0.42 disjoint: mu > mu > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(in_type,type,
% 0.16/0.42 in: mu > mu > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(set_intersection2_type,type,
% 0.16/0.42 set_intersection2: mu > mu > mu ).
% 0.16/0.42
% 0.16/0.42 thf(existence_of_set_intersection2_ax,axiom,
% 0.16/0.42 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ V1 ) @ V ) ).
% 0.16/0.42
% 0.16/0.42 thf(unordered_pair_type,type,
% 0.16/0.42 unordered_pair: mu > mu > mu ).
% 0.16/0.42
% 0.16/0.42 thf(existence_of_unordered_pair_ax,axiom,
% 0.16/0.42 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) ).
% 0.16/0.42
% 0.16/0.42 thf(reflexivity,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(symmetry,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [X: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(transitivity,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [X: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [Y: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(set_intersection2_substitution_1,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(set_intersection2_substitution_2,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_intersection2 @ C @ A ) @ ( set_intersection2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(unordered_pair_substitution_1,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(unordered_pair_substitution_2,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(disjoint_substitution_1,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( disjoint @ A @ C ) ) ) @ ( mbox_s4 @ ( disjoint @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(disjoint_substitution_2,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( disjoint @ C @ A ) ) ) @ ( mbox_s4 @ ( disjoint @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(empty_substitution_1,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( empty @ A ) ) ) @ ( mbox_s4 @ ( empty @ B ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(in_substitution_1,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ A @ C ) ) ) @ ( mbox_s4 @ ( in @ B @ C ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(in_substitution_2,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ C @ A ) ) ) @ ( mbox_s4 @ ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(antisymmetry_r2_hidden,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(commutativity_k2_tarski,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] : ( mbox_s4 @ ( qmltpeq @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(commutativity_k3_xboole_0,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] : ( mbox_s4 @ ( qmltpeq @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(d2_tarski,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] :
% 0.16/0.42 ( mand
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ C @ ( unordered_pair @ A @ B ) ) )
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ D @ C ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ D @ A ) ) @ ( mbox_s4 @ ( qmltpeq @ D @ B ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ ( qmltpeq @ D @ A ) ) @ ( mbox_s4 @ ( qmltpeq @ D @ B ) ) ) @ ( mbox_s4 @ ( in @ D @ C ) ) ) ) ) ) ) ) )
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mimplies
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ D @ C ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ D @ A ) ) @ ( mbox_s4 @ ( qmltpeq @ D @ B ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ ( qmltpeq @ D @ A ) ) @ ( mbox_s4 @ ( qmltpeq @ D @ B ) ) ) @ ( mbox_s4 @ ( in @ D @ C ) ) ) ) ) ) )
% 0.16/0.42 @ ( mbox_s4 @ ( qmltpeq @ C @ ( unordered_pair @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(d3_xboole_0,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [C: mu] :
% 0.16/0.42 ( mand
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ C @ ( set_intersection2 @ A @ B ) ) )
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ D @ C ) ) @ ( mand @ ( mbox_s4 @ ( in @ D @ A ) ) @ ( mbox_s4 @ ( in @ D @ B ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( in @ D @ A ) ) @ ( mbox_s4 @ ( in @ D @ B ) ) ) @ ( mbox_s4 @ ( in @ D @ C ) ) ) ) ) ) ) ) )
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mimplies
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ D @ C ) ) @ ( mand @ ( mbox_s4 @ ( in @ D @ A ) ) @ ( mbox_s4 @ ( in @ D @ B ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( in @ D @ A ) ) @ ( mbox_s4 @ ( in @ D @ B ) ) ) @ ( mbox_s4 @ ( in @ D @ C ) ) ) ) ) ) )
% 0.16/0.42 @ ( mbox_s4 @ ( qmltpeq @ C @ ( set_intersection2 @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(idempotence_k3_xboole_0,axiom,
% 0.16/0.42 ( mvalid
% 0.16/0.42 @ ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [A: mu] :
% 0.16/0.42 ( mbox_s4
% 0.16/0.42 @ ( mforall_ind
% 0.16/0.42 @ ^ [B: mu] : ( mbox_s4 @ ( qmltpeq @ ( set_intersection2 @ A @ A ) @ A ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(rc1_xboole_0,axiom,
% 0.16/0.43 ( mvalid
% 0.16/0.43 @ ( mexists_ind
% 0.16/0.43 @ ^ [A: mu] : ( mbox_s4 @ ( empty @ A ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(rc2_xboole_0,axiom,
% 0.16/0.43 ( mvalid
% 0.16/0.43 @ ( mexists_ind
% 0.16/0.43 @ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( empty @ A ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(symmetry_r1_xboole_0,axiom,
% 0.16/0.43 ( mvalid
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [A: mu] :
% 0.16/0.43 ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( disjoint @ A @ B ) ) @ ( mbox_s4 @ ( disjoint @ B @ A ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(t4_xboole_0,axiom,
% 0.16/0.43 ( mvalid
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [A: mu] :
% 0.16/0.43 ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [B: mu] :
% 0.16/0.43 ( mand
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mnot
% 0.16/0.43 @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( disjoint @ A @ B ) ) ) )
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [C: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ C @ ( set_intersection2 @ A @ B ) ) ) ) ) ) ) ) ) )
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mnot
% 0.16/0.43 @ ( mand
% 0.16/0.43 @ ( mexists_ind
% 0.16/0.43 @ ^ [C: mu] : ( mbox_s4 @ ( in @ C @ ( set_intersection2 @ A @ B ) ) ) )
% 0.16/0.43 @ ( mbox_s4 @ ( disjoint @ A @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(t57_zfmisc_1,conjecture,
% 0.16/0.43 ( mvalid
% 0.16/0.43 @ ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [A: mu] :
% 0.16/0.43 ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [B: mu] :
% 0.16/0.43 ( mbox_s4
% 0.16/0.43 @ ( mforall_ind
% 0.16/0.43 @ ^ [C: mu] : ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ C @ B ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Arta9I8y7k/cvc5---1.0.5_31164.p...
% 0.16/0.43 (declare-sort $$unsorted 0)
% 0.16/0.43 (declare-sort tptp.mu 0)
% 0.16/0.43 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.16/0.43 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.16/0.43 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.16/0.43 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.16/0.43 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.16/0.43 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.16/0.43 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.16/0.43 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.16/0.43 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.16/0.43 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.16/0.43 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.16/0.43 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.16/0.43 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.16/0.43 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.16/0.43 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.16/0.43 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.16/0.43 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.16/0.43 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.16/0.43 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.16/0.43 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.16/0.43 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.16/0.43 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.16/0.43 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.16/0.43 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.16/0.43 (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)))))))))
% 0.16/0.43 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.16/0.43 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.16/0.43 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.16/0.43 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.16/0.43 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.16/0.43 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.16/0.43 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.16/0.43 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.16/0.43 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.16/0.43 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.16/0.43 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.16/0.43 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.16/0.43 (declare-fun tptp.empty (tptp.mu $$unsorted) Bool)
% 0.16/0.43 (declare-fun tptp.disjoint (tptp.mu tptp.mu $$unsorted) Bool)
% 0.16/0.43 (declare-fun tptp.in (tptp.mu tptp.mu $$unsorted) Bool)
% 0.16/0.43 (declare-fun tptp.set_intersection2 (tptp.mu tptp.mu) tptp.mu)
% 0.16/0.43 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.set_intersection2 V2) V1)) V)))
% 0.16/0.43 (declare-fun tptp.unordered_pair (tptp.mu tptp.mu) tptp.mu)
% 0.16/0.43 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.unordered_pair V2) V1)) V)))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) X)) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq X) Y))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq Y) X)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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))))))
% 0.16/0.43 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) C)) (@ (@ tptp.set_intersection2 B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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_intersection2 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))))))
% 0.16/0.43 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.unordered_pair 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))))))
% 0.16/0.43 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.disjoint A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.disjoint B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.disjoint 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))))))
% 0.16/0.43 (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))))))
% 0.16/0.43 (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 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq A) B))) (@ tptp.mbox_s4 (@ (@ tptp.in A) C)))) (@ tptp.mbox_s4 (@ (@ tptp.in B) C)))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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))))))
% 0.16/0.43 (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))))))
% 0.16/0.43 (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.qmltpeq (@ (@ tptp.unordered_pair A) B)) (@ (@ tptp.unordered_pair B) A))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (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.qmltpeq (@ (@ tptp.set_intersection2 A) B)) (@ (@ tptp.set_intersection2 B) A))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (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 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.qmltpeq C) (@ (@ tptp.unordered_pair A) B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.in D) C)))) (let ((_let_2 (@ tptp.qmltpeq D))) (let ((_let_3 (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_2 A))) (@ tptp.mbox_s4 (@ _let_2 B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_3))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_3) _let_1))) __flatten_var_0)))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox_s4 (@ (@ tptp.in D) C)))) (let ((_let_2 (@ tptp.qmltpeq D))) (let ((_let_3 (@ (@ tptp.mor (@ tptp.mbox_s4 (@ _let_2 A))) (@ tptp.mbox_s4 (@ _let_2 B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) _let_3))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_3) _let_1))) __flatten_var_0)))))))) _let_1))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 0.16/0.43 (assert (@ tptp.mvalid (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.mbox_s4 (@ (@ tptp.qmltpeq C) (@ (@ tptp.set_intersection2 A) B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_1) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.in D))) (let ((_let_2 (@ tptp.mbox_s4 (@ _let_1 C)))) (let ((_let_3 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 A))) (@ tptp.mbox_s4 (@ _let_1 B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_3))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_3) _let_2))) __flatten_var_0)))))))))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.in D))) (let ((_let_2 (@ tptp.mbox_s4 (@ _let_1 C)))) (let ((_let_3 (@ (@ tptp.mand (@ tptp.mbox_s4 (@ _let_1 A))) (@ /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 1230 Alarm clock ( read result; case "$result" in
% 299.60/300.15 unsat)
% 299.60/300.15 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.60/300.15 ;;
% 299.60/300.15 sat)
% 299.60/300.15 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.60/300.15 ;;
% 299.60/300.15 esac; exit 1 )
% 299.60/300.15 tptp.mbox_s4 (@ _let_1 B))))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_2) _let_3))) (@ tptp.mbox_s4 (@ (@ tptp.mimplies _let_3) _let_2))) __flatten_var_0)))))))) _let_1))) __flatten_var_0))))) __flatten_var_0)))) __flatten_var_0))))))
% 299.60/300.15 (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.qmltpeq (@ (@ tptp.set_intersection2 A) A)) A)) __flatten_var_0)))) __flatten_var_0))))))
% 299.60/300.15 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.empty A)) __flatten_var_0)))))
% 299.60/300.15 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.empty A)))) __flatten_var_0)))))
% 299.60/300.15 (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.disjoint A) B))) (@ tptp.mbox_s4 (@ (@ tptp.disjoint B) A)))) __flatten_var_0)))) __flatten_var_0))))))
% 299.60/300.15 (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.disjoint A) B)))) (@ (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot _let_1))) (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.in C) (@ (@ tptp.set_intersection2 A) B))))) __flatten_var_0)))))))) (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mexists_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ (@ tptp.in C) (@ (@ tptp.set_intersection2 A) B))) __flatten_var_0)))) _let_1)))) __flatten_var_0))))) __flatten_var_0))))))
% 299.60/300.15 (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)) (@ (@ tptp.mbox_s4 (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mbox_s4 (@ tptp.mnot (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.in A) B))))) (@ (@ tptp.mand (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.in C) B))))) (@ tptp.mbox_s4 (@ tptp.mnot (@ tptp.mbox_s4 (@ (@ tptp.disjoint (@ (@ tptp.unordered_pair A) C)) B)))))))) __flatten_var_0)))) __flatten_var_0)))) __flatten_var_0)))))))
% 299.60/300.15 (set-info :filename cvc5---1.0.5_31164)
% 299.60/300.15 (check-sat-assuming ( true ))
% 299.60/300.15 ------- get file name : TPTP file name is SET916^7
% 299.60/300.15 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31164.smt2...
% 299.60/300.15 --- Run --ho-elim --full-saturate-quant at 10...
% 299.60/300.15 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 299.60/300.15 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 299.60/300.15 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 299.60/300.15 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 299.60/300.15 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 299.60/300.15 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 299.60/300.15 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 299.60/300.15 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 299.60/300.15 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 299.60/300.15 % cvc5---1.0.5 exiting
% 299.60/300.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------