TSTP Solution File: SET914^7 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET914^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 14:40:58 EDT 2023
% Result : Theorem 0.22s 0.72s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SET914^7 : TPTP v8.1.2. Released v5.5.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 08:15:39 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : SET914^7 : TPTP v8.1.2. Released v5.5.0.
% 0.22/0.52 % Domain : Set Theory
% 0.22/0.52 % Problem : ~ ( disjoint(unordered_pair(A,B),C) & in(A,C) )
% 0.22/0.52 % Version : [Ben12] axioms.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.22/0.52 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.22/0.52 % Source : [Ben12]
% 0.22/0.52 % Names : s4-cumul-SET914+1 [Ben12]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.62 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.67 v7.3.0, 0.78 v7.2.0, 0.75 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0
% 0.22/0.52 % Syntax : Number of formulae : 106 ( 36 unt; 42 typ; 32 def)
% 0.22/0.52 % Number of atoms : 278 ( 36 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 12 ( 4 avg)
% 0.22/0.52 % Number of connectives : 435 ( 5 ~; 5 |; 9 &; 406 @)
% 0.22/0.52 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 16 ( 5 avg)
% 0.22/0.52 % Number of types : 3 ( 1 usr)
% 0.22/0.52 % Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 53 ( 51 usr; 12 con; 0-3 aty)
% 0.22/0.52 % Number of variables : 156 ( 108 ^; 41 !; 7 ?; 156 :)
% 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(empty_type,type,
% 0.22/0.52 empty: mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(in_type,type,
% 0.22/0.52 in: mu > mu > $i > $o ).
% 0.22/0.52
% 0.22/0.52 thf(disjoint_type,type,
% 0.22/0.52 disjoint: mu > mu > $i > $o ).
% 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(set_intersection2_type,type,
% 0.22/0.52 set_intersection2: mu > mu > mu ).
% 0.22/0.52
% 0.22/0.52 thf(existence_of_set_intersection2_ax,axiom,
% 0.22/0.52 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_intersection2 @ V2 @ 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(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(set_intersection2_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 @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(set_intersection2_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 @ ( set_intersection2 @ C @ A ) @ ( set_intersection2 @ 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(disjoint_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 ) @ ( disjoint @ A @ C ) ) @ ( disjoint @ B @ C ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(disjoint_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 ) @ ( disjoint @ C @ A ) ) @ ( disjoint @ C @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(empty_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 @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(in_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 ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(in_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 ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(antisymmetry_r2_hidden,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 @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(commutativity_k2_tarski,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] : ( qmltpeq @ ( unordered_pair @ A @ B ) @ ( unordered_pair @ B @ A ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(commutativity_k3_xboole_0,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] : ( qmltpeq @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(d1_xboole_0,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [A: mu] :
% 0.22/0.52 ( mequiv @ ( qmltpeq @ A @ empty_set )
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [B: mu] : ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(d2_tarski,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] :
% 0.22/0.52 ( mequiv @ ( qmltpeq @ C @ ( unordered_pair @ A @ B ) )
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.52 @ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mor @ ( qmltpeq @ D @ A ) @ ( qmltpeq @ D @ B ) ) ) ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(d3_xboole_0,axiom,
% 0.22/0.52 ( mvalid
% 0.22/0.52 @ ( mforall_ind
% 0.22/0.54 @ ^ [A: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [B: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [C: mu] :
% 0.22/0.54 ( mequiv @ ( qmltpeq @ C @ ( set_intersection2 @ A @ B ) )
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [D: mu] : ( mequiv @ ( in @ D @ C ) @ ( mand @ ( in @ D @ A ) @ ( in @ D @ B ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(d7_xboole_0,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [A: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [B: mu] : ( mequiv @ ( disjoint @ A @ B ) @ ( qmltpeq @ ( set_intersection2 @ A @ B ) @ empty_set ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(fc1_xboole_0,axiom,
% 0.22/0.54 mvalid @ ( empty @ empty_set ) ).
% 0.22/0.54
% 0.22/0.54 thf(idempotence_k3_xboole_0,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [A: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [B: mu] : ( qmltpeq @ ( set_intersection2 @ A @ A ) @ A ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(rc1_xboole_0,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mexists_ind
% 0.22/0.54 @ ^ [A: mu] : ( empty @ A ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(rc2_xboole_0,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mexists_ind
% 0.22/0.54 @ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(symmetry_r1_xboole_0,axiom,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [A: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [B: mu] : ( mimplies @ ( disjoint @ A @ B ) @ ( disjoint @ B @ A ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(t55_zfmisc_1,conjecture,
% 0.22/0.54 ( mvalid
% 0.22/0.54 @ ( mforall_ind
% 0.22/0.54 @ ^ [A: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [B: mu] :
% 0.22/0.54 ( mforall_ind
% 0.22/0.54 @ ^ [C: mu] : ( mnot @ ( mand @ ( disjoint @ ( unordered_pair @ A @ B ) @ C ) @ ( in @ A @ C ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1EH1CwlnxF/cvc5---1.0.5_13695.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.mu 0)
% 0.22/0.54 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.22/0.54 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.22/0.54 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.22/0.54 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.22/0.54 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.22/0.54 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.22/0.54 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.22/0.54 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.22/0.54 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.54 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.22/0.54 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.22/0.54 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.22/0.54 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.22/0.54 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.22/0.54 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.22/0.54 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.22/0.54 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.22/0.54 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.54 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.54 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.54 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.54 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.22/0.54 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.54 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.54 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.22/0.54 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.22/0.54 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.22/0.54 (declare-fun tptp.empty (tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.in (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.disjoint (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.54 (declare-fun tptp.empty_set () tptp.mu)
% 0.22/0.54 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.empty_set) V)))
% 0.22/0.54 (declare-fun tptp.set_intersection2 (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.54 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.set_intersection2 V2) V1)) V)))
% 0.22/0.54 (declare-fun tptp.unordered_pair (tptp.mu tptp.mu) tptp.mu)
% 0.22/0.54 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.unordered_pair V2) V1)) V)))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))
% 0.22/0.54 (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)))))
% 0.22/0.54 (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 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ _let_1 Y)) (@ (@ tptp.qmltpeq Y) Z))) (@ _let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.set_intersection2 A) C)) (@ (@ tptp.set_intersection2 B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (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 $$unsorted)) (let ((_let_1 (@ tptp.set_intersection2 C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)))))
% 0.22/0.54 (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 $$unsorted)) (let ((_let_1 (@ tptp.unordered_pair C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.disjoint A) C))) (@ (@ tptp.disjoint B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (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 $$unsorted)) (let ((_let_1 (@ tptp.disjoint C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.in A) C))) (@ (@ tptp.in B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (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 $$unsorted)) (let ((_let_1 (@ tptp.in C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) B)) (@ (@ tptp.unordered_pair B) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) B)) (@ (@ tptp.set_intersection2 B) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.54 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq A) tptp.empty_set)) (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.in B) A)) __flatten_var_0)))) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq C) (@ (@ tptp.unordered_pair A) B))) (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq D))) (@ (@ (@ tptp.mequiv (@ (@ tptp.in D) C)) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq C) (@ (@ tptp.set_intersection2 A) B))) (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.in D))) (@ (@ (@ tptp.mequiv (@ _let_1 C)) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.disjoint A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) B)) tptp.empty_set)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.empty tptp.empty_set)))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) A)) A) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.empty A) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))))
% 0.22/0.72 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.disjoint A) B)) (@ (@ tptp.disjoint B) A)) __flatten_var_0))) __flatten_var_0)))))
% 0.22/0.72 (assert (not (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mand (@ (@ tptp.disjoint (@ (@ tptp.unordered_pair A) B)) C)) (@ (@ tptp.in A) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))))))
% 0.22/0.72 (set-info :filename cvc5---1.0.5_13695)
% 0.22/0.72 (check-sat-assuming ( true ))
% 0.22/0.72 ------- get file name : TPTP file name is SET914^7
% 0.22/0.72 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13695.smt2...
% 0.22/0.72 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.72 % SZS status Theorem for SET914^7
% 0.22/0.72 % SZS output start Proof for SET914^7
% 0.22/0.72 (
% 0.22/0.72 (let ((_let_1 (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.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mand (@ (@ tptp.disjoint (@ (@ tptp.unordered_pair A) B)) C)) (@ (@ tptp.in A) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))))))) (let ((_let_2 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.in A) B)) (@ tptp.mnot (@ (@ tptp.in B) A))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_3 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.in A) C))) (@ (@ tptp.in B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_4 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))) (let ((_let_5 (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_6 (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))) (let ((_let_7 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_8 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_9 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_10 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_11 (= 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_12 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_13 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_14 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_15 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_16 (= tptp.meuclidean (lambda ((R (-> $$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_17 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_18 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_19 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_20 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_21 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_22 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_23 (= 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_24 (= 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_25 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_26 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_27 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_28 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_29 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_30 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_31 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_32 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_33 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_34 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_35 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_36 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_37 (forall ((W $$unsorted) (BOUND_VARIABLE_4677 tptp.mu) (BOUND_VARIABLE_4675 tptp.mu) (BOUND_VARIABLE_4665 tptp.mu)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4665) W)) (not (ho_4 (ho_3 (ho_12 k_11 BOUND_VARIABLE_4665) BOUND_VARIABLE_4665) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4675) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4677) W)) (ho_4 (ho_3 (ho_12 k_15 BOUND_VARIABLE_4677) BOUND_VARIABLE_4677) W) (not (ho_4 (ho_3 (ho_12 k_15 BOUND_VARIABLE_4675) BOUND_VARIABLE_4677) W)))))) (let ((_let_38 (ho_4 (ho_3 (ho_12 k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_39 (not _let_38))) (let ((_let_40 (ho_4 (ho_3 (ho_12 k_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_41 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_42 (not _let_41))) (let ((_let_43 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_44 (not _let_43))) (let ((_let_45 (ho_4 (ho_3 (ho_12 k_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_46 (not _let_45))) (let ((_let_47 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46 _let_44 _let_42 _let_40 _let_39))) (let ((_let_50 (ASSUME :args (_let_36)))) (let ((_let_51 (ASSUME :args (_let_35)))) (let ((_let_52 (ASSUME :args (_let_34)))) (let ((_let_53 (ASSUME :args (_let_33)))) (let ((_let_54 (ASSUME :args (_let_32)))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_24)) (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 _let_51 _let_50) :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_22)) (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 _let_51 _let_50) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_20)))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (ASSUME :args (_let_10)))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (ASSUME :args (_let_7)))) (let ((_let_80 (ASSUME :args (_let_6)))) (let ((_let_81 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO _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_51 _let_50) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) _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_51 _let_50))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_81 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (BOUND_VARIABLE_4677 tptp.mu) (BOUND_VARIABLE_4675 tptp.mu) (BOUND_VARIABLE_4665 tptp.mu)) (or (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4665) W)) (not (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_4665) BOUND_VARIABLE_4665) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4675) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4677) W)) (@ (@ (@ tptp.in BOUND_VARIABLE_4677) BOUND_VARIABLE_4677) W) (not (@ (@ (@ tptp.in BOUND_VARIABLE_4675) BOUND_VARIABLE_4677) W)))) _let_37))))))) (let ((_let_83 (not _let_49))) (let ((_let_84 (not _let_40))) (let ((_let_85 (or _let_42 _let_42 _let_84))) (let ((_let_86 (forall ((W $$unsorted) (BOUND_VARIABLE_5097 tptp.mu) (BOUND_VARIABLE_5087 tptp.mu)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_5097) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_5087) W)) (not (ho_4 (ho_3 (ho_12 k_15 BOUND_VARIABLE_5087) BOUND_VARIABLE_5087) W)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_81 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (BOUND_VARIABLE_5097 tptp.mu) (BOUND_VARIABLE_5087 tptp.mu)) (or (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_5097) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_5087) W)) (not (@ (@ (@ tptp.in BOUND_VARIABLE_5087) BOUND_VARIABLE_5087) W)))) _let_86))))))) (let ((_let_88 (or _let_48 _let_44 _let_42 (not (ho_4 (ho_3 (ho_12 k_13 (ho_9 (ho_8 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) _let_39))) (let ((_let_89 (forall ((W $$unsorted) (BOUND_VARIABLE_7514 tptp.mu) (BOUND_VARIABLE_7512 tptp.mu) (BOUND_VARIABLE_7507 tptp.mu)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_7507) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_7512) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_7514) W)) (not (ho_4 (ho_3 (ho_12 k_13 (ho_9 (ho_8 k_10 BOUND_VARIABLE_7512) BOUND_VARIABLE_7514)) BOUND_VARIABLE_7514) W)) (not (ho_4 (ho_3 (ho_12 k_15 BOUND_VARIABLE_7512) BOUND_VARIABLE_7514) W)))))) (let ((_let_90 (not _let_88))) (let ((_let_91 (not _let_89))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_81 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((W $$unsorted) (BOUND_VARIABLE_7514 tptp.mu) (BOUND_VARIABLE_7512 tptp.mu) (BOUND_VARIABLE_7507 tptp.mu)) (or (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_7507) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_7512) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_7514) W)) (not (@ (@ (@ tptp.disjoint (@ (@ tptp.unordered_pair BOUND_VARIABLE_7512) BOUND_VARIABLE_7514)) BOUND_VARIABLE_7514) W)) (not (@ (@ (@ tptp.in BOUND_VARIABLE_7512) BOUND_VARIABLE_7514) W))))) _let_91))))))) (let ((_let_93 (or))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_92) :args (_let_91))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_89))) (REFL :args (_let_90)) :args _let_93)) _let_92 :args (_let_90 true _let_89)))) (let ((_let_95 (REFL :args (_let_88)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_88 2)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_93)) :args ((or _let_41 _let_88))) _let_94 :args (_let_41 true _let_88)))) (let ((_let_97 (or _let_48 _let_45))) (let ((_let_98 (forall ((W $$unsorted) (X tptp.mu)) (or (not (ho_4 (ho_3 k_2 X) W)) (ho_4 (ho_3 (ho_12 k_11 X) X) W))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_81 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (X tptp.mu)) (or (not (@ (@ tptp.exists_in_world X) W)) (@ (@ (@ tptp.qmltpeq X) X) W))) _let_98))))))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_88 0)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_93)) :args ((or _let_47 _let_88))) _let_94 :args (_let_47 true _let_88)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_44 _let_42 _let_39 _let_46 _let_40 _let_83))) _let_100 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_88 1)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_93)) :args ((or _let_43 _let_88))) _let_94 :args (_let_43 true _let_88)) _let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_88 4)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_93)) :args ((or _let_38 _let_88))) _let_94 :args (_let_38 true _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_48 _let_45 (not _let_97)))) _let_100 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 X) W) false))))) :args (_let_98))) _let_99 :args (_let_97 false _let_98)) :args (_let_45 false _let_47 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_85))) :args ((or _let_42 _let_84 (not _let_85)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 BOUND_VARIABLE_5097) W) false)) (ho_3 k_2 BOUND_VARIABLE_5087)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_84 false _let_41 false _let_85)) :args (_let_83 false _let_47 false _let_43 false _let_41 false _let_38 false _let_45 true _let_40)) _let_82 :args (false true _let_49 false _let_37)) :args (_let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))) _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 (@ tptp.mreflexive tptp.rel_s4) (@ tptp.mtransitive tptp.rel_s4) (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))) (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.empty_set) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.set_intersection2 V2) V1)) V)) (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.unordered_pair V2) V1)) V)) _let_4 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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)))) (@ 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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) C)) (@ (@ tptp.set_intersection2 B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.set_intersection2 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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.disjoint A) C))) (@ (@ tptp.disjoint B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.disjoint 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.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ tptp.empty A))) (@ tptp.empty B)) __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.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.in C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) _let_2 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) B)) (@ (@ tptp.unordered_pair B) A)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) B)) (@ (@ tptp.set_intersection2 B) A)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq A) tptp.empty_set)) (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.in B) A)) __flatten_var_0)))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq C) (@ (@ tptp.unordered_pair A) B))) (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq D))) (@ (@ (@ tptp.mequiv (@ (@ tptp.in D) C)) (@ (@ tptp.mor (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.qmltpeq C) (@ (@ tptp.set_intersection2 A) B))) (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.in D))) (@ (@ (@ tptp.mequiv (@ _let_1 C)) (@ (@ tptp.mand (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.disjoint A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) B)) tptp.empty_set)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.empty tptp.empty_set)) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.set_intersection2 A) A)) A) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.empty A) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.empty A)) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.disjoint A) B)) (@ (@ tptp.disjoint B) A)) __flatten_var_0))) __flatten_var_0)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.72 )
% 0.22/0.72 % SZS output end Proof for SET914^7
% 0.22/0.72 % cvc5---1.0.5 exiting
% 0.22/0.72 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------