TSTP Solution File: SET018^7 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET018^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:36:50 EDT 2023
% Result : Theorem 0.77s 0.97s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SET018^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat Aug 26 12:46:43 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.52 %----Proving TH0
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 % File : SET018^7 : TPTP v8.1.2. Released v5.5.0.
% 0.23/0.53 % Domain : Set Theory
% 0.23/0.53 % Problem : Second components of equal ordered pairs are equal
% 0.23/0.53 % Version : [Ben12] axioms.
% 0.23/0.53 % English :
% 0.23/0.53
% 0.23/0.53 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.23/0.53 % : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.23/0.53 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.23/0.53 % Source : [Ben12]
% 0.23/0.53 % Names : s4-cumul-SET018+1 [Ben12]
% 0.23/0.53
% 0.23/0.53 % Status : Theorem
% 0.23/0.53 % Rating : 1.00 v5.5.0
% 0.23/0.53 % Syntax : Number of formulae : 213 ( 59 unt; 67 typ; 32 def)
% 0.23/0.53 % Number of atoms : 711 ( 36 equ; 0 cnn)
% 0.23/0.53 % Maximal formula atoms : 11 ( 4 avg)
% 0.23/0.53 % Number of connectives : 1347 ( 5 ~; 5 |; 9 &;1318 @)
% 0.23/0.53 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.23/0.53 % Maximal formula depth : 19 ( 8 avg)
% 0.23/0.53 % Number of types : 3 ( 1 usr)
% 0.23/0.53 % Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% 0.23/0.53 % Number of symbols : 78 ( 76 usr; 16 con; 0-3 aty)
% 0.23/0.53 % Number of variables : 345 ( 247 ^; 91 !; 7 ?; 345 :)
% 0.23/0.53 % SPC : TH0_THM_EQU_NAR
% 0.23/0.53
% 0.23/0.53 % Comments :
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %----Include axioms for Modal logic S4 under cumulative domains
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %----Declaration of additional base type mu
% 0.23/0.53 thf(mu_type,type,
% 0.23/0.53 mu: $tType ).
% 0.23/0.53
% 0.23/0.53 %----Equality
% 0.23/0.53 thf(qmltpeq_type,type,
% 0.23/0.53 qmltpeq: mu > mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 % originale Definition
% 0.23/0.53 %thf(qmltpeq,definition,
% 0.23/0.53 % ( qmltpeq
% 0.23/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) )).
% 0.23/0.53
% 0.23/0.53 % erweiterte Leibnitz-Definition
% 0.23/0.53 %thf(qmltpeq,definition,
% 0.23/0.53 % ( qmltpeq
% 0.23/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : (![P: mu > $i > $o]: ( (P @ X @ W) <=> (P @ Y @ W) ) ) ) )).
% 0.23/0.53
% 0.23/0.53 % Leibnitz-Definition
% 0.23/0.53 %thf(qmltpeq,definition,
% 0.23/0.53 % ( qmltpeq
% 0.23/0.53 % = ( ^ [X: mu,Y: mu,W: $i] : (! [P: mu > $o]: ( (P @ X) <=> (P @ Y) ) ) ) )).
% 0.23/0.53
% 0.23/0.53 thf(meq_prop_type,type,
% 0.23/0.53 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(meq_prop,definition,
% 0.23/0.53 ( meq_prop
% 0.23/0.53 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.23/0.53 ( ( X @ W )
% 0.23/0.53 = ( Y @ W ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Modal operators not, or, box, Pi
% 0.23/0.53 thf(mnot_type,type,
% 0.23/0.53 mnot: ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mnot,definition,
% 0.23/0.53 ( mnot
% 0.23/0.53 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.53 ~ ( Phi @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mor_type,type,
% 0.23/0.53 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mor,definition,
% 0.23/0.53 ( mor
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.23/0.53 ( ( Phi @ W )
% 0.23/0.53 | ( Psi @ W ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mbox_type,type,
% 0.23/0.53 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mbox,definition,
% 0.23/0.53 ( mbox
% 0.23/0.53 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.23/0.53 ! [V: $i] :
% 0.23/0.53 ( ~ ( R @ W @ V )
% 0.23/0.53 | ( Phi @ V ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mforall_prop_type,type,
% 0.23/0.53 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mforall_prop,definition,
% 0.23/0.53 ( mforall_prop
% 0.23/0.53 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.23/0.53 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Further modal operators
% 0.23/0.53 thf(mtrue_type,type,
% 0.23/0.53 mtrue: $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mtrue,definition,
% 0.23/0.53 ( mtrue
% 0.23/0.53 = ( ^ [W: $i] : $true ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mfalse_type,type,
% 0.23/0.53 mfalse: $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mfalse,definition,
% 0.23/0.53 ( mfalse
% 0.23/0.53 = ( mnot @ mtrue ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mand_type,type,
% 0.23/0.53 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mand,definition,
% 0.23/0.53 ( mand
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mimplies_type,type,
% 0.23/0.53 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mimplies,definition,
% 0.23/0.53 ( mimplies
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mimplied_type,type,
% 0.23/0.53 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mimplied,definition,
% 0.23/0.53 ( mimplied
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mequiv_type,type,
% 0.23/0.53 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mequiv,definition,
% 0.23/0.53 ( mequiv
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mxor_type,type,
% 0.23/0.53 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mxor,definition,
% 0.23/0.53 ( mxor
% 0.23/0.53 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mdia_type,type,
% 0.23/0.53 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mdia,definition,
% 0.23/0.53 ( mdia
% 0.23/0.53 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %--- (new for cumulative)
% 0.23/0.53 %---Declaration of existence predicate for simulating cumulative domain
% 0.23/0.53 thf(exists_in_world_type,type,
% 0.23/0.53 exists_in_world: mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 %----The domains are non-empty
% 0.23/0.53 thf(nonempty_ax,axiom,
% 0.23/0.53 ! [V: $i] :
% 0.23/0.53 ? [X: mu] : ( exists_in_world @ X @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(mforall_ind_type,type,
% 0.23/0.53 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 %--- (new for cumulative)
% 0.23/0.53 thf(mforall_ind,definition,
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.53 ! [X: mu] :
% 0.23/0.53 ( ( exists_in_world @ X @ W )
% 0.23/0.53 => ( Phi @ X @ W ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %thf(mforall_ind,definition,
% 0.23/0.53 % ( mforall_ind
% 0.23/0.53 % = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.53 % ! [X: mu] :
% 0.23/0.53 % ( Phi @ X @ W ) ) )).
% 0.23/0.53
% 0.23/0.53 thf(mexists_ind_type,type,
% 0.23/0.53 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mexists_ind,definition,
% 0.23/0.53 ( mexists_ind
% 0.23/0.53 = ( ^ [Phi: mu > $i > $o] :
% 0.23/0.53 ( mnot
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mexists_prop_type,type,
% 0.23/0.53 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mexists_prop,definition,
% 0.23/0.53 ( mexists_prop
% 0.23/0.53 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.23/0.53 ( mnot
% 0.23/0.53 @ ( mforall_prop
% 0.23/0.53 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Definition of properties of accessibility relations
% 0.23/0.53 thf(mreflexive_type,type,
% 0.23/0.53 mreflexive: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mreflexive,definition,
% 0.23/0.53 ( mreflexive
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(msymmetric_type,type,
% 0.23/0.53 msymmetric: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(msymmetric,definition,
% 0.23/0.53 ( msymmetric
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i] :
% 0.23/0.53 ( ( R @ S @ T )
% 0.23/0.53 => ( R @ T @ S ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mserial_type,type,
% 0.23/0.53 mserial: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mserial,definition,
% 0.23/0.53 ( mserial
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i] :
% 0.23/0.53 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mtransitive_type,type,
% 0.23/0.53 mtransitive: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mtransitive,definition,
% 0.23/0.53 ( mtransitive
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( ( R @ S @ T )
% 0.23/0.53 & ( R @ T @ U ) )
% 0.23/0.53 => ( R @ S @ U ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(meuclidean_type,type,
% 0.23/0.53 meuclidean: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(meuclidean,definition,
% 0.23/0.53 ( meuclidean
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( ( R @ S @ T )
% 0.23/0.53 & ( R @ S @ U ) )
% 0.23/0.53 => ( R @ T @ U ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mpartially_functional_type,type,
% 0.23/0.53 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mpartially_functional,definition,
% 0.23/0.53 ( mpartially_functional
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( ( R @ S @ T )
% 0.23/0.53 & ( R @ S @ U ) )
% 0.23/0.53 => ( T = U ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mfunctional_type,type,
% 0.23/0.53 mfunctional: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mfunctional,definition,
% 0.23/0.53 ( mfunctional
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i] :
% 0.23/0.53 ? [T: $i] :
% 0.23/0.53 ( ( R @ S @ T )
% 0.23/0.53 & ! [U: $i] :
% 0.23/0.53 ( ( R @ S @ U )
% 0.23/0.53 => ( T = U ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_dense_type,type,
% 0.23/0.53 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_dense,definition,
% 0.23/0.53 ( mweakly_dense
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( R @ S @ T )
% 0.23/0.53 => ? [U: $i] :
% 0.23/0.53 ( ( R @ S @ U )
% 0.23/0.53 & ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_connected_type,type,
% 0.23/0.53 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_connected,definition,
% 0.23/0.53 ( mweakly_connected
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( ( R @ S @ T )
% 0.23/0.53 & ( R @ S @ U ) )
% 0.23/0.53 => ( ( R @ T @ U )
% 0.23/0.53 | ( T = U )
% 0.23/0.53 | ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_directed_type,type,
% 0.23/0.53 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mweakly_directed,definition,
% 0.23/0.53 ( mweakly_directed
% 0.23/0.53 = ( ^ [R: $i > $i > $o] :
% 0.23/0.53 ! [S: $i,T: $i,U: $i] :
% 0.23/0.53 ( ( ( R @ S @ T )
% 0.23/0.53 & ( R @ S @ U ) )
% 0.23/0.53 => ? [V: $i] :
% 0.23/0.53 ( ( R @ T @ V )
% 0.23/0.53 & ( R @ U @ V ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Definition of validity
% 0.23/0.53 thf(mvalid_type,type,
% 0.23/0.53 mvalid: ( $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mvalid,definition,
% 0.23/0.53 ( mvalid
% 0.23/0.53 = ( ^ [Phi: $i > $o] :
% 0.23/0.53 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Definition of satisfiability
% 0.23/0.53 thf(msatisfiable_type,type,
% 0.23/0.53 msatisfiable: ( $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(msatisfiable,definition,
% 0.23/0.53 ( msatisfiable
% 0.23/0.53 = ( ^ [Phi: $i > $o] :
% 0.23/0.53 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Definition of countersatisfiability
% 0.23/0.53 thf(mcountersatisfiable_type,type,
% 0.23/0.53 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mcountersatisfiable,definition,
% 0.23/0.53 ( mcountersatisfiable
% 0.23/0.53 = ( ^ [Phi: $i > $o] :
% 0.23/0.53 ? [W: $i] :
% 0.23/0.53 ~ ( Phi @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----Definition of invalidity
% 0.23/0.53 thf(minvalid_type,type,
% 0.23/0.53 minvalid: ( $i > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(minvalid,definition,
% 0.23/0.53 ( minvalid
% 0.23/0.53 = ( ^ [Phi: $i > $o] :
% 0.23/0.53 ! [W: $i] :
% 0.23/0.53 ~ ( Phi @ W ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %----We reserve an accessibility relation constant rel_s4
% 0.23/0.53 thf(rel_s4_type,type,
% 0.23/0.53 rel_s4: $i > $i > $o ).
% 0.23/0.53
% 0.23/0.53 %----We define mbox_s4 and mdia_s4 based on rel_s4
% 0.23/0.53 thf(mbox_s4_type,type,
% 0.23/0.53 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mbox_s4,definition,
% 0.23/0.53 ( mbox_s4
% 0.23/0.53 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.53 ! [V: $i] :
% 0.23/0.53 ( ~ ( rel_s4 @ W @ V )
% 0.23/0.53 | ( Phi @ V ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(mdia_s4_type,type,
% 0.23/0.53 mdia_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mdia_s4,definition,
% 0.23/0.53 ( mdia_s4
% 0.23/0.53 = ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 %----We have now two options for stating the B conditions:
% 0.23/0.53 %----We can (i) directly formulate conditions for the accessibility relation
% 0.23/0.53 %----constant or we can (ii) state corresponding axioms. We here prefer (i)
% 0.23/0.53 thf(a1,axiom,
% 0.23/0.53 mreflexive @ rel_s4 ).
% 0.23/0.53
% 0.23/0.53 thf(a2,axiom,
% 0.23/0.53 mtransitive @ rel_s4 ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(cumulative_ax,axiom,
% 0.23/0.53 ! [X: mu,V: $i,W: $i] :
% 0.23/0.53 ( ( ( exists_in_world @ X @ V )
% 0.23/0.53 & ( rel_s4 @ V @ W ) )
% 0.23/0.53 => ( exists_in_world @ X @ W ) ) ).
% 0.23/0.53
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(inductive_type,type,
% 0.23/0.53 inductive: mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(subclass_type,type,
% 0.23/0.53 subclass: mu > mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(disjoint_type,type,
% 0.23/0.53 disjoint: mu > mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(function_type,type,
% 0.23/0.53 function: mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(member_type,type,
% 0.23/0.53 member: mu > mu > $i > $o ).
% 0.23/0.53
% 0.23/0.53 thf(unordered_pair_type,type,
% 0.23/0.53 unordered_pair: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_unordered_pair_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(second_type,type,
% 0.23/0.53 second: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_second_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( second @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(first_type,type,
% 0.23/0.53 first: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_first_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( first @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(element_relation_type,type,
% 0.23/0.53 element_relation: mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_element_relation_ax,axiom,
% 0.23/0.53 ! [V: $i] : ( exists_in_world @ element_relation @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(complement_type,type,
% 0.23/0.53 complement: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_complement_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( complement @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(intersection_type,type,
% 0.23/0.53 intersection: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_intersection_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( intersection @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(rotate_type,type,
% 0.23/0.53 rotate: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_rotate_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( rotate @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(union_type,type,
% 0.23/0.53 union: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_union_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_type,type,
% 0.23/0.53 successor: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_successor_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( successor @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(flip_type,type,
% 0.23/0.53 flip: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_flip_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( flip @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(domain_of_type,type,
% 0.23/0.53 domain_of: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_domain_of_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( domain_of @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(restrict_type,type,
% 0.23/0.53 restrict: mu > mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_restrict_ax,axiom,
% 0.23/0.53 ! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( restrict @ V3 @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(range_of_type,type,
% 0.23/0.53 range_of: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_range_of_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( range_of @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_relation_type,type,
% 0.23/0.53 successor_relation: mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_successor_relation_ax,axiom,
% 0.23/0.53 ! [V: $i] : ( exists_in_world @ successor_relation @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(power_class_type,type,
% 0.23/0.53 power_class: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_power_class_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( power_class @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(identity_relation_type,type,
% 0.23/0.53 identity_relation: mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_identity_relation_ax,axiom,
% 0.23/0.53 ! [V: $i] : ( exists_in_world @ identity_relation @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(inverse_type,type,
% 0.23/0.53 inverse: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_inverse_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( inverse @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(compose_type,type,
% 0.23/0.53 compose: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_compose_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( compose @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(cross_product_type,type,
% 0.23/0.53 cross_product: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_cross_product_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( cross_product @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(singleton_type,type,
% 0.23/0.53 singleton: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_singleton_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(image_type,type,
% 0.23/0.53 image: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_image_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( image @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(sum_class_type,type,
% 0.23/0.53 sum_class: mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_sum_class_ax,axiom,
% 0.23/0.53 ! [V: $i,V1: mu] : ( exists_in_world @ ( sum_class @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(apply_type,type,
% 0.23/0.53 apply: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_apply_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( apply @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(null_class_type,type,
% 0.23/0.53 null_class: mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_null_class_ax,axiom,
% 0.23/0.53 ! [V: $i] : ( exists_in_world @ null_class @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(universal_class_type,type,
% 0.23/0.53 universal_class: mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_universal_class_ax,axiom,
% 0.23/0.53 ! [V: $i] : ( exists_in_world @ universal_class @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(ordered_pair_type,type,
% 0.23/0.53 ordered_pair: mu > mu > mu ).
% 0.23/0.53
% 0.23/0.53 thf(existence_of_ordered_pair_ax,axiom,
% 0.23/0.53 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( ordered_pair @ V2 @ V1 ) @ V ) ).
% 0.23/0.53
% 0.23/0.53 thf(reflexivity,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(symmetry,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(transitivity,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(apply_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(apply_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(complement_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(compose_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(compose_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cross_product_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cross_product_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(domain_of_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(first_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( first @ A ) @ ( first @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(flip_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(image_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(image_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(intersection_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(intersection_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(inverse_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ordered_pair_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ordered_pair_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(power_class_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(range_of_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(restrict_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [D: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(restrict_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [D: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(restrict_substitution_3,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [D: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(rotate_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(second_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( second @ A ) @ ( second @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(singleton_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(sum_class_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(union_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(union_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(unordered_pair_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(unordered_pair_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(disjoint_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ A @ C ) ) @ ( disjoint @ B @ C ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(disjoint_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ C @ A ) ) @ ( disjoint @ C @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(function_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( function @ A ) ) @ ( function @ B ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(inductive_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( inductive @ A ) ) @ ( inductive @ B ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(member_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(member_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(subclass_substitution_1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ A @ C ) ) @ ( subclass @ B @ C ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(subclass_substitution_2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [A: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [B: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ C @ A ) ) @ ( subclass @ C @ B ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(subclass_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] :
% 0.23/0.53 ( mequiv @ ( subclass @ X @ Y )
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] : ( mimplies @ ( member @ U @ X ) @ ( member @ U @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(class_elements_are_sets,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( subclass @ X @ universal_class ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(extensionality,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mequiv @ ( qmltpeq @ X @ Y ) @ ( mand @ ( subclass @ X @ Y ) @ ( subclass @ Y @ X ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(unordered_pair_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mequiv @ ( member @ U @ ( unordered_pair @ X @ Y ) ) @ ( mand @ ( member @ U @ universal_class ) @ ( mor @ ( qmltpeq @ U @ X ) @ ( qmltpeq @ U @ Y ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(unordered_pair,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(singleton_set_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( qmltpeq @ ( singleton @ X ) @ ( unordered_pair @ X @ X ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ordered_pair_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( qmltpeq @ ( ordered_pair @ X @ Y ) @ ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cross_product_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [V: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mequiv @ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) @ ( mand @ ( member @ U @ X ) @ ( member @ V @ Y ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(cross_product,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mimplies @ ( member @ Z @ ( cross_product @ X @ Y ) ) @ ( qmltpeq @ Z @ ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(element_relation_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mequiv @ ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) @ ( mand @ ( member @ Y @ universal_class ) @ ( member @ X @ Y ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(element_relation,axiom,
% 0.23/0.53 mvalid @ ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(intersection,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mequiv @ ( member @ Z @ ( intersection @ X @ Y ) ) @ ( mand @ ( member @ Z @ X ) @ ( member @ Z @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(complement,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mequiv @ ( member @ Z @ ( complement @ X ) ) @ ( mand @ ( member @ Z @ universal_class ) @ ( mnot @ ( member @ Z @ X ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(restrict_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [XR: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( qmltpeq @ ( restrict @ XR @ X @ Y ) @ ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(null_class_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mnot @ ( member @ X @ null_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(domain_of,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mequiv @ ( member @ Z @ ( domain_of @ X ) ) @ ( mand @ ( member @ Z @ universal_class ) @ ( mnot @ ( qmltpeq @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(rotate_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [V: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [W: mu] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(rotate,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(flip_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [V: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [W: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(flip,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(union_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( mequiv @ ( member @ Z @ ( union @ X @ Y ) ) @ ( mor @ ( member @ Z @ X ) @ ( member @ Z @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( qmltpeq @ ( successor @ X ) @ ( union @ X @ ( singleton @ X ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_relation_defn1,axiom,
% 0.23/0.53 mvalid @ ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(successor_relation_defn2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mequiv @ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) @ ( mand @ ( member @ X @ universal_class ) @ ( mand @ ( member @ Y @ universal_class ) @ ( qmltpeq @ ( successor @ X ) @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(inverse_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( qmltpeq @ ( inverse @ Y ) @ ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(range_of_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [Z: mu] : ( qmltpeq @ ( range_of @ Z ) @ ( domain_of @ ( inverse @ Z ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(image_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [XR: mu] : ( qmltpeq @ ( image @ XR @ X ) @ ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(inductive_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mequiv @ ( inductive @ X ) @ ( mand @ ( member @ null_class @ X ) @ ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(infinity,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mexists_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mand @ ( member @ X @ universal_class )
% 0.23/0.53 @ ( mand @ ( inductive @ X )
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mimplies @ ( inductive @ Y ) @ ( subclass @ X @ Y ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(sum_class_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mequiv @ ( member @ U @ ( sum_class @ X ) )
% 0.23/0.53 @ ( mexists_ind
% 0.23/0.53 @ ^ [Y: mu] : ( mand @ ( member @ U @ Y ) @ ( member @ Y @ X ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(sum_class,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mimplies @ ( member @ X @ universal_class ) @ ( member @ ( sum_class @ X ) @ universal_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(power_class_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] : ( mequiv @ ( member @ U @ ( power_class @ X ) ) @ ( mand @ ( member @ U @ universal_class ) @ ( subclass @ U @ X ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(power_class,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] : ( mimplies @ ( member @ U @ universal_class ) @ ( member @ ( power_class @ U ) @ universal_class ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(compose_defn1,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [XR: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [YR: mu] : ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(compose_defn2,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [XR: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [YR: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [U: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [V: mu] : ( mequiv @ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) @ ( mand @ ( member @ U @ universal_class ) @ ( member @ V @ ( image @ YR @ ( image @ YR @ ( singleton @ U ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(function_defn,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [XF: mu] : ( mequiv @ ( function @ XF ) @ ( mand @ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) @ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(replacement,axiom,
% 0.23/0.53 ( mvalid
% 0.23/0.53 @ ( mforall_ind
% 0.23/0.53 @ ^ [X: mu] :
% 0.23/0.53 ( mforall_ind
% 0.23/0.53 @ ^ [XF: mu] : ( mimplies @ ( mand @ ( member @ X @ universal_class ) @ ( function @ XF ) ) @ ( member @ ( image @ XF @ X ) @ universal_class ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(disjoint_defn,axiom,
% 0.23/0.57 ( mvalid
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [X: mu] :
% 0.23/0.57 ( mforall_ind
% 0.23/0.57 @ ^ [Y: mu] :
% 0.23/0.57 ( mequiv @ ( disjoint @ X @ Y )
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [U: mu] : ( mnot @ ( mand @ ( member @ U @ X ) @ ( member @ U @ Y ) ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(regularity,axiom,
% 0.23/0.57 ( mvalid
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [X: mu] :
% 0.23/0.57 ( mimplies @ ( mnot @ ( qmltpeq @ X @ null_class ) )
% 0.23/0.57 @ ( mexists_ind
% 0.23/0.57 @ ^ [U: mu] : ( mand @ ( member @ U @ universal_class ) @ ( mand @ ( member @ U @ X ) @ ( disjoint @ U @ X ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(apply_defn,axiom,
% 0.23/0.57 ( mvalid
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [XF: mu] :
% 0.23/0.57 ( mforall_ind
% 0.23/0.57 @ ^ [Y: mu] : ( qmltpeq @ ( apply @ XF @ Y ) @ ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(choice,axiom,
% 0.23/0.57 ( mvalid
% 0.23/0.57 @ ( mexists_ind
% 0.23/0.57 @ ^ [XF: mu] :
% 0.23/0.57 ( mand @ ( function @ XF )
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [Y: mu] : ( mimplies @ ( member @ Y @ universal_class ) @ ( mor @ ( qmltpeq @ Y @ null_class ) @ ( member @ ( apply @ XF @ Y ) @ Y ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(ordered_pair_determines_components2,conjecture,
% 0.23/0.57 ( mvalid
% 0.23/0.57 @ ( mforall_ind
% 0.23/0.57 @ ^ [W: mu] :
% 0.23/0.57 ( mforall_ind
% 0.23/0.57 @ ^ [X: mu] :
% 0.23/0.57 ( mforall_ind
% 0.23/0.57 @ ^ [Y: mu] :
% 0.23/0.57 ( mforall_ind
% 0.23/0.57 @ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ ( ordered_pair @ W @ X ) @ ( ordered_pair @ Y @ Z ) ) @ ( member @ X @ universal_class ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.oz0iJCmUz6/cvc5---1.0.5_13964.p...
% 0.23/0.57 (declare-sort $$unsorted 0)
% 0.23/0.57 (declare-sort tptp.mu 0)
% 0.23/0.57 (declare-fun tptp.qmltpeq (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.23/0.57 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.23/0.57 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.23/0.57 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.23/0.57 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.23/0.57 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.23/0.57 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.23/0.57 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.57 (declare-fun tptp.exists_in_world (tptp.mu $$unsorted) Bool)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (exists ((X tptp.mu)) (@ (@ tptp.exists_in_world X) V))))
% 0.23/0.57 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (=> (@ (@ tptp.exists_in_world X) W) (@ (@ Phi X) W))))))
% 0.23/0.57 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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))))
% 0.23/0.57 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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))))
% 0.23/0.57 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.23/0.57 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.23/0.57 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.23/0.57 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mtransitive (lambda ((R (-> $$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)))))))
% 0.23/0.57 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.23/0.57 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.23/0.57 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.23/0.57 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.23/0.57 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mweakly_connected (lambda ((R (-> $$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))))))))
% 0.23/0.57 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.57 (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)))))))))
% 0.23/0.57 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.57 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.57 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.57 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.57 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.57 (declare-fun tptp.rel_s4 ($$unsorted $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ tptp.rel_s4 W) V)) (@ Phi V))))))
% 0.23/0.57 (declare-fun tptp.mdia_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.57 (assert (@ tptp.mreflexive tptp.rel_s4))
% 0.23/0.57 (assert (@ tptp.mtransitive tptp.rel_s4))
% 0.23/0.57 (assert (forall ((X tptp.mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (@ tptp.exists_in_world X))) (=> (and (@ _let_1 V) (@ (@ tptp.rel_s4 V) W)) (@ _let_1 W)))))
% 0.23/0.57 (declare-fun tptp.inductive (tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.subclass (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.disjoint (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.function (tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.member (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.57 (declare-fun tptp.unordered_pair (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.unordered_pair V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.second (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.second V1)) V)))
% 0.23/0.57 (declare-fun tptp.first (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.first V1)) V)))
% 0.23/0.57 (declare-fun tptp.element_relation () tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.element_relation) V)))
% 0.23/0.57 (declare-fun tptp.complement (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.complement V1)) V)))
% 0.23/0.57 (declare-fun tptp.intersection (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.intersection V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.rotate (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.rotate V1)) V)))
% 0.23/0.57 (declare-fun tptp.union (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.union V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.successor (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.successor V1)) V)))
% 0.23/0.57 (declare-fun tptp.flip (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.flip V1)) V)))
% 0.23/0.57 (declare-fun tptp.domain_of (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.domain_of V1)) V)))
% 0.23/0.57 (declare-fun tptp.restrict (tptp.mu tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V3 tptp.mu) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ (@ tptp.restrict V3) V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.range_of (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.range_of V1)) V)))
% 0.23/0.57 (declare-fun tptp.successor_relation () tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.successor_relation) V)))
% 0.23/0.57 (declare-fun tptp.power_class (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.power_class V1)) V)))
% 0.23/0.57 (declare-fun tptp.identity_relation () tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.identity_relation) V)))
% 0.23/0.57 (declare-fun tptp.inverse (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.inverse V1)) V)))
% 0.23/0.57 (declare-fun tptp.compose (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.compose V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.cross_product (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.cross_product V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.singleton (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.singleton V1)) V)))
% 0.23/0.57 (declare-fun tptp.image (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.image V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.sum_class (tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ tptp.sum_class V1)) V)))
% 0.23/0.57 (declare-fun tptp.apply (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.apply V2) V1)) V)))
% 0.23/0.57 (declare-fun tptp.null_class () tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.null_class) V)))
% 0.23/0.57 (declare-fun tptp.universal_class () tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted)) (@ (@ tptp.exists_in_world tptp.universal_class) V)))
% 0.23/0.57 (declare-fun tptp.ordered_pair (tptp.mu tptp.mu) tptp.mu)
% 0.23/0.57 (assert (forall ((V $$unsorted) (V2 tptp.mu) (V1 tptp.mu)) (@ (@ tptp.exists_in_world (@ (@ tptp.ordered_pair V2) V1)) V)))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq X) X) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.qmltpeq Y) X)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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)))))
% 0.23/0.57 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.apply A) C)) (@ (@ tptp.apply B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.apply C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.complement A)) (@ tptp.complement B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.compose A) C)) (@ (@ tptp.compose B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.compose C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.cross_product A) C)) (@ (@ tptp.cross_product B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.cross_product C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.domain_of A)) (@ tptp.domain_of B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.first A)) (@ tptp.first B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.flip A)) (@ tptp.flip B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.57 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.image A) C)) (@ (@ tptp.image B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.image C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.intersection A) C)) (@ (@ tptp.intersection B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.intersection C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.inverse A)) (@ tptp.inverse B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.ordered_pair A) C)) (@ (@ tptp.ordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.ordered_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)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.power_class A)) (@ tptp.power_class B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.range_of A)) (@ tptp.range_of B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ (@ tptp.restrict A) C) D)) (@ (@ (@ tptp.restrict B) C) D))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.restrict C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ _let_1 A) D)) (@ (@ _let_1 B) D))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((D tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.restrict C) D))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.rotate A)) (@ tptp.rotate B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.second A)) (@ tptp.second B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.singleton A)) (@ tptp.singleton B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.successor A)) (@ tptp.successor B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ tptp.sum_class A)) (@ tptp.sum_class B))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.union A) C)) (@ (@ tptp.union B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.union C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ _let_1 A)) (@ _let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.qmltpeq (@ (@ tptp.unordered_pair A) C)) (@ (@ tptp.unordered_pair B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.disjoint A) C))) (@ (@ tptp.disjoint B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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)))))
% 0.23/0.58 (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.function A))) (@ tptp.function B)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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.inductive A))) (@ tptp.inductive B)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.member A) C))) (@ (@ tptp.member B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((B tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((C tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ (@ tptp.subclass A) C))) (@ (@ tptp.subclass B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((A tptp.mu) (__flatten_var_0 $$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.subclass C))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq A) B)) (@ _let_1 A))) (@ _let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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.mequiv (@ (@ tptp.subclass X) Y)) (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ (@ tptp.mimplies (@ _let_1 X)) (@ _let_1 Y)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.subclass X) tptp.universal_class) __flatten_var_0)))))
% 0.23/0.58 (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.mequiv (@ (@ tptp.qmltpeq X) Y)) (@ (@ tptp.mand (@ (@ tptp.subclass X) Y)) (@ (@ tptp.subclass Y) X))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq U))) (let ((_let_2 (@ tptp.member U))) (@ (@ (@ tptp.mequiv (@ _let_2 (@ (@ tptp.unordered_pair X) Y))) (@ (@ tptp.mand (@ _let_2 tptp.universal_class)) (@ (@ tptp.mor (@ _let_1 X)) (@ _let_1 Y)))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.member (@ (@ tptp.unordered_pair X) Y)) tptp.universal_class) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ tptp.singleton X)) (@ (@ tptp.unordered_pair X) X)) __flatten_var_0)))))
% 0.23/0.58 (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.qmltpeq (@ (@ tptp.ordered_pair X) Y)) (@ (@ tptp.unordered_pair (@ tptp.singleton X)) (@ (@ tptp.unordered_pair X) (@ tptp.singleton Y)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member (@ (@ tptp.ordered_pair U) V)) (@ (@ tptp.cross_product X) Y))) (@ (@ tptp.mand (@ (@ tptp.member U) X)) (@ (@ tptp.member V) Y))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Z) (@ (@ tptp.cross_product X) Y))) (@ (@ tptp.qmltpeq Z) (@ (@ tptp.ordered_pair (@ tptp.first Z)) (@ tptp.second Z)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member (@ (@ tptp.ordered_pair X) Y)) tptp.element_relation)) (@ (@ tptp.mand (@ (@ tptp.member Y) tptp.universal_class)) (@ (@ tptp.member X) Y))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ (@ tptp.subclass tptp.element_relation) (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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.member Z))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.intersection X) Y))) (@ (@ tptp.mand (@ _let_1 X)) (@ _let_1 Y))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member Z))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ tptp.complement X))) (@ (@ tptp.mand (@ _let_1 tptp.universal_class)) (@ tptp.mnot (@ _let_1 X)))) __flatten_var_0)))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((XR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ (@ tptp.restrict XR) X) Y)) (@ (@ tptp.intersection XR) (@ (@ tptp.cross_product X) Y))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.member X) tptp.null_class)) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member Z))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ tptp.domain_of X))) (@ (@ tptp.mand (@ _let_1 tptp.universal_class)) (@ tptp.mnot (@ (@ tptp.qmltpeq (@ (@ (@ tptp.restrict X) (@ tptp.singleton Z)) tptp.universal_class)) tptp.null_class)))) __flatten_var_0)))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member (@ (@ tptp.ordered_pair (@ (@ tptp.ordered_pair U) V)) W)))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ tptp.rotate X))) (@ (@ tptp.mand (@ _let_1 (@ (@ tptp.cross_product (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class)) tptp.universal_class))) (@ (@ tptp.member (@ (@ tptp.ordered_pair (@ (@ tptp.ordered_pair V) W)) U)) X))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.subclass (@ tptp.rotate X)) (@ (@ tptp.cross_product (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class)) tptp.universal_class)) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member (@ (@ tptp.ordered_pair (@ (@ tptp.ordered_pair U) V)) W)))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ tptp.flip X))) (@ (@ tptp.mand (@ _let_1 (@ (@ tptp.cross_product (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class)) tptp.universal_class))) (@ (@ tptp.member (@ (@ tptp.ordered_pair (@ (@ tptp.ordered_pair V) U)) W)) X))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.subclass (@ tptp.flip X)) (@ (@ tptp.cross_product (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class)) tptp.universal_class)) __flatten_var_0)))))
% 0.23/0.58 (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 $$unsorted)) (let ((_let_1 (@ tptp.member Z))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ (@ tptp.union X) Y))) (@ (@ tptp.mor (@ _let_1 X)) (@ _let_1 Y))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ tptp.successor X)) (@ (@ tptp.union X) (@ tptp.singleton X))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ (@ tptp.subclass tptp.successor_relation) (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class))))
% 0.23/0.58 (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.mequiv (@ (@ tptp.member (@ (@ tptp.ordered_pair X) Y)) tptp.successor_relation)) (@ (@ tptp.mand (@ (@ tptp.member X) tptp.universal_class)) (@ (@ tptp.mand (@ (@ tptp.member Y) tptp.universal_class)) (@ (@ tptp.qmltpeq (@ tptp.successor X)) Y)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ tptp.inverse Y)) (@ tptp.domain_of (@ tptp.flip (@ (@ tptp.cross_product Y) tptp.universal_class)))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ tptp.range_of Z)) (@ tptp.domain_of (@ tptp.inverse Z))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((XR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.image XR) X)) (@ tptp.range_of (@ (@ (@ tptp.restrict XR) X) tptp.universal_class))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ tptp.inductive X)) (@ (@ tptp.mand (@ (@ tptp.member tptp.null_class) X)) (@ (@ tptp.subclass (@ (@ tptp.image tptp.successor_relation) X)) X))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.member X) tptp.universal_class)) (@ (@ tptp.mand (@ tptp.inductive X)) (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.inductive Y)) (@ (@ tptp.subclass X) Y)) __flatten_var_0))))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.member U) (@ tptp.sum_class X))) (@ tptp.mexists_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.member U) Y)) (@ (@ tptp.member Y) X)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member X) tptp.universal_class)) (@ (@ tptp.member (@ tptp.sum_class X)) tptp.universal_class)) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ (@ tptp.mequiv (@ _let_1 (@ tptp.power_class X))) (@ (@ tptp.mand (@ _let_1 tptp.universal_class)) (@ (@ tptp.subclass U) X))) __flatten_var_0)))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member U) tptp.universal_class)) (@ (@ tptp.member (@ tptp.power_class U)) tptp.universal_class)) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((YR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.subclass (@ (@ tptp.compose YR) XR)) (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((YR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.image YR))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member (@ (@ tptp.ordered_pair U) V)) (@ (@ tptp.compose YR) XR))) (@ (@ tptp.mand (@ (@ tptp.member U) tptp.universal_class)) (@ (@ tptp.member V) (@ _let_1 (@ _let_1 (@ tptp.singleton U)))))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ tptp.function XF)) (@ (@ tptp.mand (@ (@ tptp.subclass XF) (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class))) (@ (@ tptp.subclass (@ (@ tptp.compose XF) (@ tptp.inverse XF))) tptp.identity_relation))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.member X) tptp.universal_class)) (@ tptp.function XF))) (@ (@ tptp.member (@ (@ tptp.image XF) X)) tptp.universal_class)) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ (@ tptp.disjoint X) Y)) (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ tptp.mnot (@ (@ tptp.mand (@ _let_1 X)) (@ _let_1 Y))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.23/0.58 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mnot (@ (@ tptp.qmltpeq X) tptp.null_class))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ (@ tptp.mand (@ _let_1 tptp.universal_class)) (@ (@ tptp.mand (@ _let_1 X)) (@ (@ tptp.disjoint U) X))) __flatten_var_0))))) __flatten_var_0)))))
% 0.77/0.97 (assert (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.apply XF) Y)) (@ tptp.sum_class (@ (@ tptp.image XF) (@ tptp.singleton Y)))) __flatten_var_0))) __flatten_var_0)))))
% 0.77/0.97 (assert (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ tptp.function XF)) (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) tptp.universal_class)) (@ (@ tptp.mor (@ (@ tptp.qmltpeq Y) tptp.null_class)) (@ (@ tptp.member (@ (@ tptp.apply XF) Y)) Y))) __flatten_var_0)))) __flatten_var_0)))))
% 0.77/0.97 (assert (not (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq (@ (@ tptp.ordered_pair W) X)) (@ (@ tptp.ordered_pair Y) Z))) (@ (@ tptp.member X) tptp.universal_class))) (@ (@ tptp.qmltpeq X) Z)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))))))
% 0.77/0.97 (set-info :filename cvc5---1.0.5_13964)
% 0.77/0.97 (check-sat-assuming ( true ))
% 0.77/0.97 ------- get file name : TPTP file name is SET018^7
% 0.77/0.97 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13964.smt2...
% 0.77/0.97 --- Run --ho-elim --full-saturate-quant at 10...
% 0.77/0.97 % SZS status Theorem for SET018^7
% 0.77/0.97 % SZS output start Proof for SET018^7
% 0.77/0.97 (
% 0.77/0.97 (let ((_let_1 (not (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((W tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Z tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.qmltpeq (@ (@ tptp.ordered_pair W) X)) (@ (@ tptp.ordered_pair Y) Z))) (@ (@ tptp.member X) tptp.universal_class))) (@ (@ tptp.qmltpeq X) Z)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0))))))) (let ((_let_2 (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class))) (let ((_let_3 (@ 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 $$unsorted)) (let ((_let_1 (@ tptp.qmltpeq X))) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ _let_1 Y)) (@ (@ tptp.qmltpeq Y) Z))) (@ _let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_4 (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$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_4690 tptp.mu) (BOUND_VARIABLE_4688 tptp.mu) (BOUND_VARIABLE_4678 tptp.mu)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4678) W)) (not (ho_4 (ho_3 (ho_32 k_31 BOUND_VARIABLE_4678) BOUND_VARIABLE_4678) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4688) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_4690) W)) (ho_4 (ho_3 (ho_32 k_31 BOUND_VARIABLE_4688) BOUND_VARIABLE_4690) W) (not (ho_4 (ho_3 (ho_32 k_31 BOUND_VARIABLE_4690) BOUND_VARIABLE_4690) W)))))) (let ((_let_38 (ho_4 (ho_3 (ho_32 k_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_39 (not _let_38))) (let ((_let_40 (ho_4 (ho_3 (ho_32 k_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_41 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_42 (not _let_41))) (let ((_let_43 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_44 (not _let_43))) (let ((_let_45 (ho_4 (ho_3 (ho_32 k_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_46 (not _let_45))) (let ((_let_47 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (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_4690 tptp.mu) (BOUND_VARIABLE_4688 tptp.mu) (BOUND_VARIABLE_4678 tptp.mu)) (or (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4678) W)) (not (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_4678) BOUND_VARIABLE_4678) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4688) W)) (not (@ (@ tptp.exists_in_world BOUND_VARIABLE_4690) W)) (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_4688) BOUND_VARIABLE_4690) W) (not (@ (@ (@ tptp.qmltpeq BOUND_VARIABLE_4690) BOUND_VARIABLE_4690) W)))) _let_37))))))) (let ((_let_83 (not _let_49))) (let ((_let_84 (or _let_42 _let_38))) (let ((_let_85 (forall ((W $$unsorted) (X tptp.mu)) (or (not (ho_4 (ho_3 k_2 X) W)) (ho_4 (ho_3 (ho_32 k_31 X) X) W))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_81 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (X tptp.mu)) (or (not (@ (@ tptp.exists_in_world X) W)) (@ (@ (@ tptp.qmltpeq X) X) W))) _let_85))))))) (let ((_let_87 (_let_85))) (let ((_let_88 ((not (= (ho_4 (ho_3 k_2 X) W) false))))) (let ((_let_89 (or _let_48 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38)) _let_44 (not (ho_4 (ho_3 (ho_32 k_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41) tptp.universal_class) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38)) _let_42 _let_40 (not (ho_4 (ho_3 (ho_32 k_31 (ho_9 (ho_8 k_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41)) (ho_9 (ho_8 k_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))))) (let ((_let_90 (forall ((W $$unsorted) (BOUND_VARIABLE_21377 tptp.mu) (BOUND_VARIABLE_21401 tptp.mu) (BOUND_VARIABLE_21375 tptp.mu) (BOUND_VARIABLE_21370 tptp.mu)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_21370) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_21401) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_21375) W)) (not (ho_4 (ho_3 (ho_32 k_36 BOUND_VARIABLE_21375) tptp.universal_class) W)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_21377) W)) (ho_4 (ho_3 (ho_32 k_31 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tptp.universal_class)) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((YR tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((V tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.image YR))) (@ (@ (@ tptp.mequiv (@ (@ tptp.member (@ (@ tptp.ordered_pair U) V)) (@ (@ tptp.compose YR) XR))) (@ (@ tptp.mand (@ (@ tptp.member U) tptp.universal_class)) (@ (@ tptp.member V) (@ _let_1 (@ _let_1 (@ tptp.singleton U)))))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mequiv (@ tptp.function XF)) (@ (@ tptp.mand (@ (@ tptp.subclass XF) (@ (@ tptp.cross_product tptp.universal_class) tptp.universal_class))) (@ (@ tptp.subclass (@ (@ tptp.compose XF) (@ tptp.inverse XF))) tptp.identity_relation))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mand (@ (@ tptp.member X) tptp.universal_class)) (@ tptp.function XF))) (@ (@ tptp.member (@ (@ tptp.image XF) X)) tptp.universal_class)) __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.mequiv (@ (@ tptp.disjoint X) Y)) (@ tptp.mforall_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ tptp.mnot (@ (@ tptp.mand (@ _let_1 X)) (@ _let_1 Y))) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mnot (@ (@ tptp.qmltpeq X) tptp.null_class))) (@ tptp.mexists_ind (lambda ((U tptp.mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.member U))) (@ (@ (@ tptp.mand (@ _let_1 tptp.universal_class)) (@ (@ tptp.mand (@ _let_1 X)) (@ (@ tptp.disjoint U) X))) __flatten_var_0))))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.qmltpeq (@ (@ tptp.apply XF) Y)) (@ tptp.sum_class (@ (@ tptp.image XF) (@ tptp.singleton Y)))) __flatten_var_0))) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mexists_ind (lambda ((XF tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ tptp.function XF)) (@ tptp.mforall_ind (lambda ((Y tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.member Y) tptp.universal_class)) (@ (@ tptp.mor (@ (@ tptp.qmltpeq Y) tptp.null_class)) (@ (@ tptp.member (@ (@ tptp.apply XF) Y)) Y))) __flatten_var_0)))) __flatten_var_0)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.77/0.97 )
% 0.77/0.97 % SZS output end Proof for SET018^7
% 0.77/0.97 % cvc5---1.0.5 exiting
% 0.77/0.98 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------