TSTP Solution File: PUZ087^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ087^2 : TPTP v8.1.2. Released v5.2.0.
% 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 13:13:20 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ087^2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 22:00:58 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : PUZ087^2 : TPTP v8.1.2. Released v5.2.0.
% 0.21/0.50 % Domain : Puzzles
% 0.21/0.50 % Problem : Wise men puzzle
% 0.21/0.50 % Version : [Ben11] axioms.
% 0.21/0.50 % English : Once upon a time, a king wanted to find the wisest out of his
% 0.21/0.50 % three wisest men. He arranged them in a circle and told them that
% 0.21/0.50 % he would put a white or a black spot on their foreheads and that
% 0.21/0.50 % one of the three spots would certainly be white. The three wise
% 0.21/0.50 % men could see and hear each other but, of course, they could not
% 0.21/0.50 % see their faces reflected anywhere. The king, then, asked to each
% 0.21/0.50 % of them to find out the colour of his own spot. After a while, the
% 0.21/0.50 % wisest correctly answered that his spot was white.
% 0.21/0.50
% 0.21/0.50 % Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% 0.21/0.50 % : [Ben11] Benzmueller (2011), Combining and Automating Classical
% 0.21/0.50 % Source : [Ben11]
% 0.21/0.50 % Names : Ex_9_2 [Ben11]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 0.69 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.89 v7.3.0, 0.78 v7.2.0, 0.75 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0
% 0.21/0.50 % Syntax : Number of formulae : 106 ( 32 unt; 39 typ; 32 def)
% 0.21/0.50 % Number of atoms : 425 ( 37 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 12 ( 6 avg)
% 0.21/0.50 % Number of connectives : 456 ( 5 ~; 4 |; 8 &; 431 @)
% 0.21/0.50 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 9 ( 4 avg)
% 0.21/0.50 % Number of types : 3 ( 1 usr)
% 0.21/0.50 % Number of type conns : 204 ( 204 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 47 ( 45 usr; 8 con; 0-3 aty)
% 0.21/0.50 % Number of variables : 103 ( 67 ^; 30 !; 6 ?; 103 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include embedding of quantified multimodal logic in simple type theory
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Declaration of additional base type mu
% 0.21/0.50 thf(mu_type,type,
% 0.21/0.50 mu: $tType ).
% 0.21/0.50
% 0.21/0.50 %----Equality
% 0.21/0.50 thf(meq_ind_type,type,
% 0.21/0.50 meq_ind: mu > mu > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(meq_ind,definition,
% 0.21/0.50 ( meq_ind
% 0.21/0.50 = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(meq_prop_type,type,
% 0.21/0.50 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(meq_prop,definition,
% 0.21/0.50 ( meq_prop
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.21/0.50 ( ( X @ W )
% 0.21/0.50 = ( Y @ W ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Modal operators not, or, box, Pi
% 0.21/0.50 thf(mnot_type,type,
% 0.21/0.50 mnot: ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mnot,definition,
% 0.21/0.50 ( mnot
% 0.21/0.50 = ( ^ [Phi: $i > $o,W: $i] :
% 0.21/0.50 ~ ( Phi @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mor_type,type,
% 0.21/0.50 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mor,definition,
% 0.21/0.50 ( mor
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.21/0.50 ( ( Phi @ W )
% 0.21/0.50 | ( Psi @ W ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mand_type,type,
% 0.21/0.50 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mand,definition,
% 0.21/0.50 ( mand
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mimplies_type,type,
% 0.21/0.50 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mimplies,definition,
% 0.21/0.50 ( mimplies
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mimplied_type,type,
% 0.21/0.50 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mimplied,definition,
% 0.21/0.50 ( mimplied
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mequiv_type,type,
% 0.21/0.50 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mequiv,definition,
% 0.21/0.50 ( mequiv
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mxor_type,type,
% 0.21/0.50 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mxor,definition,
% 0.21/0.50 ( mxor
% 0.21/0.50 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Universal quantification: individuals
% 0.21/0.50 thf(mforall_ind_type,type,
% 0.21/0.50 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mforall_ind,definition,
% 0.21/0.50 ( mforall_ind
% 0.21/0.50 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.21/0.50 ! [X: mu] : ( Phi @ X @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mforall_prop_type,type,
% 0.21/0.50 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mforall_prop,definition,
% 0.21/0.50 ( mforall_prop
% 0.21/0.50 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.21/0.50 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mexists_ind_type,type,
% 0.21/0.50 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mexists_ind,definition,
% 0.21/0.50 ( mexists_ind
% 0.21/0.50 = ( ^ [Phi: mu > $i > $o] :
% 0.21/0.50 ( mnot
% 0.21/0.50 @ ( mforall_ind
% 0.21/0.50 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mexists_prop_type,type,
% 0.21/0.50 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mexists_prop,definition,
% 0.21/0.50 ( mexists_prop
% 0.21/0.50 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.21/0.50 ( mnot
% 0.21/0.50 @ ( mforall_prop
% 0.21/0.50 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mtrue_type,type,
% 0.21/0.50 mtrue: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mtrue,definition,
% 0.21/0.50 ( mtrue
% 0.21/0.50 = ( ^ [W: $i] : $true ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mfalse_type,type,
% 0.21/0.50 mfalse: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mfalse,definition,
% 0.21/0.50 ( mfalse
% 0.21/0.50 = ( mnot @ mtrue ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mbox_type,type,
% 0.21/0.50 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mbox,definition,
% 0.21/0.50 ( mbox
% 0.21/0.50 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.21/0.50 ! [V: $i] :
% 0.21/0.50 ( ~ ( R @ W @ V )
% 0.21/0.50 | ( Phi @ V ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mdia_type,type,
% 0.21/0.50 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mdia,definition,
% 0.21/0.50 ( mdia
% 0.21/0.50 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Definition of properties of accessibility relations
% 0.21/0.50 thf(mreflexive_type,type,
% 0.21/0.50 mreflexive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mreflexive,definition,
% 0.21/0.50 ( mreflexive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(msymmetric_type,type,
% 0.21/0.50 msymmetric: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(msymmetric,definition,
% 0.21/0.50 ( msymmetric
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i] :
% 0.21/0.50 ( ( R @ S @ T )
% 0.21/0.50 => ( R @ T @ S ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mserial_type,type,
% 0.21/0.50 mserial: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mserial,definition,
% 0.21/0.50 ( mserial
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i] :
% 0.21/0.50 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mtransitive_type,type,
% 0.21/0.50 mtransitive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mtransitive,definition,
% 0.21/0.50 ( mtransitive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( ( R @ S @ T )
% 0.21/0.50 & ( R @ T @ U ) )
% 0.21/0.50 => ( R @ S @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(meuclidean_type,type,
% 0.21/0.50 meuclidean: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(meuclidean,definition,
% 0.21/0.50 ( meuclidean
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( ( R @ S @ T )
% 0.21/0.50 & ( R @ S @ U ) )
% 0.21/0.50 => ( R @ T @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mpartially_functional_type,type,
% 0.21/0.50 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mpartially_functional,definition,
% 0.21/0.50 ( mpartially_functional
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( ( R @ S @ T )
% 0.21/0.50 & ( R @ S @ U ) )
% 0.21/0.50 => ( T = U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mfunctional_type,type,
% 0.21/0.50 mfunctional: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mfunctional,definition,
% 0.21/0.50 ( mfunctional
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i] :
% 0.21/0.50 ? [T: $i] :
% 0.21/0.50 ( ( R @ S @ T )
% 0.21/0.50 & ! [U: $i] :
% 0.21/0.50 ( ( R @ S @ U )
% 0.21/0.50 => ( T = U ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_dense_type,type,
% 0.21/0.50 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_dense,definition,
% 0.21/0.50 ( mweakly_dense
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( R @ S @ T )
% 0.21/0.50 => ? [U: $i] :
% 0.21/0.50 ( ( R @ S @ U )
% 0.21/0.50 & ( R @ U @ T ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_connected_type,type,
% 0.21/0.50 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_connected,definition,
% 0.21/0.50 ( mweakly_connected
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( ( R @ S @ T )
% 0.21/0.50 & ( R @ S @ U ) )
% 0.21/0.50 => ( ( R @ T @ U )
% 0.21/0.50 | ( T = U )
% 0.21/0.50 | ( R @ U @ T ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_directed_type,type,
% 0.21/0.50 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mweakly_directed,definition,
% 0.21/0.50 ( mweakly_directed
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [S: $i,T: $i,U: $i] :
% 0.21/0.50 ( ( ( R @ S @ T )
% 0.21/0.50 & ( R @ S @ U ) )
% 0.21/0.50 => ? [V: $i] :
% 0.21/0.50 ( ( R @ T @ V )
% 0.21/0.50 & ( R @ U @ V ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Definition of validity
% 0.21/0.50 thf(mvalid_type,type,
% 0.21/0.50 mvalid: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mvalid,definition,
% 0.21/0.50 ( mvalid
% 0.21/0.50 = ( ^ [Phi: $i > $o] :
% 0.21/0.50 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Definition of invalidity
% 0.21/0.50 thf(minvalid_type,type,
% 0.21/0.50 minvalid: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(minvalid,definition,
% 0.21/0.50 ( minvalid
% 0.21/0.50 = ( ^ [Phi: $i > $o] :
% 0.21/0.50 ! [W: $i] :
% 0.21/0.50 ~ ( Phi @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Definition of satisfiability
% 0.21/0.50 thf(msatisfiable_type,type,
% 0.21/0.50 msatisfiable: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(msatisfiable,definition,
% 0.21/0.50 ( msatisfiable
% 0.21/0.50 = ( ^ [Phi: $i > $o] :
% 0.21/0.50 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %----Definition of countersatisfiability
% 0.21/0.50 thf(mcountersatisfiable_type,type,
% 0.21/0.50 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(mcountersatisfiable,definition,
% 0.21/0.50 ( mcountersatisfiable
% 0.21/0.50 = ( ^ [Phi: $i > $o] :
% 0.21/0.50 ? [W: $i] :
% 0.21/0.50 ~ ( Phi @ W ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(a_type,type,
% 0.21/0.50 a: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(b_type,type,
% 0.21/0.50 b: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(c_type,type,
% 0.21/0.50 c: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(fool_type,type,
% 0.21/0.50 fool: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(ws_type,type,
% 0.21/0.50 ws: ( $i > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(priorG_type,type,
% 0.21/0.50 priorG: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(irreflexiv_type,type,
% 0.21/0.50 irreflexive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(irreflexive_def,definition,
% 0.21/0.50 ( irreflexive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ~ ( R @ X @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_priorG_irreflexive,axiom,
% 0.21/0.50 irreflexive @ priorG ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_priorG_transitive,axiom,
% 0.21/0.50 mtransitive @ priorG ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_1,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_a_b,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ b @ ( ws @ a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_a_c,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ a ) @ ( mbox @ c @ ( ws @ a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_b_a,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ a @ ( ws @ b ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_b_c,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ b ) @ ( mbox @ c @ ( ws @ b ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_c_a,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ a @ ( ws @ c ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_2_c_b,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( ws @ c ) @ ( mbox @ b @ ( ws @ c ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_a_b,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ b @ ( mnot @ ( ws @ a ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_a_c,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_b_a,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ a @ ( mnot @ ( ws @ b ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_b_c,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_c_a,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ a @ ( mnot @ ( ws @ c ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(axiom_3_c_b,axiom,
% 0.21/0.50 mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ c ) ) @ ( mbox @ b @ ( mnot @ ( ws @ c ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(t_axiom_for_fool,axiom,
% 0.21/0.50 ( mvalid
% 0.21/0.50 @ ( mforall_prop
% 0.21/0.50 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(k_axiom_for_fool,axiom,
% 0.21/0.50 ( mvalid
% 0.21/0.50 @ ( mforall_prop
% 0.21/0.50 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(i_axiom_for_fool_a,axiom,
% 0.21/0.50 ( mvalid
% 0.21/0.50 @ ( mforall_prop
% 0.21/0.50 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(i_axiom_for_fool_b,axiom,
% 0.21/0.50 ( mvalid
% 0.21/0.50 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ b @ Phi ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(i_axiom_for_fool_c,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ c @ Phi ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_a_b,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ b @ ( mbox @ a @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_a_c,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ a @ Phi ) @ ( mbox @ c @ ( mbox @ a @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_b_a,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ a @ ( mbox @ b @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_b_c,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ b @ Phi ) @ ( mbox @ c @ ( mbox @ b @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_c_a,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ a @ ( mbox @ c @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a7_axiom_for_fool_c_b,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ c @ Phi ) @ ( mbox @ b @ ( mbox @ c @ Phi ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_a_b,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_a_c,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ a @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ a @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_b_a,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_b_c,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ b @ Phi ) ) @ ( mbox @ c @ ( mnot @ ( mbox @ b @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_c_a,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(a6_axiom_for_fool_c_b,axiom,
% 0.21/0.52 ( mvalid
% 0.21/0.52 @ ( mforall_prop
% 0.21/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ Phi ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ c @ Phi ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(axiom_4,axiom,
% 0.21/0.52 mvalid @ ( mbox @ priorG @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(axiom_5,axiom,
% 0.21/0.52 mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj,conjecture,
% 0.21/0.52 mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ c @ ( ws @ c ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Xr6iesPmLU/cvc5---1.0.5_15976.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.mu 0)
% 0.21/0.52 (declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.21/0.52 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.21/0.52 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.21/0.52 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.21/0.52 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.21/0.52 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.21/0.52 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.21/0.52 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.21/0.52 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.21/0.52 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.21/0.52 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.21/0.52 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.21/0.52 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.21/0.52 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.21/0.52 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.21/0.52 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.21/0.52 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.21/0.52 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.21/0.52 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.21/0.52 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.21/0.52 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.21/0.52 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.21/0.52 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.21/0.52 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.21/0.52 (declare-fun tptp.a ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.b ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.c ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.fool ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.ws ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.priorG ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.irreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))
% 0.21/0.52 (assert (@ tptp.irreflexive tptp.priorG))
% 0.21/0.52 (assert (@ tptp.mtransitive tptp.priorG))
% 0.21/0.52 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mor (@ tptp.ws tptp.a)) (@ (@ tptp.mor (@ tptp.ws tptp.b)) (@ tptp.ws tptp.c))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.a))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.a))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.b))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.b))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.c))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.ws tptp.c))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.a)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.a)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.b)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.b)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.c)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1))))))
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.mnot (@ tptp.ws tptp.c)))) (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) A)) A) __flatten_var_0)))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.fool))) (let ((_let_2 (@ _let_1 A))) (@ (@ (@ tptp.mimplies _let_2) (@ _let_1 _let_2)) __flatten_var_0)))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.a) Phi)) __flatten_var_0)))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.b) Phi)) __flatten_var_0)))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.c) Phi)) __flatten_var_0)))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.b) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.b) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.c) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.c) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.a) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.a) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.b) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))))
% 0.21/0.52 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.b) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))))
% 0.21/0.61 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.c) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))))
% 0.21/0.61 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.c) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))))
% 0.21/0.61 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.priorG) (@ tptp.mnot (@ (@ tptp.mbox tptp.a) (@ tptp.ws tptp.a))))))
% 0.21/0.61 (assert (let ((_let_1 (@ tptp.mbox tptp.priorG))) (@ tptp.mvalid (@ _let_1 (@ _let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.b) (@ tptp.ws tptp.b))))))))
% 0.21/0.61 (assert (let ((_let_1 (@ tptp.mbox tptp.priorG))) (not (@ tptp.mvalid (@ _let_1 (@ _let_1 (@ _let_1 (@ (@ tptp.mbox tptp.c) (@ tptp.ws tptp.c)))))))))
% 0.21/0.61 (set-info :filename cvc5---1.0.5_15976)
% 0.21/0.61 (check-sat-assuming ( true ))
% 0.21/0.61 ------- get file name : TPTP file name is PUZ087^2
% 0.21/0.61 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15976.smt2...
% 0.21/0.61 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.61 % SZS status Theorem for PUZ087^2
% 0.21/0.61 % SZS output start Proof for PUZ087^2
% 0.21/0.61 (
% 0.21/0.61 (let ((_let_1 (@ tptp.ws tptp.c))) (let ((_let_2 (@ tptp.mbox tptp.c))) (let ((_let_3 (@ tptp.mbox tptp.priorG))) (let ((_let_4 (not (@ tptp.mvalid (@ _let_3 (@ _let_3 (@ _let_3 (@ _let_2 _let_1)))))))) (let ((_let_5 (@ tptp.ws tptp.b))) (let ((_let_6 (@ tptp.mbox tptp.b))) (let ((_let_7 (@ tptp.ws tptp.a))) (let ((_let_8 (@ tptp.mbox tptp.a))) (let ((_let_9 (@ tptp.mnot _let_1))) (let ((_let_10 (@ tptp.mimplies _let_9))) (let ((_let_11 (@ tptp.mbox tptp.fool))) (let ((_let_12 (@ tptp.mnot _let_5))) (let ((_let_13 (@ tptp.mimplies _let_12))) (let ((_let_14 (@ tptp.mnot _let_7))) (let ((_let_15 (@ tptp.mimplies _let_14))) (let ((_let_16 (@ tptp.mimplies _let_1))) (let ((_let_17 (@ tptp.mimplies _let_5))) (let ((_let_18 (@ tptp.mimplies _let_7))) (let ((_let_19 (@ tptp.irreflexive tptp.priorG))) (let ((_let_20 (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))) (let ((_let_21 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_22 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_23 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_24 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_25 (= 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_26 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_27 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_28 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_29 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_30 (= tptp.meuclidean (lambda ((R (-> $$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_31 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_32 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_33 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_34 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_35 (= 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_36 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_37 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_38 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_39 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_40 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_41 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_42 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_43 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_44 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_45 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_46 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_47 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_48 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_49 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_50 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_51 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) (let ((_let_52 (forall ((BOUND_VARIABLE_5012 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_5012) BOUND_VARIABLE_5012))))) (let ((_let_53 (forall ((X $$unsorted)) (not (ho_4 (ho_3 k_2 X) X))))) (let ((_let_54 (ASSUME :args (_let_51)))) (let ((_let_55 (ASSUME :args (_let_50)))) (let ((_let_56 (ASSUME :args (_let_49)))) (let ((_let_57 (ASSUME :args (_let_48)))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_57 _let_56 _let_55 _let_54) :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (ASSUME :args (_let_42)))) (let ((_let_64 (ASSUME :args (_let_41)))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_40)) (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) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (ASSUME :args (_let_36)))) (let ((_let_70 (AND_INTRO (ASSUME :args (_let_20)) (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_23)) (ASSUME :args (_let_24)) (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_34)) (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :args (_let_35 SB_DEFAULT SBA_FIXPOINT))) _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))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_70 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (forall ((BOUND_VARIABLE_5052 $$unsorted)) (or (not (@ (@ tptp.c BOUND_VARIABLE_5052) BOUND_VARIABLE_5052)) (@ (@ tptp.ws tptp.c) BOUND_VARIABLE_5052))) (forall ((BOUND_VARIABLE_5012 $$unsorted)) (not (@ (@ tptp.priorG BOUND_VARIABLE_5012) BOUND_VARIABLE_5012))) (forall ((W $$unsorted) (V $$unsorted)) (not (@ (@ tptp.priorG W) V))))) (not (or (forall ((BOUND_VARIABLE_5052 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_5052) BOUND_VARIABLE_5052)) (ho_4 (ho_7 k_6 k_5) BOUND_VARIABLE_5052))) _let_52 (forall ((W $$unsorted) (V $$unsorted)) (not (ho_4 (ho_3 k_2 W) V)))))))))) :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_53 (= X BOUND_VARIABLE_5012)))) :args ((or _let_52 (not _let_53)))) (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO _let_70 :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X $$unsorted)) (not (@ (@ tptp.priorG X) X))) _let_53))))) :args (_let_52 false _let_53)) :args (false false _let_52)) :args (_let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 (@ tptp.mtransitive tptp.priorG) (@ tptp.mvalid (@ _let_11 (@ (@ tptp.mor _let_7) (@ (@ tptp.mor _let_5) _let_1)))) (@ tptp.mvalid (@ _let_11 (@ _let_18 (@ _let_6 _let_7)))) (@ tptp.mvalid (@ _let_11 (@ _let_18 (@ _let_2 _let_7)))) (@ tptp.mvalid (@ _let_11 (@ _let_17 (@ _let_8 _let_5)))) (@ tptp.mvalid (@ _let_11 (@ _let_17 (@ _let_2 _let_5)))) (@ tptp.mvalid (@ _let_11 (@ _let_16 (@ _let_8 _let_1)))) (@ tptp.mvalid (@ _let_11 (@ _let_16 (@ _let_6 _let_1)))) (@ tptp.mvalid (@ _let_11 (@ _let_15 (@ _let_6 _let_14)))) (@ tptp.mvalid (@ _let_11 (@ _let_15 (@ _let_2 _let_14)))) (@ tptp.mvalid (@ _let_11 (@ _let_13 (@ _let_8 _let_12)))) (@ tptp.mvalid (@ _let_11 (@ _let_13 (@ _let_2 _let_12)))) (@ tptp.mvalid (@ _let_11 (@ _let_10 (@ _let_8 _let_9)))) (@ tptp.mvalid (@ _let_11 (@ _let_10 (@ _let_6 _let_9)))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) A)) A) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.fool))) (let ((_let_2 (@ _let_1 A))) (@ (@ (@ tptp.mimplies _let_2) (@ _let_1 _let_2)) __flatten_var_0)))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.a) Phi)) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.b) Phi)) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.c) Phi)) __flatten_var_0)))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.a) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.b) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.b) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.c) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ (@ tptp.mbox tptp.c) Phi))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.a) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.a) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.b) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.b) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.c) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.c) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.a) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox tptp.c) Phi)))) (@ (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox tptp.b) _let_1)) __flatten_var_0))))) (@ tptp.mvalid (@ _let_3 (@ tptp.mnot (@ _let_8 _let_7)))) (@ tptp.mvalid (@ _let_3 (@ _let_3 (@ tptp.mnot (@ _let_6 _let_5))))) _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.61 )
% 0.21/0.61 % SZS output end Proof for PUZ087^2
% 0.21/0.61 % cvc5---1.0.5 exiting
% 0.21/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------