TSTP Solution File: PUZ086^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ086^1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 13:13:19 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ086^1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 22:14:47 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : PUZ086^1 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.49 % Domain : Logic Calculi (Espistemic logic)
% 0.20/0.49 % Problem : The friends puzzle - they both know
% 0.20/0.49 % Version : [Ben09] axioms.
% 0.20/0.49 % English : (i) Peter is a friend of John, so if Peter knows that John knows
% 0.20/0.49 % something then John knows that Peter knows the same thing.
% 0.20/0.49 % (ii) Peter is married, so if Peter's wife knows something, then
% 0.20/0.49 % Peter knows the same thing. John and Peter have an appointment,
% 0.20/0.49 % let us consider the following situation: (a) Peter knows the time
% 0.20/0.49 % of their appointment. (b) Peter also knows that John knows the
% 0.20/0.49 % place of their appointment. Moreover, (c) Peter's wife knows that
% 0.20/0.49 % if Peter knows the time of their appointment, then John knows
% 0.20/0.49 % that too (since John and Peter are friends). Finally, (d) Peter
% 0.20/0.49 % knows that if John knows the place and the time of their
% 0.20/0.49 % appointment, then John knows that he has an appointment. From
% 0.20/0.49 % this situation we want to prove (e) that each of the two friends
% 0.20/0.49 % knows that the other one knows that he has an appointment.
% 0.20/0.49
% 0.20/0.49 % Refs : [Gol92] Goldblatt (1992), Logics of Time and Computation
% 0.20/0.49 % : [Bal98] Baldoni (1998), Normal Multimodal Logics: Automatic De
% 0.20/0.49 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Ben09]
% 0.20/0.49 % Names : mmex3.p [Ben09]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.20/0.49 % Syntax : Number of formulae : 82 ( 31 unt; 38 typ; 31 def)
% 0.20/0.49 % Number of atoms : 168 ( 36 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 12 ( 3 avg)
% 0.20/0.49 % Number of connectives : 190 ( 4 ~; 4 |; 8 &; 166 @)
% 0.20/0.49 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 9 ( 2 avg)
% 0.20/0.49 % Number of types : 3 ( 1 usr)
% 0.20/0.49 % Number of type conns : 182 ( 182 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 46 ( 44 usr; 8 con; 0-3 aty)
% 0.20/0.49 % Number of variables : 86 ( 51 ^; 29 !; 6 ?; 86 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments :
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Include embedding of quantified multimodal logic in simple type theory
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Declaration of additional base type mu
% 0.20/0.49 thf(mu_type,type,
% 0.20/0.49 mu: $tType ).
% 0.20/0.49
% 0.20/0.49 %----Equality
% 0.20/0.49 thf(meq_ind_type,type,
% 0.20/0.49 meq_ind: mu > mu > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(meq_ind,definition,
% 0.20/0.49 ( meq_ind
% 0.20/0.49 = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(meq_prop_type,type,
% 0.20/0.49 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(meq_prop,definition,
% 0.20/0.49 ( meq_prop
% 0.20/0.49 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.20/0.49 ( ( X @ W )
% 0.20/0.49 = ( Y @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Modal operators not, or, box, Pi
% 0.20/0.49 thf(mnot_type,type,
% 0.20/0.49 mnot: ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mnot,definition,
% 0.20/0.49 ( mnot
% 0.20/0.49 = ( ^ [Phi: $i > $o,W: $i] :
% 0.20/0.49 ~ ( Phi @ W ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mor_type,type,
% 0.20/0.49 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mor,definition,
% 0.20/0.49 ( mor
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.20/0.49 ( ( Phi @ W )
% 0.20/0.49 | ( Psi @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mand_type,type,
% 0.20/0.49 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mand,definition,
% 0.20/0.49 ( mand
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mimplies_type,type,
% 0.20/0.49 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mimplies,definition,
% 0.20/0.49 ( mimplies
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mimplied_type,type,
% 0.20/0.49 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mimplied,definition,
% 0.20/0.49 ( mimplied
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mequiv_type,type,
% 0.20/0.49 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mequiv,definition,
% 0.20/0.49 ( mequiv
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mxor_type,type,
% 0.20/0.49 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mxor,definition,
% 0.20/0.49 ( mxor
% 0.20/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Universal quantification: individuals
% 0.20/0.49 thf(mforall_ind_type,type,
% 0.20/0.49 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mforall_ind,definition,
% 0.20/0.49 ( mforall_ind
% 0.20/0.49 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.20/0.49 ! [X: mu] : ( Phi @ X @ W ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mforall_prop_type,type,
% 0.20/0.49 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mforall_prop,definition,
% 0.20/0.49 ( mforall_prop
% 0.20/0.49 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.20/0.49 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_ind_type,type,
% 0.20/0.49 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_ind,definition,
% 0.20/0.49 ( mexists_ind
% 0.20/0.49 = ( ^ [Phi: mu > $i > $o] :
% 0.20/0.49 ( mnot
% 0.20/0.49 @ ( mforall_ind
% 0.20/0.49 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_prop_type,type,
% 0.20/0.49 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_prop,definition,
% 0.20/0.49 ( mexists_prop
% 0.20/0.49 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.20/0.49 ( mnot
% 0.20/0.49 @ ( mforall_prop
% 0.20/0.49 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mtrue_type,type,
% 0.20/0.49 mtrue: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mtrue,definition,
% 0.20/0.49 ( mtrue
% 0.20/0.49 = ( ^ [W: $i] : $true ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mfalse_type,type,
% 0.20/0.49 mfalse: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mfalse,definition,
% 0.20/0.49 ( mfalse
% 0.20/0.49 = ( mnot @ mtrue ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mbox_type,type,
% 0.20/0.49 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mbox,definition,
% 0.20/0.49 ( mbox
% 0.20/0.49 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.20/0.49 ! [V: $i] :
% 0.20/0.49 ( ~ ( R @ W @ V )
% 0.20/0.49 | ( Phi @ V ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mdia_type,type,
% 0.20/0.49 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mdia,definition,
% 0.20/0.49 ( mdia
% 0.20/0.49 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----Definition of properties of accessibility relations
% 0.20/0.49 thf(mreflexive_type,type,
% 0.20/0.49 mreflexive: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mreflexive,definition,
% 0.20/0.49 ( mreflexive
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(msymmetric_type,type,
% 0.20/0.49 msymmetric: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(msymmetric,definition,
% 0.20/0.49 ( msymmetric
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i,T: $i] :
% 0.20/0.49 ( ( R @ S @ T )
% 0.20/0.49 => ( R @ T @ S ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mserial_type,type,
% 0.20/0.49 mserial: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mserial,definition,
% 0.20/0.49 ( mserial
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i] :
% 0.20/0.49 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mtransitive_type,type,
% 0.20/0.49 mtransitive: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mtransitive,definition,
% 0.20/0.49 ( mtransitive
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i,T: $i,U: $i] :
% 0.20/0.49 ( ( ( R @ S @ T )
% 0.20/0.49 & ( R @ T @ U ) )
% 0.20/0.49 => ( R @ S @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(meuclidean_type,type,
% 0.20/0.49 meuclidean: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(meuclidean,definition,
% 0.20/0.49 ( meuclidean
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i,T: $i,U: $i] :
% 0.20/0.49 ( ( ( R @ S @ T )
% 0.20/0.49 & ( R @ S @ U ) )
% 0.20/0.49 => ( R @ T @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mpartially_functional_type,type,
% 0.20/0.49 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mpartially_functional,definition,
% 0.20/0.49 ( mpartially_functional
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i,T: $i,U: $i] :
% 0.20/0.49 ( ( ( R @ S @ T )
% 0.20/0.49 & ( R @ S @ U ) )
% 0.20/0.49 => ( T = U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mfunctional_type,type,
% 0.20/0.49 mfunctional: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mfunctional,definition,
% 0.20/0.49 ( mfunctional
% 0.20/0.49 = ( ^ [R: $i > $i > $o] :
% 0.20/0.49 ! [S: $i] :
% 0.20/0.49 ? [T: $i] :
% 0.20/0.49 ( ( R @ S @ T )
% 0.20/0.49 & ! [U: $i] :
% 0.20/0.49 ( ( R @ S @ U )
% 0.20/0.49 => ( T = U ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mweakly_dense_type,type,
% 0.20/0.49 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mweakly_dense,definition,
% 0.20/0.49 ( mweakly_dense
% 0.20/0.50 = ( ^ [R: $i > $i > $o] :
% 0.20/0.50 ! [S: $i,T: $i,U: $i] :
% 0.20/0.50 ( ( R @ S @ T )
% 0.20/0.50 => ? [U: $i] :
% 0.20/0.50 ( ( R @ S @ U )
% 0.20/0.50 & ( R @ U @ T ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mweakly_connected_type,type,
% 0.20/0.50 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mweakly_connected,definition,
% 0.20/0.50 ( mweakly_connected
% 0.20/0.50 = ( ^ [R: $i > $i > $o] :
% 0.20/0.50 ! [S: $i,T: $i,U: $i] :
% 0.20/0.50 ( ( ( R @ S @ T )
% 0.20/0.50 & ( R @ S @ U ) )
% 0.20/0.50 => ( ( R @ T @ U )
% 0.20/0.50 | ( T = U )
% 0.20/0.50 | ( R @ U @ T ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mweakly_directed_type,type,
% 0.20/0.50 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mweakly_directed,definition,
% 0.20/0.50 ( mweakly_directed
% 0.20/0.50 = ( ^ [R: $i > $i > $o] :
% 0.20/0.50 ! [S: $i,T: $i,U: $i] :
% 0.20/0.50 ( ( ( R @ S @ T )
% 0.20/0.50 & ( R @ S @ U ) )
% 0.20/0.50 => ? [V: $i] :
% 0.20/0.50 ( ( R @ T @ V )
% 0.20/0.50 & ( R @ U @ V ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of validity
% 0.20/0.50 thf(mvalid_type,type,
% 0.20/0.50 mvalid: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mvalid,definition,
% 0.20/0.50 ( mvalid
% 0.20/0.50 = ( ^ [Phi: $i > $o] :
% 0.20/0.50 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of invalidity
% 0.20/0.50 thf(minvalid_type,type,
% 0.20/0.50 minvalid: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(minvalid,definition,
% 0.20/0.50 ( minvalid
% 0.20/0.50 = ( ^ [Phi: $i > $o] :
% 0.20/0.50 ! [W: $i] :
% 0.20/0.50 ~ ( Phi @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of satisfiability
% 0.20/0.50 thf(msatisfiable_type,type,
% 0.20/0.50 msatisfiable: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(msatisfiable,definition,
% 0.20/0.50 ( msatisfiable
% 0.20/0.50 = ( ^ [Phi: $i > $o] :
% 0.20/0.50 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Definition of countersatisfiability
% 0.20/0.50 thf(mcountersatisfiable_type,type,
% 0.20/0.50 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mcountersatisfiable,definition,
% 0.20/0.50 ( mcountersatisfiable
% 0.20/0.50 = ( ^ [Phi: $i > $o] :
% 0.20/0.50 ? [W: $i] :
% 0.20/0.50 ~ ( Phi @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(peter,type,
% 0.20/0.50 peter: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(john,type,
% 0.20/0.50 john: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(wife,type,
% 0.20/0.50 wife: ( $i > $i > $o ) > $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(refl_peter,axiom,
% 0.20/0.50 mreflexive @ peter ).
% 0.20/0.50
% 0.20/0.50 thf(refl_john,axiom,
% 0.20/0.50 mreflexive @ john ).
% 0.20/0.50
% 0.20/0.50 thf(refl_wife_peter,axiom,
% 0.20/0.50 mreflexive @ ( wife @ peter ) ).
% 0.20/0.50
% 0.20/0.50 thf(trans_peter,axiom,
% 0.20/0.50 mtransitive @ peter ).
% 0.20/0.50
% 0.20/0.50 thf(trans_john,axiom,
% 0.20/0.50 mtransitive @ john ).
% 0.20/0.50
% 0.20/0.50 thf(trans_wife_peter,axiom,
% 0.20/0.50 mtransitive @ ( wife @ peter ) ).
% 0.20/0.50
% 0.20/0.50 thf(ax_i,axiom,
% 0.20/0.50 ( mvalid
% 0.20/0.50 @ ( mforall_prop
% 0.20/0.50 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ peter @ ( mbox @ john @ A ) ) @ ( mbox @ john @ ( mbox @ peter @ A ) ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(ax_ii,axiom,
% 0.20/0.50 ( mvalid
% 0.20/0.50 @ ( mforall_prop
% 0.20/0.50 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ peter @ A ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(time,type,
% 0.20/0.50 time: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(place,type,
% 0.20/0.50 place: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(appointment,type,
% 0.20/0.50 appointment: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(ax_a,axiom,
% 0.20/0.50 mvalid @ ( mbox @ peter @ time ) ).
% 0.20/0.50
% 0.20/0.50 thf(ax_b,axiom,
% 0.20/0.50 mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(ax_c,axiom,
% 0.20/0.50 mvalid @ ( mbox @ ( wife @ peter ) @ ( mimplies @ ( mbox @ peter @ time ) @ ( mbox @ john @ time ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(ax_d,axiom,
% 0.20/0.50 mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(conj,conjecture,
% 0.20/0.50 mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.epmVCfu0Yg/cvc5---1.0.5_31969.p...
% 0.20/0.50 (declare-sort $$unsorted 0)
% 0.20/0.50 (declare-sort tptp.mu 0)
% 0.20/0.50 (declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.20/0.50 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.20/0.50 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.20/0.50 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.20/0.50 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.20/0.50 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.20/0.50 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (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 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.20/0.50 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.20/0.50 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.20/0.50 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.50 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.20/0.50 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.20/0.50 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.20/0.50 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.20/0.50 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.20/0.50 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.meuclidean (lambda ((R (-> $$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)))))))
% 0.20/0.50 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.20/0.50 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.20/0.50 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (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))))))))
% 0.20/0.50 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.20/0.50 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.20/0.50 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.20/0.50 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.20/0.50 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.20/0.50 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.20/0.50 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.20/0.50 (declare-fun tptp.peter ($$unsorted $$unsorted) Bool)
% 0.20/0.50 (declare-fun tptp.john ($$unsorted $$unsorted) Bool)
% 0.20/0.50 (declare-fun tptp.wife ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.20/0.50 (assert (@ tptp.mreflexive tptp.peter))
% 0.20/0.50 (assert (@ tptp.mreflexive tptp.john))
% 0.20/0.50 (assert (@ tptp.mreflexive (@ tptp.wife tptp.peter)))
% 0.20/0.50 (assert (@ tptp.mtransitive tptp.peter))
% 0.20/0.50 (assert (@ tptp.mtransitive tptp.john))
% 0.20/0.50 (assert (@ tptp.mtransitive (@ tptp.wife tptp.peter)))
% 0.20/0.50 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.peter))) (let ((_let_2 (@ tptp.mbox tptp.john))) (@ (@ (@ tptp.mimplies (@ _let_1 (@ _let_2 A))) (@ _let_2 (@ _let_1 A))) __flatten_var_0)))))))
% 0.20/0.50 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox (@ tptp.wife tptp.peter)) A)) (@ (@ tptp.mbox tptp.peter) A)) __flatten_var_0)))))
% 0.20/0.50 (declare-fun tptp.time ($$unsorted) Bool)
% 0.20/0.50 (declare-fun tptp.place ($$unsorted) Bool)
% 0.20/0.50 (declare-fun tptp.appointment ($$unsorted) Bool)
% 0.20/0.50 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.peter) tptp.time)))
% 0.20/0.50 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.peter) (@ (@ tptp.mbox tptp.john) tptp.place))))
% 0.20/0.50 (assert (@ tptp.mvalid (@ (@ tptp.mbox (@ tptp.wife tptp.peter)) (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.peter) tptp.time)) (@ (@ tptp.mbox tptp.john) tptp.time)))))
% 0.20/0.59 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.peter) (@ (@ tptp.mbox tptp.john) (@ (@ tptp.mimplies (@ (@ tptp.mand tptp.place) tptp.time)) tptp.appointment)))))
% 0.20/0.59 (assert (let ((_let_1 (@ tptp.mbox tptp.peter))) (let ((_let_2 (@ tptp.mbox tptp.john))) (not (@ tptp.mvalid (@ (@ tptp.mand (@ _let_1 (@ _let_2 tptp.appointment))) (@ _let_2 (@ _let_1 tptp.appointment))))))))
% 0.20/0.59 (set-info :filename cvc5---1.0.5_31969)
% 0.20/0.59 (check-sat-assuming ( true ))
% 0.20/0.59 ------- get file name : TPTP file name is PUZ086^1
% 0.20/0.59 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31969.smt2...
% 0.20/0.59 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.59 % SZS status Theorem for PUZ086^1
% 0.20/0.59 % SZS output start Proof for PUZ086^1
% 0.20/0.59 (
% 0.20/0.59 (let ((_let_1 (@ tptp.mbox tptp.peter))) (let ((_let_2 (@ tptp.mbox tptp.john))) (let ((_let_3 (not (@ tptp.mvalid (@ (@ tptp.mand (@ _let_1 (@ _let_2 tptp.appointment))) (@ _let_2 (@ _let_1 tptp.appointment))))))) (let ((_let_4 (@ tptp.mvalid (@ _let_1 (@ _let_2 (@ (@ tptp.mimplies (@ (@ tptp.mand tptp.place) tptp.time)) tptp.appointment)))))) (let ((_let_5 (@ _let_1 tptp.time))) (let ((_let_6 (@ tptp.wife tptp.peter))) (let ((_let_7 (@ tptp.mvalid (@ _let_1 (@ _let_2 tptp.place))))) (let ((_let_8 (@ tptp.mvalid _let_5))) (let ((_let_9 (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.peter))) (let ((_let_2 (@ tptp.mbox tptp.john))) (@ (@ (@ tptp.mimplies (@ _let_1 (@ _let_2 A))) (@ _let_2 (@ _let_1 A))) __flatten_var_0)))))))) (let ((_let_10 (@ tptp.mreflexive tptp.john))) (let ((_let_11 (@ tptp.mreflexive tptp.peter))) (let ((_let_12 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_13 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_14 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_15 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_16 (= 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_17 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_18 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_19 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_20 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_21 (= tptp.meuclidean (lambda ((R (-> $$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_22 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_23 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_24 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_25 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_26 (= 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_27 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_28 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_29 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_30 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_31 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_32 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_33 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_34 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_35 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_36 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_37 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_38 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_39 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_40 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_41 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_42 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) (let ((_let_43 (forall ((W $$unsorted) (V $$unsorted)) (or (not (ho_4 (ho_3 k_2 W) V)) (ho_4 k_8 V))))) (let ((_let_44 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_45 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44))) (let ((_let_48 (ASSUME :args (_let_42)))) (let ((_let_49 (ASSUME :args (_let_41)))) (let ((_let_50 (ASSUME :args (_let_40)))) (let ((_let_51 (ASSUME :args (_let_39)))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_51 _let_50 _let_49 _let_48) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_52 _let_51 _let_50 _let_49 _let_48) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_53 _let_52 _let_51 _let_50 _let_49 _let_48) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48) :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (ASSUME :args (_let_33)))) (let ((_let_58 (ASSUME :args (_let_32)))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_30)) (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 _let_49 _let_48) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_28)) (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 _let_49 _let_48) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (ASSUME :args (_let_27)))) (let ((_let_64 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_14)) (ASSUME :args (_let_15)) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (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))) (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_25)) (EQ_RESOLVE (ASSUME :args (_let_26)) (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 _let_49 _let_48) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) _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_49 _let_48))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (V $$unsorted)) (or (not (@ (@ tptp.peter W) V)) (@ tptp.time V))) _let_43))))))) (let ((_let_66 (not _let_47))) (let ((_let_67 (not _let_44))) (let ((_let_68 (ho_4 k_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_69 (not _let_68))) (let ((_let_70 (ho_4 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_71 (ho_4 (ho_3 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_70 _let_69 _let_67))) (let ((_let_74 (forall ((BOUND_VARIABLE_2189 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_2189) BOUND_VARIABLE_2189)) (ho_4 k_10 BOUND_VARIABLE_2189) (not (ho_4 k_9 BOUND_VARIABLE_2189)) (not (ho_4 k_8 BOUND_VARIABLE_2189)))))) (let ((_let_75 (forall ((W $$unsorted) (V $$unsorted)) (not (ho_4 (ho_3 k_2 W) V))))) (let ((_let_76 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_77 (forall ((S $$unsorted)) (ho_4 (ho_3 k_2 S) S)))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((S $$unsorted)) (@ (@ tptp.peter S) S)) _let_77))))))) (let ((_let_79 (_let_77))) (let ((_let_80 (_let_75))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args ((not _let_75) false _let_76)))) (let ((_let_82 (forall ((W $$unsorted) (V $$unsorted)) (not (@ (@ tptp.peter W) V))))) (let ((_let_83 (_let_74))) (let ((_let_84 (or _let_72 _let_68))) (let ((_let_85 (forall ((BOUND_VARIABLE_2027 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_2027) BOUND_VARIABLE_2027)) (ho_4 k_9 BOUND_VARIABLE_2027))))) (let ((_let_86 (_let_85))) (let ((_let_87 (forall ((S $$unsorted)) (ho_4 (ho_3 k_5 S) S)))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((S $$unsorted)) (@ (@ tptp.john S) S)) _let_87))))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_87))) _let_88 :args (_let_71 false _let_87)))) (let ((_let_90 (or _let_72 _let_70))) (let ((_let_91 (forall ((BOUND_VARIABLE_2235 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_2235) BOUND_VARIABLE_2235)) (ho_4 k_10 BOUND_VARIABLE_2235))))) (let ((_let_92 (not _let_90))) (let ((_let_93 (or _let_91 (forall ((BOUND_VARIABLE_2317 $$unsorted) (V $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2317) V)))))) (let ((_let_94 (forall ((BOUND_VARIABLE_1702 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_1702) BOUND_VARIABLE_1702)) (ho_4 k_10 BOUND_VARIABLE_1702))))) (let ((_let_95 (forall ((BOUND_VARIABLE_2326 $$unsorted) (V $$unsorted)) (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_2326) V))))) (let ((_let_96 (forall ((BOUND_VARIABLE_2276 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2276) BOUND_VARIABLE_2276)) (ho_4 k_10 BOUND_VARIABLE_2276))))) (let ((_let_97 (or _let_96 _let_95))) (let ((_let_98 (not _let_94))) (let ((_let_99 (and _let_98 (not (forall ((V $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) V))))))) (let ((_let_100 (ho_4 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_101 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_102 (not _let_101))) (let ((_let_103 (or _let_102 _let_100))) (let ((_let_104 (ho_4 (ho_3 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_99 _let_102 _let_100))) (let ((_let_107 (not _let_91))) (let ((_let_108 (or))) (let ((_let_109 (not _let_96))) (let ((_let_110 (_let_109))) (let ((_let_111 (not _let_95))) (let ((_let_112 (_let_111))) (let ((_let_113 (forall ((W $$unsorted) (BOUND_VARIABLE_1861 $$unsorted) (BOUND_VARIABLE_2475 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1855 $$unsorted)) (or (not (ho_4 (ho_3 k_5 W) BOUND_VARIABLE_1855)) (and (not (forall ((BOUND_VARIABLE_1702 $$unsorted)) (or (not (ho_4 (ho_3 k_5 BOUND_VARIABLE_1702) BOUND_VARIABLE_1702)) (ho_4 BOUND_VARIABLE_2475 BOUND_VARIABLE_1702)))) (not (forall ((V $$unsorted)) (not (ho_4 (ho_3 k_2 W) V))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1861) BOUND_VARIABLE_1861)) (ho_4 BOUND_VARIABLE_2475 BOUND_VARIABLE_1861))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W $$unsorted) (BOUND_VARIABLE_1861 $$unsorted) (BOUND_VARIABLE_1859 (-> $$unsorted Bool)) (BOUND_VARIABLE_1855 $$unsorted)) (or (not (@ (@ tptp.john W) BOUND_VARIABLE_1855)) (and (not (forall ((BOUND_VARIABLE_1702 $$unsorted)) (or (not (@ (@ tptp.john BOUND_VARIABLE_1702) BOUND_VARIABLE_1702)) (@ BOUND_VARIABLE_1859 BOUND_VARIABLE_1702)))) (not (forall ((V $$unsorted)) (not (@ (@ tptp.peter W) V))))) (not (@ (@ tptp.peter BOUND_VARIABLE_1861) BOUND_VARIABLE_1861)) (@ BOUND_VARIABLE_1859 BOUND_VARIABLE_1861))) _let_113))))))) (let ((_let_115 (_let_107))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_43))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_44 _let_66))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_2 S)))) :args _let_79)) _let_78 :args (_let_45 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_70 _let_69 _let_67 (not _let_73)))) _let_89 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_90 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_115)) :args _let_115)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_91))) (REFL :args (_let_92)) :args _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_102 _let_100 _let_105 _let_99 (not _let_106)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_5 W) BOUND_VARIABLE_1855) false)) (not (= (ho_4 BOUND_VARIABLE_2475 BOUND_VARIABLE_1861) true))))) :args (_let_113))) _let_114 :args (_let_106 false _let_113)) (CNF_OR_NEG :args (_let_103 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_103 0)) (CONG (REFL :args (_let_103)) (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_101))) :args _let_108)) :args ((or _let_101 _let_103))) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_112)) :args _let_112) (REWRITE :args ((=> _let_111 (not _let_105)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_95))) (REFL :args (_let_104)) :args _let_108)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_96))) (REFL :args ((not _let_103))) :args _let_108)) (CNF_OR_NEG :args (_let_97 1)) (CNF_OR_NEG :args (_let_97 0)) (REORDERING (CNF_AND_POS :args (_let_99 0)) :args ((or _let_98 (not _let_99)))) (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (or (forall ((BOUND_VARIABLE_2235 $$unsorted)) (or (not (@ (@ tptp.john BOUND_VARIABLE_2235) BOUND_VARIABLE_2235)) (@ tptp.appointment BOUND_VARIABLE_2235))) (forall ((BOUND_VARIABLE_2317 $$unsorted) (V $$unsorted)) (not (@ (@ tptp.peter BOUND_VARIABLE_2317) V)))) (or (forall ((BOUND_VARIABLE_2276 $$unsorted)) (or (not (@ (@ tptp.peter BOUND_VARIABLE_2276) BOUND_VARIABLE_2276)) (@ tptp.appointment BOUND_VARIABLE_2276))) (forall ((BOUND_VARIABLE_2326 $$unsorted) (V $$unsorted)) (not (@ (@ tptp.john BOUND_VARIABLE_2326) V)))))) (not (and _let_93 _let_97)))))))) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_91 (= BOUND_VARIABLE_2235 BOUND_VARIABLE_1702)))) (CNF_OR_NEG :args (_let_93 0)) :args (_let_107 false _let_106 true _let_100 false _let_101 false _let_104 true _let_103 true _let_95 true _let_96 true _let_99 true _let_97 false _let_94 false _let_93)) :args (_let_92 true _let_91)) :args ((not _let_70) true _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_72 _let_68 (not _let_84)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_86) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_5 BOUND_VARIABLE_2027)))) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_2027 $$unsorted)) (or (not (@ (@ tptp.john BOUND_VARIABLE_2027) BOUND_VARIABLE_2027)) (@ tptp.place BOUND_VARIABLE_2027))) _let_82) (or _let_85 _let_75)))))) :args ((or _let_75 _let_85))) _let_81 :args (_let_85 true _let_75)) :args (_let_84 false _let_85)) :args (_let_68 false _let_71 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_83) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_5 BOUND_VARIABLE_2189)))) :args _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_64 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_2189 $$unsorted)) (or (not (@ (@ tptp.john BOUND_VARIABLE_2189) BOUND_VARIABLE_2189)) (@ tptp.appointment BOUND_VARIABLE_2189) (not (@ tptp.place BOUND_VARIABLE_2189)) (not (@ tptp.time BOUND_VARIABLE_2189)))) _let_82) (or _let_74 _let_75)))))) :args ((or _let_75 _let_74))) _let_81 :args (_let_74 true _let_75)) :args (_let_73 false _let_74)) :args (_let_67 false _let_71 true _let_70 false _let_68 false _let_73)) :args (_let_66 false _let_45 true _let_44)) _let_65 :args (false true _let_47 false _let_43)) :args (_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 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 (@ tptp.mreflexive _let_6) (@ tptp.mtransitive tptp.peter) (@ tptp.mtransitive tptp.john) (@ tptp.mtransitive _let_6) _let_9 (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox (@ tptp.wife tptp.peter)) A)) (@ (@ tptp.mbox tptp.peter) A)) __flatten_var_0)))) _let_8 _let_7 (@ tptp.mvalid (@ (@ tptp.mbox _let_6) (@ (@ tptp.mimplies _let_5) (@ _let_2 tptp.time)))) _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.59 )
% 0.20/0.59 % SZS output end Proof for PUZ086^1
% 0.20/0.59 % cvc5---1.0.5 exiting
% 0.20/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------