TSTP Solution File: GEG018^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEG018^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 : Wed Aug 30 22:40:02 EDT 2023
% Result : Theorem 0.22s 0.69s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEG018^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 01:08:16 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 % File : GEG018^1 : TPTP v8.1.2. Released v4.1.0.
% 0.22/0.49 % Domain : Geography
% 0.22/0.49 % Problem : Some places are non-tangential proper parts
% 0.22/0.49 % Version : [RCC92] axioms.
% 0.22/0.49 % English :
% 0.22/0.49
% 0.22/0.49 % Refs : [RCC92] Randell et al. (1992), A Spatial Logic Based on Region
% 0.22/0.49 % : [Ben10a] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.22/0.49 % : [Ben10b] Benzmueller (2010), Simple Type Theory as a Framework
% 0.22/0.49 % Source : [Ben10a]
% 0.22/0.49 % Names : Problem 77 [Ben10b]
% 0.22/0.49
% 0.22/0.49 % Status : Theorem
% 0.22/0.49 % Rating : 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0
% 0.22/0.49 % Syntax : Number of formulae : 98 ( 41 unt; 49 typ; 40 def)
% 0.22/0.49 % Number of atoms : 170 ( 45 equ; 0 cnn)
% 0.22/0.49 % Maximal formula atoms : 9 ( 3 avg)
% 0.22/0.49 % Number of connectives : 232 ( 11 ~; 4 |; 18 &; 189 @)
% 0.22/0.49 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.22/0.49 % Maximal formula depth : 9 ( 2 avg)
% 0.22/0.49 % Number of types : 4 ( 2 usr)
% 0.22/0.49 % Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% 0.22/0.49 % Number of symbols : 56 ( 54 usr; 12 con; 0-3 aty)
% 0.22/0.49 % Number of variables : 118 ( 74 ^; 34 !; 10 ?; 118 :)
% 0.22/0.49 % SPC : TH0_THM_EQU_NAR
% 0.22/0.49
% 0.22/0.49 % Comments :
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %----Include Region Connection Calculus axioms
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %----Declaration of additional base type mu
% 0.22/0.49 thf(mu_type,type,
% 0.22/0.49 mu: $tType ).
% 0.22/0.49
% 0.22/0.49 %----Equality
% 0.22/0.49 thf(meq_ind_type,type,
% 0.22/0.49 meq_ind: mu > mu > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(meq_ind,definition,
% 0.22/0.49 ( meq_ind
% 0.22/0.49 = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(meq_prop_type,type,
% 0.22/0.49 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(meq_prop,definition,
% 0.22/0.49 ( meq_prop
% 0.22/0.49 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.22/0.49 ( ( X @ W )
% 0.22/0.49 = ( Y @ W ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Modal operators not, or, box, Pi
% 0.22/0.49 thf(mnot_type,type,
% 0.22/0.49 mnot: ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mnot,definition,
% 0.22/0.49 ( mnot
% 0.22/0.49 = ( ^ [Phi: $i > $o,W: $i] :
% 0.22/0.49 ~ ( Phi @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mor_type,type,
% 0.22/0.49 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mor,definition,
% 0.22/0.49 ( mor
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.22/0.49 ( ( Phi @ W )
% 0.22/0.49 | ( Psi @ W ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mand_type,type,
% 0.22/0.49 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mand,definition,
% 0.22/0.49 ( mand
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mimplies_type,type,
% 0.22/0.49 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mimplies,definition,
% 0.22/0.49 ( mimplies
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mimplied_type,type,
% 0.22/0.49 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mimplied,definition,
% 0.22/0.49 ( mimplied
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mequiv_type,type,
% 0.22/0.49 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mequiv,definition,
% 0.22/0.49 ( mequiv
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mxor_type,type,
% 0.22/0.49 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mxor,definition,
% 0.22/0.49 ( mxor
% 0.22/0.49 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Universal quantification: individuals
% 0.22/0.49 thf(mforall_ind_type,type,
% 0.22/0.49 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mforall_ind,definition,
% 0.22/0.49 ( mforall_ind
% 0.22/0.49 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.22/0.49 ! [X: mu] : ( Phi @ X @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mforall_prop_type,type,
% 0.22/0.49 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mforall_prop,definition,
% 0.22/0.49 ( mforall_prop
% 0.22/0.49 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.22/0.49 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mexists_ind_type,type,
% 0.22/0.49 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mexists_ind,definition,
% 0.22/0.49 ( mexists_ind
% 0.22/0.49 = ( ^ [Phi: mu > $i > $o] :
% 0.22/0.49 ( mnot
% 0.22/0.49 @ ( mforall_ind
% 0.22/0.49 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mexists_prop_type,type,
% 0.22/0.49 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mexists_prop,definition,
% 0.22/0.49 ( mexists_prop
% 0.22/0.49 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.22/0.49 ( mnot
% 0.22/0.49 @ ( mforall_prop
% 0.22/0.49 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mtrue_type,type,
% 0.22/0.49 mtrue: $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mtrue,definition,
% 0.22/0.49 ( mtrue
% 0.22/0.49 = ( ^ [W: $i] : $true ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mfalse_type,type,
% 0.22/0.49 mfalse: $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mfalse,definition,
% 0.22/0.49 ( mfalse
% 0.22/0.49 = ( mnot @ mtrue ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mbox_type,type,
% 0.22/0.49 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mbox,definition,
% 0.22/0.49 ( mbox
% 0.22/0.49 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.22/0.49 ! [V: $i] :
% 0.22/0.49 ( ~ ( R @ W @ V )
% 0.22/0.49 | ( Phi @ V ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mdia_type,type,
% 0.22/0.49 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mdia,definition,
% 0.22/0.49 ( mdia
% 0.22/0.49 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of properties of accessibility relations
% 0.22/0.49 thf(mreflexive_type,type,
% 0.22/0.49 mreflexive: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mreflexive,definition,
% 0.22/0.49 ( mreflexive
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(msymmetric_type,type,
% 0.22/0.49 msymmetric: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(msymmetric,definition,
% 0.22/0.49 ( msymmetric
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i] :
% 0.22/0.49 ( ( R @ S @ T )
% 0.22/0.49 => ( R @ T @ S ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mserial_type,type,
% 0.22/0.49 mserial: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mserial,definition,
% 0.22/0.49 ( mserial
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i] :
% 0.22/0.49 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mtransitive_type,type,
% 0.22/0.49 mtransitive: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mtransitive,definition,
% 0.22/0.49 ( mtransitive
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( ( R @ S @ T )
% 0.22/0.49 & ( R @ T @ U ) )
% 0.22/0.49 => ( R @ S @ U ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(meuclidean_type,type,
% 0.22/0.49 meuclidean: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(meuclidean,definition,
% 0.22/0.49 ( meuclidean
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( ( R @ S @ T )
% 0.22/0.49 & ( R @ S @ U ) )
% 0.22/0.49 => ( R @ T @ U ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mpartially_functional_type,type,
% 0.22/0.49 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mpartially_functional,definition,
% 0.22/0.49 ( mpartially_functional
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( ( R @ S @ T )
% 0.22/0.49 & ( R @ S @ U ) )
% 0.22/0.49 => ( T = U ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mfunctional_type,type,
% 0.22/0.49 mfunctional: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mfunctional,definition,
% 0.22/0.49 ( mfunctional
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i] :
% 0.22/0.49 ? [T: $i] :
% 0.22/0.49 ( ( R @ S @ T )
% 0.22/0.49 & ! [U: $i] :
% 0.22/0.49 ( ( R @ S @ U )
% 0.22/0.49 => ( T = U ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_dense_type,type,
% 0.22/0.49 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_dense,definition,
% 0.22/0.49 ( mweakly_dense
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( R @ S @ T )
% 0.22/0.49 => ? [U: $i] :
% 0.22/0.49 ( ( R @ S @ U )
% 0.22/0.49 & ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_connected_type,type,
% 0.22/0.49 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_connected,definition,
% 0.22/0.49 ( mweakly_connected
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( ( R @ S @ T )
% 0.22/0.49 & ( R @ S @ U ) )
% 0.22/0.49 => ( ( R @ T @ U )
% 0.22/0.49 | ( T = U )
% 0.22/0.49 | ( R @ U @ T ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_directed_type,type,
% 0.22/0.49 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mweakly_directed,definition,
% 0.22/0.49 ( mweakly_directed
% 0.22/0.49 = ( ^ [R: $i > $i > $o] :
% 0.22/0.49 ! [S: $i,T: $i,U: $i] :
% 0.22/0.49 ( ( ( R @ S @ T )
% 0.22/0.49 & ( R @ S @ U ) )
% 0.22/0.49 => ? [V: $i] :
% 0.22/0.49 ( ( R @ T @ V )
% 0.22/0.49 & ( R @ U @ V ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of validity
% 0.22/0.49 thf(mvalid_type,type,
% 0.22/0.49 mvalid: ( $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mvalid,definition,
% 0.22/0.49 ( mvalid
% 0.22/0.49 = ( ^ [Phi: $i > $o] :
% 0.22/0.49 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of invalidity
% 0.22/0.49 thf(minvalid_type,type,
% 0.22/0.49 minvalid: ( $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(minvalid,definition,
% 0.22/0.49 ( minvalid
% 0.22/0.49 = ( ^ [Phi: $i > $o] :
% 0.22/0.49 ! [W: $i] :
% 0.22/0.49 ~ ( Phi @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of satisfiability
% 0.22/0.49 thf(msatisfiable_type,type,
% 0.22/0.49 msatisfiable: ( $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(msatisfiable,definition,
% 0.22/0.49 ( msatisfiable
% 0.22/0.49 = ( ^ [Phi: $i > $o] :
% 0.22/0.49 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %----Definition of countersatisfiability
% 0.22/0.49 thf(mcountersatisfiable_type,type,
% 0.22/0.49 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.22/0.49
% 0.22/0.49 thf(mcountersatisfiable,definition,
% 0.22/0.49 ( mcountersatisfiable
% 0.22/0.49 = ( ^ [Phi: $i > $o] :
% 0.22/0.49 ? [W: $i] :
% 0.22/0.49 ~ ( Phi @ W ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 thf(reg_type,type,
% 0.22/0.49 reg: $tType ).
% 0.22/0.49
% 0.22/0.49 thf(c_type,type,
% 0.22/0.49 c: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(dc_type,type,
% 0.22/0.49 dc: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(p_type,type,
% 0.22/0.49 p: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(eq_type,type,
% 0.22/0.49 eq: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(o_type,type,
% 0.22/0.49 o: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(po_type,type,
% 0.22/0.49 po: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(ec_type,type,
% 0.22/0.49 ec: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(pp_type,type,
% 0.22/0.49 pp: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(tpp_type,type,
% 0.22/0.49 tpp: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(ntpp_type,type,
% 0.22/0.49 ntpp: reg > reg > $o ).
% 0.22/0.49
% 0.22/0.49 thf(c_reflexive,axiom,
% 0.22/0.49 ! [X: reg] : ( c @ X @ X ) ).
% 0.22/0.49
% 0.22/0.49 thf(c_symmetric,axiom,
% 0.22/0.49 ! [X: reg,Y: reg] :
% 0.22/0.49 ( ( c @ X @ Y )
% 0.22/0.49 => ( c @ Y @ X ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(dc,definition,
% 0.22/0.49 ( dc
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ~ ( c @ X @ Y ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(p,definition,
% 0.22/0.49 ( p
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ! [Z: reg] :
% 0.22/0.49 ( ( c @ Z @ X )
% 0.22/0.49 => ( c @ Z @ Y ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(eq,definition,
% 0.22/0.49 ( eq
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( p @ X @ Y )
% 0.22/0.49 & ( p @ Y @ X ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(o,definition,
% 0.22/0.49 ( o
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ? [Z: reg] :
% 0.22/0.49 ( ( p @ Z @ X )
% 0.22/0.49 & ( p @ Z @ Y ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(po,definition,
% 0.22/0.49 ( po
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( o @ X @ Y )
% 0.22/0.49 & ~ ( p @ X @ Y )
% 0.22/0.49 & ~ ( p @ Y @ X ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ec,definition,
% 0.22/0.49 ( ec
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( c @ X @ Y )
% 0.22/0.49 & ~ ( o @ X @ Y ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(pp,definition,
% 0.22/0.49 ( pp
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( p @ X @ Y )
% 0.22/0.49 & ~ ( p @ Y @ X ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(tpp,definition,
% 0.22/0.49 ( tpp
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( pp @ X @ Y )
% 0.22/0.49 & ? [Z: reg] :
% 0.22/0.49 ( ( ec @ Z @ X )
% 0.22/0.49 & ( ec @ Z @ Y ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ntpp,definition,
% 0.22/0.49 ( ntpp
% 0.22/0.49 = ( ^ [X: reg,Y: reg] :
% 0.22/0.49 ( ( pp @ X @ Y )
% 0.22/0.49 & ~ ? [Z: reg] :
% 0.22/0.49 ( ( ec @ Z @ X )
% 0.22/0.49 & ( ec @ Z @ Y ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.49 thf(catalunya,type,
% 0.22/0.49 catalunya: reg ).
% 0.22/0.49
% 0.22/0.49 thf(france,type,
% 0.22/0.49 france: reg ).
% 0.22/0.49
% 0.22/0.49 thf(spain,type,
% 0.22/0.49 spain: reg ).
% 0.22/0.49
% 0.22/0.49 thf(paris,type,
% 0.22/0.49 paris: reg ).
% 0.22/0.49
% 0.22/0.49 thf(a,type,
% 0.22/0.49 a: $i > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(fool,type,
% 0.22/0.49 fool: $i > $i > $o ).
% 0.22/0.49
% 0.22/0.49 thf(t_axiom_for_fool,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mforall_prop
% 0.22/0.49 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(k_axiom_for_fool,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mforall_prop
% 0.22/0.49 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(i_axiom_for_fool_a,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mforall_prop
% 0.22/0.49 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax1,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mbox @ a
% 0.22/0.49 @ ^ [X: $i] : ( tpp @ catalunya @ spain ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax2,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mbox @ fool
% 0.22/0.49 @ ^ [X: $i] : ( ec @ spain @ france ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(ax3,axiom,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mbox @ a
% 0.22/0.49 @ ^ [X: $i] : ( ntpp @ paris @ france ) ) ) ).
% 0.22/0.49
% 0.22/0.49 thf(con,conjecture,
% 0.22/0.49 ( mvalid
% 0.22/0.49 @ ( mbox @ fool
% 0.22/0.49 @ ^ [X: $i] :
% 0.22/0.49 ~ ? [Z: reg] :
% 0.22/0.49 ! [Y: reg] : ( ntpp @ Z @ Y ) ) ) ).
% 0.22/0.49
% 0.22/0.49 %------------------------------------------------------------------------------
% 0.22/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.LMM8UoRQqR/cvc5---1.0.5_17413.p...
% 0.22/0.51 (declare-sort $$unsorted 0)
% 0.22/0.51 (declare-sort tptp.mu 0)
% 0.22/0.51 (declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.22/0.51 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.22/0.51 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.22/0.51 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.22/0.51 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.22/0.51 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.22/0.51 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.22/0.51 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.22/0.51 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.22/0.51 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.22/0.51 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.22/0.51 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.22/0.51 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.22/0.51 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.22/0.51 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.22/0.51 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.22/0.51 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.22/0.51 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.22/0.51 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.22/0.51 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.22/0.51 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.22/0.51 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.51 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.51 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.22/0.51 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.22/0.51 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.22/0.51 (declare-sort tptp.reg 0)
% 0.22/0.51 (declare-fun tptp.c (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.dc (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.p (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.eq (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.o (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.po (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.ec (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.pp (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.tpp (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (declare-fun tptp.ntpp (tptp.reg tptp.reg) Bool)
% 0.22/0.51 (assert (forall ((X tptp.reg)) (@ (@ tptp.c X) X)))
% 0.22/0.51 (assert (forall ((X tptp.reg) (Y tptp.reg)) (=> (@ (@ tptp.c X) Y) (@ (@ tptp.c Y) X))))
% 0.22/0.51 (assert (= tptp.dc (lambda ((X tptp.reg) (Y tptp.reg)) (not (@ (@ tptp.c X) Y)))))
% 0.22/0.69 (assert (= tptp.p (lambda ((X tptp.reg) (Y tptp.reg)) (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (=> (@ _let_1 X) (@ _let_1 Y)))))))
% 0.22/0.69 (assert (= tptp.eq (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (@ (@ tptp.p Y) X)))))
% 0.22/0.69 (assert (= tptp.o (lambda ((X tptp.reg) (Y tptp.reg)) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.p Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))
% 0.22/0.69 (assert (= tptp.po (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.o X) Y) (not (@ (@ tptp.p X) Y)) (not (@ (@ tptp.p Y) X))))))
% 0.22/0.69 (assert (= tptp.ec (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.c X) Y) (not (@ (@ tptp.o X) Y))))))
% 0.22/0.69 (assert (= tptp.pp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (not (@ (@ tptp.p Y) X))))))
% 0.22/0.69 (assert (= tptp.tpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y))))))))
% 0.22/0.69 (assert (= tptp.ntpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (not (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))))
% 0.22/0.69 (declare-fun tptp.catalunya () tptp.reg)
% 0.22/0.69 (declare-fun tptp.france () tptp.reg)
% 0.22/0.69 (declare-fun tptp.spain () tptp.reg)
% 0.22/0.69 (declare-fun tptp.paris () tptp.reg)
% 0.22/0.69 (declare-fun tptp.a ($$unsorted $$unsorted) Bool)
% 0.22/0.69 (declare-fun tptp.fool ($$unsorted $$unsorted) Bool)
% 0.22/0.69 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) A)) A) __flatten_var_0)))))
% 0.22/0.69 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.fool))) (let ((_let_2 (@ _let_1 A))) (@ (@ (@ tptp.mimplies _let_2) (@ _let_1 _let_2)) __flatten_var_0)))))))
% 0.22/0.69 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.a) Phi)) __flatten_var_0)))))
% 0.22/0.69 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.a) (lambda ((X $$unsorted)) (@ (@ tptp.tpp tptp.catalunya) tptp.spain)))))
% 0.22/0.69 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (lambda ((X $$unsorted)) (@ (@ tptp.ec tptp.spain) tptp.france)))))
% 0.22/0.69 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.a) (lambda ((X $$unsorted)) (@ (@ tptp.ntpp tptp.paris) tptp.france)))))
% 0.22/0.69 (assert (not (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (lambda ((X $$unsorted)) (not (exists ((Z tptp.reg)) (forall ((Y tptp.reg)) (@ (@ tptp.ntpp Z) Y)))))))))
% 0.22/0.69 (set-info :filename cvc5---1.0.5_17413)
% 0.22/0.69 (check-sat-assuming ( true ))
% 0.22/0.69 ------- get file name : TPTP file name is GEG018^1
% 0.22/0.69 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17413.smt2...
% 0.22/0.69 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.69 % SZS status Theorem for GEG018^1
% 0.22/0.69 % SZS output start Proof for GEG018^1
% 0.22/0.69 (
% 0.22/0.69 (let ((_let_1 (@ tptp.mbox tptp.fool))) (let ((_let_2 (not (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (not (exists ((Z tptp.reg)) (forall ((Y tptp.reg)) (@ (@ tptp.ntpp Z) Y)))))))))) (let ((_let_3 (@ tptp.mbox tptp.a))) (let ((_let_4 (= tptp.ntpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (not (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))))) (let ((_let_5 (= tptp.tpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y))))))))) (let ((_let_6 (= tptp.pp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (not (@ (@ tptp.p Y) X))))))) (let ((_let_7 (= tptp.ec (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.c X) Y) (not (@ (@ tptp.o X) Y))))))) (let ((_let_8 (= tptp.po (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.o X) Y) (not (@ (@ tptp.p X) Y)) (not (@ (@ tptp.p Y) X))))))) (let ((_let_9 (= tptp.o (lambda ((X tptp.reg) (Y tptp.reg)) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.p Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))) (let ((_let_10 (= tptp.eq (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (@ (@ tptp.p Y) X)))))) (let ((_let_11 (= tptp.p (lambda ((X tptp.reg) (Y tptp.reg)) (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (=> (@ _let_1 X) (@ _let_1 Y)))))))) (let ((_let_12 (= tptp.dc (lambda ((X tptp.reg) (Y tptp.reg)) (not (@ (@ tptp.c X) Y)))))) (let ((_let_13 (forall ((X tptp.reg)) (@ (@ tptp.c X) X)))) (let ((_let_14 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_15 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_16 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_17 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_18 (= 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_19 (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))) (let ((_let_20 (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))) (let ((_let_21 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_22 (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))) (let ((_let_23 (= tptp.meuclidean (lambda ((R (-> $$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_24 (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))) (let ((_let_25 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_26 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_27 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_28 (= 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_29 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_30 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_31 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_32 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_33 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$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_34 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_35 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_36 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_37 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_38 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_39 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_40 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_41 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_42 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_43 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_44 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) (let ((_let_45 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_46 (forall ((Z tptp.reg)) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not _let_45))) (let ((_let_49 (or _let_48 _let_47 _let_48 _let_47))) (let ((_let_50 (forall ((X tptp.reg)) (ho_4 (ho_3 k_2 X) X)))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_13)) (PREPROCESS :args ((= _let_13 _let_50)))))) (let ((_let_52 (forall ((BOUND_VARIABLE_2713 tptp.reg)) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 BOUND_VARIABLE_2713)) (ho_4 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (forall ((BOUND_VARIABLE_2691 tptp.reg) (Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))))) (not (ho_4 _let_1 BOUND_VARIABLE_2691)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 BOUND_VARIABLE_2691))))))))))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 (not (forall ((BOUND_VARIABLE_2706 tptp.reg) (Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (ho_4 _let_1 BOUND_VARIABLE_2706))))) _let_53))) (let ((_let_57 (forall ((Z tptp.reg)) (or (not (forall ((BOUND_VARIABLE_2691 tptp.reg) (Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z)))))))) (not (ho_4 _let_1 BOUND_VARIABLE_2691)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 BOUND_VARIABLE_2691)))))))))))) (not (forall ((BOUND_VARIABLE_2706 tptp.reg) (Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 BOUND_VARIABLE_2706))))) (not (forall ((BOUND_VARIABLE_2713 tptp.reg)) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 BOUND_VARIABLE_2713)) (ho_4 _let_1 Z))))))))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (ASSUME :args (_let_44)))) (let ((_let_60 (ASSUME :args (_let_43)))) (let ((_let_61 (ASSUME :args (_let_42)))) (let ((_let_62 (ASSUME :args (_let_41)))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_62 _let_61 _let_60 _let_59) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (ASSUME :args (_let_35)))) (let ((_let_69 (ASSUME :args (_let_34)))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_33)) (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) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (ASSUME :args (_let_29)))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (ASSUME :args (_let_27)))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (ASSUME :args (_let_17)))) (let ((_let_87 (ASSUME :args (_let_16)))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (ASSUME :args (_let_12)))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args ((= tptp.o (lambda ((X tptp.reg) (Y tptp.reg)) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.p Z))) (or (not (@ _let_1 X)) (not (@ _let_1 Y)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args ((= tptp.tpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (or (not (@ _let_1 X)) (not (@ _let_1 Y))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (or))) (let ((_let_99 (not _let_57))) (let ((_let_100 (_let_99))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_100)) :args _let_100)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_57))) (REFL :args (_let_58)) :args _let_98)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args ((= tptp.ntpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (or (not (@ _let_1 X)) (not (@ _let_1 Y)))))))) SB_DEFAULT SBA_FIXPOINT))) _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59) :args ((not (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (forall ((Z tptp.reg)) (not (forall ((Y tptp.reg)) (@ (@ tptp.ntpp Z) Y)))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (forall ((Z tptp.reg)) (or (not (forall ((BOUND_VARIABLE_2691 tptp.reg) (Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (@ _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (@ _let_1 Z)))))))) (not (@ _let_1 BOUND_VARIABLE_2691)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (@ _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (@ _let_1 BOUND_VARIABLE_2691)))))))))))) (not (forall ((BOUND_VARIABLE_2706 tptp.reg) (Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 Z)) (@ _let_1 BOUND_VARIABLE_2706))))) (not (forall ((BOUND_VARIABLE_2713 tptp.reg)) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 BOUND_VARIABLE_2713)) (@ _let_1 Z))))))))) (forall ((W $$unsorted) (V $$unsorted)) (not (@ (@ tptp.fool W) V))))) (not (or _let_57 (forall ((W $$unsorted) (V $$unsorted)) (not (ho_5 (ho_7 k_6 W) V)))))))))) :args (0)) :args (_let_58 true _let_57)))) (let ((_let_102 (REFL :args (_let_56)))) (let ((_let_103 (_let_54))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_49))) :args ((or _let_48 _let_47 (not _let_49)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_103) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_3 k_2 Z) BOUND_VARIABLE_2691) false))))) :args _let_103))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_102 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_98)) :args ((or _let_54 _let_56))) _let_101 :args (_let_54 true _let_56)) :args (_let_49 false _let_54)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_52 (= Z Z) (= BOUND_VARIABLE_2713 Z)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_102 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_98)) :args ((or _let_52 _let_56))) _let_101 :args (_let_52 true _let_56)) :args (_let_46 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_2 X)))) :args (_let_50))) _let_51 :args (_let_45 false _let_50)) :args (false false _let_49 false _let_46 false _let_45)) :args (_let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 (forall ((X tptp.reg) (Y tptp.reg)) (=> (@ (@ tptp.c X) Y) (@ (@ tptp.c Y) X))) _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$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 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.a) Phi)) __flatten_var_0)))) (@ tptp.mvalid (@ _let_3 (lambda ((X $$unsorted)) (@ (@ tptp.tpp tptp.catalunya) tptp.spain)))) (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (@ (@ tptp.ec tptp.spain) tptp.france)))) (@ tptp.mvalid (@ _let_3 (lambda ((X $$unsorted)) (@ (@ tptp.ntpp tptp.paris) tptp.france)))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.69 )
% 0.22/0.69 % SZS output end Proof for GEG018^1
% 0.22/0.69 % cvc5---1.0.5 exiting
% 0.22/0.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------