TSTP Solution File: GEG014^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GEG014^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 22:40:01 EDT 2023
% Result : Theorem 30.55s 30.82s
% Output : Proof 30.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GEG014^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 01:02:13 EDT 2023
% 0.23/0.36 % CPUTime :
% 0.23/0.51 %----Proving TH0
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 % File : GEG014^1 : TPTP v8.1.2. Released v4.1.0.
% 0.23/0.52 % Domain : Geography
% 0.23/0.52 % Problem : Two unequal regions in France
% 0.23/0.52 % Version : [RCC92] axioms.
% 0.23/0.52 % English :
% 0.23/0.52
% 0.23/0.52 % Refs : [RCC92] Randell et al. (1992), A Spatial Logic Based on Region
% 0.23/0.52 % : [Ben10a] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.23/0.52 % : [Ben10b] Benzmueller (2010), Simple Type Theory as a Framework
% 0.23/0.52 % Source : [Ben10a]
% 0.23/0.52 % Names : Problem 73 [Ben10b]
% 0.23/0.52
% 0.23/0.52 % Status : Theorem
% 0.23/0.52 % Rating : 0.46 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v5.0.0, 0.60 v4.1.0
% 0.23/0.52 % Syntax : Number of formulae : 98 ( 41 unt; 49 typ; 40 def)
% 0.23/0.52 % Number of atoms : 172 ( 45 equ; 0 cnn)
% 0.23/0.52 % Maximal formula atoms : 9 ( 3 avg)
% 0.23/0.52 % Number of connectives : 238 ( 11 ~; 4 |; 20 &; 193 @)
% 0.23/0.52 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.23/0.52 % Maximal formula depth : 10 ( 2 avg)
% 0.23/0.52 % Number of types : 4 ( 2 usr)
% 0.23/0.52 % Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% 0.23/0.52 % Number of symbols : 58 ( 56 usr; 14 con; 0-3 aty)
% 0.23/0.52 % Number of variables : 118 ( 74 ^; 33 !; 11 ?; 118 :)
% 0.23/0.52 % SPC : TH0_THM_EQU_NAR
% 0.23/0.52
% 0.23/0.52 % Comments :
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %----Include Region Connection Calculus axioms
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %----Declaration of additional base type mu
% 0.23/0.52 thf(mu_type,type,
% 0.23/0.52 mu: $tType ).
% 0.23/0.52
% 0.23/0.52 %----Equality
% 0.23/0.52 thf(meq_ind_type,type,
% 0.23/0.52 meq_ind: mu > mu > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(meq_ind,definition,
% 0.23/0.52 ( meq_ind
% 0.23/0.52 = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(meq_prop_type,type,
% 0.23/0.52 meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(meq_prop,definition,
% 0.23/0.52 ( meq_prop
% 0.23/0.52 = ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
% 0.23/0.52 ( ( X @ W )
% 0.23/0.52 = ( Y @ W ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Modal operators not, or, box, Pi
% 0.23/0.52 thf(mnot_type,type,
% 0.23/0.52 mnot: ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mnot,definition,
% 0.23/0.52 ( mnot
% 0.23/0.52 = ( ^ [Phi: $i > $o,W: $i] :
% 0.23/0.52 ~ ( Phi @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mor_type,type,
% 0.23/0.52 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mor,definition,
% 0.23/0.52 ( mor
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
% 0.23/0.52 ( ( Phi @ W )
% 0.23/0.52 | ( Psi @ W ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mand_type,type,
% 0.23/0.52 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mand,definition,
% 0.23/0.52 ( mand
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mimplies_type,type,
% 0.23/0.52 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mimplies,definition,
% 0.23/0.52 ( mimplies
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mimplied_type,type,
% 0.23/0.52 mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mimplied,definition,
% 0.23/0.52 ( mimplied
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mequiv_type,type,
% 0.23/0.52 mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mequiv,definition,
% 0.23/0.52 ( mequiv
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mxor_type,type,
% 0.23/0.52 mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mxor,definition,
% 0.23/0.52 ( mxor
% 0.23/0.52 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Universal quantification: individuals
% 0.23/0.52 thf(mforall_ind_type,type,
% 0.23/0.52 mforall_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mforall_ind,definition,
% 0.23/0.52 ( mforall_ind
% 0.23/0.52 = ( ^ [Phi: mu > $i > $o,W: $i] :
% 0.23/0.52 ! [X: mu] : ( Phi @ X @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mforall_prop_type,type,
% 0.23/0.52 mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mforall_prop,definition,
% 0.23/0.52 ( mforall_prop
% 0.23/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
% 0.23/0.52 ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mexists_ind_type,type,
% 0.23/0.52 mexists_ind: ( mu > $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mexists_ind,definition,
% 0.23/0.52 ( mexists_ind
% 0.23/0.52 = ( ^ [Phi: mu > $i > $o] :
% 0.23/0.52 ( mnot
% 0.23/0.52 @ ( mforall_ind
% 0.23/0.52 @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mexists_prop_type,type,
% 0.23/0.52 mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mexists_prop,definition,
% 0.23/0.52 ( mexists_prop
% 0.23/0.52 = ( ^ [Phi: ( $i > $o ) > $i > $o] :
% 0.23/0.52 ( mnot
% 0.23/0.52 @ ( mforall_prop
% 0.23/0.52 @ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mtrue_type,type,
% 0.23/0.52 mtrue: $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mtrue,definition,
% 0.23/0.52 ( mtrue
% 0.23/0.52 = ( ^ [W: $i] : $true ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mfalse_type,type,
% 0.23/0.52 mfalse: $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mfalse,definition,
% 0.23/0.52 ( mfalse
% 0.23/0.52 = ( mnot @ mtrue ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mbox_type,type,
% 0.23/0.52 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mbox,definition,
% 0.23/0.52 ( mbox
% 0.23/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
% 0.23/0.52 ! [V: $i] :
% 0.23/0.52 ( ~ ( R @ W @ V )
% 0.23/0.52 | ( Phi @ V ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mdia_type,type,
% 0.23/0.52 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mdia,definition,
% 0.23/0.52 ( mdia
% 0.23/0.52 = ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of properties of accessibility relations
% 0.23/0.52 thf(mreflexive_type,type,
% 0.23/0.52 mreflexive: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mreflexive,definition,
% 0.23/0.52 ( mreflexive
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i] : ( R @ S @ S ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(msymmetric_type,type,
% 0.23/0.52 msymmetric: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(msymmetric,definition,
% 0.23/0.52 ( msymmetric
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i] :
% 0.23/0.52 ( ( R @ S @ T )
% 0.23/0.52 => ( R @ T @ S ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mserial_type,type,
% 0.23/0.52 mserial: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mserial,definition,
% 0.23/0.52 ( mserial
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i] :
% 0.23/0.52 ? [T: $i] : ( R @ S @ T ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mtransitive_type,type,
% 0.23/0.52 mtransitive: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mtransitive,definition,
% 0.23/0.52 ( mtransitive
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( ( R @ S @ T )
% 0.23/0.52 & ( R @ T @ U ) )
% 0.23/0.52 => ( R @ S @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(meuclidean_type,type,
% 0.23/0.52 meuclidean: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(meuclidean,definition,
% 0.23/0.52 ( meuclidean
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( ( R @ S @ T )
% 0.23/0.52 & ( R @ S @ U ) )
% 0.23/0.52 => ( R @ T @ U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mpartially_functional_type,type,
% 0.23/0.52 mpartially_functional: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mpartially_functional,definition,
% 0.23/0.52 ( mpartially_functional
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( ( R @ S @ T )
% 0.23/0.52 & ( R @ S @ U ) )
% 0.23/0.52 => ( T = U ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mfunctional_type,type,
% 0.23/0.52 mfunctional: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mfunctional,definition,
% 0.23/0.52 ( mfunctional
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i] :
% 0.23/0.52 ? [T: $i] :
% 0.23/0.52 ( ( R @ S @ T )
% 0.23/0.52 & ! [U: $i] :
% 0.23/0.52 ( ( R @ S @ U )
% 0.23/0.52 => ( T = U ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_dense_type,type,
% 0.23/0.52 mweakly_dense: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_dense,definition,
% 0.23/0.52 ( mweakly_dense
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( R @ S @ T )
% 0.23/0.52 => ? [U: $i] :
% 0.23/0.52 ( ( R @ S @ U )
% 0.23/0.52 & ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_connected_type,type,
% 0.23/0.52 mweakly_connected: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_connected,definition,
% 0.23/0.52 ( mweakly_connected
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( ( R @ S @ T )
% 0.23/0.52 & ( R @ S @ U ) )
% 0.23/0.52 => ( ( R @ T @ U )
% 0.23/0.52 | ( T = U )
% 0.23/0.52 | ( R @ U @ T ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_directed_type,type,
% 0.23/0.52 mweakly_directed: ( $i > $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mweakly_directed,definition,
% 0.23/0.52 ( mweakly_directed
% 0.23/0.52 = ( ^ [R: $i > $i > $o] :
% 0.23/0.52 ! [S: $i,T: $i,U: $i] :
% 0.23/0.52 ( ( ( R @ S @ T )
% 0.23/0.52 & ( R @ S @ U ) )
% 0.23/0.52 => ? [V: $i] :
% 0.23/0.52 ( ( R @ T @ V )
% 0.23/0.52 & ( R @ U @ V ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of validity
% 0.23/0.52 thf(mvalid_type,type,
% 0.23/0.52 mvalid: ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mvalid,definition,
% 0.23/0.52 ( mvalid
% 0.23/0.52 = ( ^ [Phi: $i > $o] :
% 0.23/0.52 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of invalidity
% 0.23/0.52 thf(minvalid_type,type,
% 0.23/0.52 minvalid: ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(minvalid,definition,
% 0.23/0.52 ( minvalid
% 0.23/0.52 = ( ^ [Phi: $i > $o] :
% 0.23/0.52 ! [W: $i] :
% 0.23/0.52 ~ ( Phi @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of satisfiability
% 0.23/0.52 thf(msatisfiable_type,type,
% 0.23/0.52 msatisfiable: ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(msatisfiable,definition,
% 0.23/0.52 ( msatisfiable
% 0.23/0.52 = ( ^ [Phi: $i > $o] :
% 0.23/0.52 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %----Definition of countersatisfiability
% 0.23/0.52 thf(mcountersatisfiable_type,type,
% 0.23/0.52 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mcountersatisfiable,definition,
% 0.23/0.52 ( mcountersatisfiable
% 0.23/0.52 = ( ^ [Phi: $i > $o] :
% 0.23/0.52 ? [W: $i] :
% 0.23/0.52 ~ ( Phi @ W ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 thf(reg_type,type,
% 0.23/0.52 reg: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(c_type,type,
% 0.23/0.52 c: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(dc_type,type,
% 0.23/0.52 dc: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(p_type,type,
% 0.23/0.52 p: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(eq_type,type,
% 0.23/0.52 eq: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(o_type,type,
% 0.23/0.52 o: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(po_type,type,
% 0.23/0.52 po: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(ec_type,type,
% 0.23/0.52 ec: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(pp_type,type,
% 0.23/0.52 pp: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(tpp_type,type,
% 0.23/0.52 tpp: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(ntpp_type,type,
% 0.23/0.52 ntpp: reg > reg > $o ).
% 0.23/0.52
% 0.23/0.52 thf(c_reflexive,axiom,
% 0.23/0.52 ! [X: reg] : ( c @ X @ X ) ).
% 0.23/0.52
% 0.23/0.52 thf(c_symmetric,axiom,
% 0.23/0.52 ! [X: reg,Y: reg] :
% 0.23/0.52 ( ( c @ X @ Y )
% 0.23/0.52 => ( c @ Y @ X ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(dc,definition,
% 0.23/0.52 ( dc
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ~ ( c @ X @ Y ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(p,definition,
% 0.23/0.52 ( p
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ! [Z: reg] :
% 0.23/0.52 ( ( c @ Z @ X )
% 0.23/0.52 => ( c @ Z @ Y ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(eq,definition,
% 0.23/0.52 ( eq
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( p @ X @ Y )
% 0.23/0.52 & ( p @ Y @ X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(o,definition,
% 0.23/0.52 ( o
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ? [Z: reg] :
% 0.23/0.52 ( ( p @ Z @ X )
% 0.23/0.52 & ( p @ Z @ Y ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(po,definition,
% 0.23/0.52 ( po
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( o @ X @ Y )
% 0.23/0.52 & ~ ( p @ X @ Y )
% 0.23/0.52 & ~ ( p @ Y @ X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ec,definition,
% 0.23/0.52 ( ec
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( c @ X @ Y )
% 0.23/0.52 & ~ ( o @ X @ Y ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(pp,definition,
% 0.23/0.52 ( pp
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( p @ X @ Y )
% 0.23/0.52 & ~ ( p @ Y @ X ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(tpp,definition,
% 0.23/0.52 ( tpp
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( pp @ X @ Y )
% 0.23/0.52 & ? [Z: reg] :
% 0.23/0.52 ( ( ec @ Z @ X )
% 0.23/0.52 & ( ec @ Z @ Y ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ntpp,definition,
% 0.23/0.52 ( ntpp
% 0.23/0.52 = ( ^ [X: reg,Y: reg] :
% 0.23/0.52 ( ( pp @ X @ Y )
% 0.23/0.52 & ~ ? [Z: reg] :
% 0.23/0.52 ( ( ec @ Z @ X )
% 0.23/0.52 & ( ec @ Z @ Y ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 thf(catalunya,type,
% 0.23/0.52 catalunya: reg ).
% 0.23/0.52
% 0.23/0.52 thf(france,type,
% 0.23/0.52 france: reg ).
% 0.23/0.52
% 0.23/0.52 thf(spain,type,
% 0.23/0.52 spain: reg ).
% 0.23/0.52
% 0.23/0.52 thf(paris,type,
% 0.23/0.52 paris: reg ).
% 0.23/0.52
% 0.23/0.52 thf(a,type,
% 0.23/0.52 a: $i > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(fool,type,
% 0.23/0.52 fool: $i > $i > $o ).
% 0.23/0.52
% 0.23/0.52 thf(t_axiom_for_fool,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mforall_prop
% 0.23/0.52 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(k_axiom_for_fool,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mforall_prop
% 0.23/0.52 @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(i_axiom_for_fool_a,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mforall_prop
% 0.23/0.52 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ax1,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mbox @ a
% 0.23/0.52 @ ^ [X: $i] : ( tpp @ catalunya @ spain ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ax2,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mbox @ fool
% 0.23/0.52 @ ^ [X: $i] : ( ec @ spain @ france ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ax3,axiom,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mbox @ a
% 0.23/0.52 @ ^ [X: $i] : ( ntpp @ paris @ france ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(con,conjecture,
% 0.23/0.52 ( mvalid
% 0.23/0.52 @ ( mbox @ a
% 0.23/0.52 @ ^ [X: $i] :
% 0.23/0.52 ? [Z: reg,Y: reg] :
% 0.23/0.52 ( ~ ( eq @ Z @ Y )
% 0.23/0.52 & ( o @ Z @ france )
% 0.23/0.52 & ( o @ Z @ france ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vQQfNBq6KC/cvc5---1.0.5_29041.p...
% 0.23/0.54 (declare-sort $$unsorted 0)
% 0.23/0.54 (declare-sort tptp.mu 0)
% 0.23/0.54 (declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
% 0.23/0.54 (declare-fun tptp.meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))
% 0.23/0.54 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
% 0.23/0.54 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
% 0.23/0.54 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
% 0.23/0.54 (declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
% 0.23/0.54 (declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ Phi P)) __flatten_var_0)))) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
% 0.23/0.54 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))
% 0.23/0.54 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
% 0.23/0.54 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.54 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))
% 0.23/0.54 (declare-fun tptp.mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))
% 0.23/0.54 (declare-fun tptp.msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))
% 0.23/0.54 (declare-fun tptp.mserial ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))
% 0.23/0.54 (declare-fun tptp.mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ (@ R T) U)) (@ _let_1 U)))))))
% 0.23/0.54 (declare-fun tptp.meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))
% 0.23/0.54 (declare-fun tptp.mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (= T U)))))))
% 0.23/0.54 (declare-fun tptp.mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))
% 0.23/0.54 (declare-fun tptp.mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (@ (@ R S) T) (exists ((U $$unsorted)) (and (@ (@ R S) U) (@ (@ R U) T))))))))
% 0.23/0.54 (declare-fun tptp.mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (or (@ (@ R T) U) (= T U) (@ (@ R U) T))))))))
% 0.23/0.54 (declare-fun tptp.mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))
% 0.23/0.54 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.54 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.54 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.54 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.54 (assert (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.54 (declare-sort tptp.reg 0)
% 0.23/0.54 (declare-fun tptp.c (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.dc (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.p (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.eq (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.o (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.po (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.ec (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.pp (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.tpp (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (declare-fun tptp.ntpp (tptp.reg tptp.reg) Bool)
% 0.23/0.54 (assert (forall ((X tptp.reg)) (@ (@ tptp.c X) X)))
% 0.23/0.54 (assert (forall ((X tptp.reg) (Y tptp.reg)) (=> (@ (@ tptp.c X) Y) (@ (@ tptp.c Y) X))))
% 30.55/30.82 (assert (= tptp.dc (lambda ((X tptp.reg) (Y tptp.reg)) (not (@ (@ tptp.c X) Y)))))
% 30.55/30.82 (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)))))))
% 30.55/30.82 (assert (= tptp.eq (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (@ (@ tptp.p Y) X)))))
% 30.55/30.82 (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)))))))
% 30.55/30.82 (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))))))
% 30.55/30.82 (assert (= tptp.ec (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.c X) Y) (not (@ (@ tptp.o X) Y))))))
% 30.55/30.82 (assert (= tptp.pp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (not (@ (@ tptp.p Y) X))))))
% 30.55/30.82 (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))))))))
% 30.55/30.82 (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)))))))))
% 30.55/30.82 (declare-fun tptp.catalunya () tptp.reg)
% 30.55/30.82 (declare-fun tptp.france () tptp.reg)
% 30.55/30.82 (declare-fun tptp.spain () tptp.reg)
% 30.55/30.82 (declare-fun tptp.paris () tptp.reg)
% 30.55/30.82 (declare-fun tptp.a ($$unsorted $$unsorted) Bool)
% 30.55/30.82 (declare-fun tptp.fool ($$unsorted $$unsorted) Bool)
% 30.55/30.82 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) A)) A) __flatten_var_0)))))
% 30.55/30.82 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (let ((_let_1 (@ tptp.mbox tptp.fool))) (let ((_let_2 (@ _let_1 A))) (@ (@ (@ tptp.mimplies _let_2) (@ _let_1 _let_2)) __flatten_var_0)))))))
% 30.55/30.82 (assert (@ tptp.mvalid (@ tptp.mforall_prop (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ (@ tptp.mbox tptp.fool) Phi)) (@ (@ tptp.mbox tptp.a) Phi)) __flatten_var_0)))))
% 30.55/30.82 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.a) (lambda ((X $$unsorted)) (@ (@ tptp.tpp tptp.catalunya) tptp.spain)))))
% 30.55/30.82 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (lambda ((X $$unsorted)) (@ (@ tptp.ec tptp.spain) tptp.france)))))
% 30.55/30.82 (assert (@ tptp.mvalid (@ (@ tptp.mbox tptp.a) (lambda ((X $$unsorted)) (@ (@ tptp.ntpp tptp.paris) tptp.france)))))
% 30.55/30.82 (assert (not (@ tptp.mvalid (@ (@ tptp.mbox tptp.a) (lambda ((X $$unsorted)) (exists ((Z tptp.reg) (Y tptp.reg)) (let ((_let_1 (@ (@ tptp.o Z) tptp.france))) (and (not (@ (@ tptp.eq Z) Y)) _let_1 _let_1))))))))
% 30.55/30.82 (set-info :filename cvc5---1.0.5_29041)
% 30.55/30.82 (check-sat-assuming ( true ))
% 30.55/30.82 ------- get file name : TPTP file name is GEG014^1
% 30.55/30.82 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29041.smt2...
% 30.55/30.82 --- Run --ho-elim --full-saturate-quant at 10...
% 30.55/30.82 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 30.55/30.82 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 30.55/30.82 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 30.55/30.82 % SZS status Theorem for GEG014^1
% 30.55/30.82 % SZS output start Proof for GEG014^1
% 30.55/30.82 (
% 30.55/30.82 (let ((_let_1 (@ tptp.mbox tptp.a))) (let ((_let_2 (not (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (exists ((Z tptp.reg) (Y tptp.reg)) (let ((_let_1 (@ (@ tptp.o Z) tptp.france))) (and (not (@ (@ tptp.eq Z) Y)) _let_1 _let_1))))))))) (let ((_let_3 (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (@ (@ tptp.tpp tptp.catalunya) tptp.spain)))))) (let ((_let_4 (= tptp.ntpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (not (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))))) (let ((_let_5 (= tptp.tpp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.pp X) Y) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.ec Z))) (and (@ _let_1 X) (@ _let_1 Y))))))))) (let ((_let_6 (= tptp.pp (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (not (@ (@ tptp.p Y) X))))))) (let ((_let_7 (= tptp.ec (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.c X) Y) (not (@ (@ tptp.o X) Y))))))) (let ((_let_8 (= tptp.po (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.o X) Y) (not (@ (@ tptp.p X) Y)) (not (@ (@ tptp.p Y) X))))))) (let ((_let_9 (= tptp.o (lambda ((X tptp.reg) (Y tptp.reg)) (exists ((Z tptp.reg)) (let ((_let_1 (@ tptp.p Z))) (and (@ _let_1 X) (@ _let_1 Y)))))))) (let ((_let_10 (= tptp.eq (lambda ((X tptp.reg) (Y tptp.reg)) (and (@ (@ tptp.p X) Y) (@ (@ tptp.p Y) X)))))) (let ((_let_11 (= tptp.p (lambda ((X tptp.reg) (Y tptp.reg)) (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (=> (@ _let_1 X) (@ _let_1 Y)))))))) (let ((_let_12 (= tptp.dc (lambda ((X tptp.reg) (Y tptp.reg)) (not (@ (@ tptp.c X) Y)))))) (let ((_let_13 (forall ((X tptp.reg) (Y tptp.reg)) (=> (@ (@ tptp.c X) Y) (@ (@ tptp.c Y) X))))) (let ((_let_14 (forall ((X tptp.reg)) (@ (@ tptp.c X) X)))) (let ((_let_15 (= tptp.mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_16 (= tptp.msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_17 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_18 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_19 (= tptp.mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (exists ((V $$unsorted)) (and (@ (@ R T) V) (@ (@ R U) V)))))))))) (let ((_let_20 (= tptp.mweakly_connected (lambda ((R (-> $$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_21 (= 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_22 (= tptp.mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (@ (@ R S) T) (forall ((U $$unsorted)) (=> (@ (@ R S) U) (= T U)))))))))) (let ((_let_23 (= tptp.mpartially_functional (lambda ((R (-> $$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_24 (= tptp.meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (@ R S))) (=> (and (@ _let_1 T) (@ _let_1 U)) (@ (@ R T) U)))))))) (let ((_let_25 (= tptp.mtransitive (lambda ((R (-> $$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_26 (= tptp.mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (@ (@ R S) T))))))) (let ((_let_27 (= tptp.msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (@ (@ R S) T) (@ (@ R T) S))))))) (let ((_let_28 (= tptp.mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (@ (@ R S) S)))))) (let ((_let_29 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mbox R) (@ tptp.mnot Phi))) __flatten_var_0))))) (let ((_let_30 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_31 (= tptp.mfalse (@ tptp.mnot tptp.mtrue)))) (let ((_let_32 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_33 (= tptp.mexists_prop (lambda ((Phi (-> (-> $$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_34 (= 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 $$unsorted)) (@ (@ tptp.mnot (@ Phi X)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_35 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_36 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_37 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_38 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimplies Phi) Psi)) (@ (@ tptp.mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_39 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_40 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_41 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ (@ tptp.mor (@ tptp.mnot Phi)) (@ tptp.mnot Psi))) __flatten_var_0))))) (let ((_let_42 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_43 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_44 (= tptp.meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (@ X W) (@ Y W)))))) (let ((_let_45 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) (let ((_let_46 (ho_3 k_2 tptp.catalunya))) (let ((_let_47 (ho_4 _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_48 (ho_4 _let_46 tptp.france))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47))) (let ((_let_51 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_52 (ho_4 _let_51 tptp.catalunya))) (let ((_let_53 (not _let_47))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (forall ((X tptp.reg) (Y tptp.reg)) (or (not (ho_4 (ho_3 k_2 X) Y)) (ho_4 (ho_3 k_2 Y) X))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X tptp.reg) (Y tptp.reg)) (or (not (@ (@ tptp.c X) Y)) (@ (@ tptp.c Y) X))) _let_55))))))) (let ((_let_57 (or (not (ho_4 _let_51 tptp.spain)) _let_52))) (let ((_let_58 (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 tptp.spain)) (ho_4 _let_1 tptp.catalunya)))))) (let ((_let_59 (not _let_57))) (let ((_let_60 (not _let_58))) (let ((_let_61 (and (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 tptp.catalunya)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 tptp.catalunya)))))))) (not (ho_4 _let_1 tptp.spain)) (not (forall ((Z tptp.reg)) (or (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 Z)) (ho_4 _let_1 tptp.spain)))))))))))) (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 tptp.catalunya)) (ho_4 _let_1 tptp.spain)))) _let_60))) (let ((_let_62 (forall ((W $$unsorted) (V $$unsorted)) (not (ho_5 (ho_7 k_8 W) V))))) (let ((_let_63 (forall ((Z tptp.reg) (Y tptp.reg) (BOUND_VARIABLE_2704 tptp.reg) (BOUND_VARIABLE_2696 tptp.reg) (BOUND_VARIABLE_2689 tptp.reg)) (let ((_let_1 (ho_3 k_2 BOUND_VARIABLE_2696))) (let ((_let_2 (ho_3 k_2 BOUND_VARIABLE_2689))) (or (and (or (not (ho_4 _let_2 Z)) (ho_4 _let_2 Y)) (or (not (ho_4 _let_1 Y)) (ho_4 _let_1 Z))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 BOUND_VARIABLE_2704)) (ho_4 _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (ho_3 k_2 Z))) (or (not (ho_4 _let_1 BOUND_VARIABLE_2704)) (ho_4 _let_1 tptp.france))))))))))) (let ((_let_64 (forall ((W $$unsorted) (V $$unsorted)) (not (@ (@ tptp.a W) V))))) (let ((_let_65 (ASSUME :args (_let_45)))) (let ((_let_66 (ASSUME :args (_let_44)))) (let ((_let_67 (ASSUME :args (_let_43)))) (let ((_let_68 (ASSUME :args (_let_42)))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_68 _let_67 _let_66 _let_65) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (ASSUME :args (_let_36)))) (let ((_let_75 (ASSUME :args (_let_35)))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (ASSUME :args (_let_30)))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (ASSUME :args (_let_28)))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (ASSUME :args (_let_18)))) (let ((_let_93 (ASSUME :args (_let_17)))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (ASSUME :args (_let_12)))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_10)) (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) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (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_98 _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) :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_100 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_99 _let_98 _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) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_100 _let_99 _let_98 _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) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_101 _let_100 _let_99 _let_98 _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) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (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_102 _let_101 _let_100 _let_99 _let_98 _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) :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_104 (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_103 _let_102 _let_101 _let_100 _let_99 _let_98 _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) :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_103 _let_102 _let_101 _let_100 _let_99 _let_98 _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 ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_104 :args ((not (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (not (forall ((Z tptp.reg) (Y tptp.reg)) (or (@ (@ tptp.eq Z) Y) (not (@ (@ tptp.o Z) tptp.france))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (not (forall ((Z tptp.reg) (Y tptp.reg) (BOUND_VARIABLE_2704 tptp.reg) (BOUND_VARIABLE_2696 tptp.reg) (BOUND_VARIABLE_2689 tptp.reg)) (let ((_let_1 (@ tptp.c BOUND_VARIABLE_2696))) (let ((_let_2 (@ tptp.c BOUND_VARIABLE_2689))) (or (and (or (not (@ _let_2 Z)) (@ _let_2 Y)) (or (not (@ _let_1 Y)) (@ _let_1 Z))) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 BOUND_VARIABLE_2704)) (@ _let_1 Z))))) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 BOUND_VARIABLE_2704)) (@ _let_1 tptp.france)))))))))) _let_64)) (not (or (not _let_63) _let_62))))))))) (let ((_let_106 (_let_60))) (let ((_let_107 (and _let_50 (or _let_53 _let_48)))) (let ((_let_108 (NOT_NOT_ELIM (NOT_OR_ELIM _let_105 :args (0))))) (let ((_let_109 (_let_63))) (let ((_let_110 (ASSUME :args _let_109))) (let ((_let_111 (ho_4 _let_46 tptp.catalunya))) (let ((_let_112 (not _let_111))) (let ((_let_113 (or _let_112 _let_48))) (let ((_let_114 (and (or _let_49 _let_111) _let_113))) (let ((_let_115 (forall ((X tptp.reg)) (ho_4 (ho_3 k_2 X) X)))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_14)) (PREPROCESS :args ((= _let_14 _let_115)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_47 _let_49 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_112 _let_48 (not _let_113)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (tptp.catalunya QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_115))) _let_116 :args (_let_111 false _let_115)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_114 1)) :args ((or _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_110 :args (tptp.france tptp.catalunya tptp.france tptp.catalunya tptp.catalunya QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_109))) _let_108 :args (_let_114 false _let_63)) :args (_let_113 false _let_114)) :args (_let_48 false _let_111 false _let_113)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_107 0)) :args ((or _let_50 (not _let_107)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_110 :args (tptp.france SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.france tptp.catalunya tptp.catalunya QUANTIFIERS_INST_FMF_FMC_EXH)) :args _let_109))) _let_108 :args (_let_107 false _let_63)) :args (_let_50 false _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_52 _let_53 (not _let_54)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 1)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_58))) (REFL :args (_let_59)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_61 2)) :args ((or _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_104 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (and (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 tptp.catalunya)) (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 tptp.catalunya)))))))) (not (@ _let_1 tptp.spain)) (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 tptp.spain)))))))))))) (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 tptp.catalunya)) (@ _let_1 tptp.spain)))) (not (forall ((Z tptp.reg)) (let ((_let_1 (@ tptp.c Z))) (or (not (@ _let_1 tptp.spain)) (@ _let_1 tptp.catalunya)))))) _let_64) (or _let_61 _let_62)))))) :args ((or _let_62 _let_61))) (NOT_OR_ELIM _let_105 :args (1)) :args (_let_61 true _let_62)) :args (_let_60 false _let_61)) :args (_let_59 true _let_58)) :args ((not _let_52) true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.catalunya SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_53 true _let_52 false _let_54)) :args (false false _let_48 false _let_50 true _let_47)) :args (_let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _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)))) _let_3 (@ tptp.mvalid (@ (@ tptp.mbox tptp.fool) (lambda ((X $$unsorted)) (@ (@ tptp.ec tptp.spain) tptp.france)))) (@ tptp.mvalid (@ _let_1 (lambda ((X $$unsorted)) (@ (@ tptp.ntpp tptp.paris) tptp.france)))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.55/30.82 )
% 30.55/30.82 % SZS output end Proof for GEG014^1
% 30.55/30.82 % cvc5---1.0.5 exiting
% 30.55/30.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------