%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GEG007^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:27:35 PM UTC 2025
% Result : Theorem 20.24s 20.56s
% Output : Proof 20.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 110
% Syntax : Number of formulae : 121 ( 57 unt; 0 typ; 42 def)
% Number of atoms : 420 ( 47 equ; 10 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 843 ( 114 ~; 36 |; 18 &; 497 @)
% ( 31 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 85 usr; 85 con; 0-2 aty)
% Number of variables : 232 ( 87 ^; 136 !; 9 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_reg,type,
reg: $tType ).
thf(ty_spain,type,
spain: reg ).
thf(ty_catalunya,type,
catalunya: reg ).
thf(ty_paris,type,
paris: reg ).
thf(ty_a,type,
a: $i > $i > $o ).
thf(ty_c,type,
c: reg > reg > $o ).
thf(ty_eigen__11,type,
eigen__11: reg ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_france,type,
france: reg ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_fool,type,
fool: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: reg > $o,X2: reg] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: reg] :
~ ( ( c @ X1 @ paris )
=> ( c @ X1 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__1
@ ^ [X1: $i] :
~ ~ ( fool @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( fool @ eigen__0 @ X1 )
=> ~ ( ( c @ spain @ france )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ spain ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ france ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( a @ eigen__0 @ eigen__1 )
=> ~ ( ~ ( ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ france ) )
=> ! [X1: reg] :
( ( c @ X1 @ france )
=> ( c @ X1 @ paris ) ) )
=> ~ ! [X1: reg] :
( ~ ( ( c @ X1 @ paris )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ paris ) ) ) )
=> ( ( c @ X1 @ france )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ france ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ spain ) )
=> ~ ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( fool @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( fool @ X1 @ X2 )
=> ~ ( ( c @ spain @ france )
=> ~ ! [X3: reg] :
( ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ spain ) )
=> ~ ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ france ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( c @ eigen__11 @ paris )
=> ( c @ eigen__11 @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( c @ eigen__11 @ catalunya )
=> ( c @ eigen__11 @ spain ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: reg] :
( ( c @ X1 @ catalunya )
=> ( c @ X1 @ spain ) )
=> ! [X1: reg] :
( ( c @ X1 @ spain )
=> ( c @ X1 @ catalunya ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( fool @ eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( a @ X1 @ X2 )
=> ~ ( ~ sP8
=> ! [X3: reg] :
( ~ ( ( c @ X3 @ catalunya )
=> ~ ! [X4: reg] :
( ! [X5: reg] :
( ( c @ X5 @ X4 )
=> ( c @ X5 @ X3 ) )
=> ~ ! [X5: reg] :
( ( c @ X5 @ X4 )
=> ( c @ X5 @ catalunya ) ) ) )
=> ( ( c @ X3 @ spain )
=> ~ ! [X4: reg] :
( ! [X5: reg] :
( ( c @ X5 @ X4 )
=> ( c @ X5 @ X3 ) )
=> ~ ! [X5: reg] :
( ( c @ X5 @ X4 )
=> ( c @ X5 @ spain ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ spain ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP9
=> ~ ( ( c @ spain @ france )
=> ~ ! [X1: reg] :
( ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
=> ~ ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ france ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( c @ eigen__11 @ paris )
=> ( c @ eigen__11 @ spain ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( a @ eigen__0 @ eigen__1 )
=> ~ ( ~ sP8
=> ! [X1: reg] :
( ~ ( ( c @ X1 @ catalunya )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ catalunya ) ) ) )
=> ( ( c @ X1 @ spain )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ spain ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( c @ eigen__11 @ spain ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( c @ eigen__11 @ paris ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( c @ eigen__11 @ catalunya ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( fool @ X1 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP8
=> ! [X1: reg] :
( ~ ( ( c @ X1 @ catalunya )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ catalunya ) ) ) )
=> ( ( c @ X1 @ spain )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ spain ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( a @ eigen__0 @ X1 )
=> ~ ( ~ ( ! [X2: reg] :
( ( c @ X2 @ paris )
=> ( c @ X2 @ france ) )
=> ! [X2: reg] :
( ( c @ X2 @ france )
=> ( c @ X2 @ paris ) ) )
=> ~ ! [X2: reg] :
( ~ ( ( c @ X2 @ paris )
=> ~ ! [X3: reg] :
( ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ X2 ) )
=> ~ ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ paris ) ) ) )
=> ( ( c @ X2 @ france )
=> ~ ! [X3: reg] :
( ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ X2 ) )
=> ~ ! [X4: reg] :
( ( c @ X4 @ X3 )
=> ( c @ X4 @ france ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( a @ eigen__0 @ X1 )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( a @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ france ) )
=> ! [X1: reg] :
( ( c @ X1 @ france )
=> ( c @ X1 @ paris ) ) )
=> ~ ! [X1: reg] :
( ~ ( ( c @ X1 @ paris )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ paris ) ) ) )
=> ( ( c @ X1 @ france )
=> ~ ! [X2: reg] :
( ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) )
=> ~ ! [X3: reg] :
( ( c @ X3 @ X2 )
=> ( c @ X3 @ france ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( c @ spain @ france )
=> ~ ! [X1: reg] :
( ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
=> ~ ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ france ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: reg] :
( ( c @ X1 @ catalunya )
=> ( c @ X1 @ spain ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( fool @ eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ france ) )
=> ! [X1: reg] :
( ( c @ X1 @ france )
=> ( c @ X1 @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i] :
( ( a @ X1 @ X2 )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: reg] :
( ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
=> ~ ! [X2: reg] :
( ( c @ X2 @ X1 )
=> ( c @ X2 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: reg] :
( ( c @ X1 @ paris )
=> ( c @ X1 @ france ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X3 )
@ ? [X5: $i] :
( ( X1 @ X2 @ X5 )
& ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( ( X1 @ X3 @ X4 )
| ( X3 = X4 )
| ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_dc,definition,
( dc
= ( ^ [X1: reg,X2: reg] : ( (~) @ ( c @ X1 @ X2 ) ) ) ) ).
thf(def_p,definition,
( p
= ( ^ [X1: reg,X2: reg] :
! [X3: reg] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( c @ X3 @ X1 )
@ ( c @ X3 @ X2 ) ) ) ) ).
thf(def_eq,definition,
( eq
= ( ^ [X1: reg,X2: reg] :
( ( p @ X1 @ X2 )
& ( p @ X2 @ X1 ) ) ) ) ).
thf(def_o,definition,
( o
= ( ^ [X1: reg,X2: reg] :
? [X3: reg] :
( ( p @ X3 @ X1 )
& ( p @ X3 @ X2 ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: reg,X2: reg] :
( ( o @ X1 @ X2 )
& ( (~) @ ( p @ X1 @ X2 ) )
& ( (~) @ ( p @ X2 @ X1 ) ) ) ) ) ).
thf(def_ec,definition,
( ec
= ( ^ [X1: reg,X2: reg] :
( ( c @ X1 @ X2 )
& ( (~) @ ( o @ X1 @ X2 ) ) ) ) ) ).
thf(def_pp,definition,
( pp
= ( ^ [X1: reg,X2: reg] :
( ( p @ X1 @ X2 )
& ( (~) @ ( p @ X2 @ X1 ) ) ) ) ) ).
thf(def_tpp,definition,
( tpp
= ( ^ [X1: reg,X2: reg] :
( ( pp @ X1 @ X2 )
& ? [X3: reg] :
( ( ec @ X3 @ X1 )
& ( ec @ X3 @ X2 ) ) ) ) ) ).
thf(def_ntpp,definition,
( ntpp
= ( ^ [X1: reg,X2: reg] :
( ( pp @ X1 @ X2 )
& ( (~)
@ ? [X3: reg] :
( ( ec @ X3 @ X1 )
& ( ec @ X3 @ X2 ) ) ) ) ) ) ).
thf(con,conjecture,
! [X1: $i,X2: $i] :
( ( a @ X1 @ X2 )
=> ( ! [X3: reg] :
( ( c @ X3 @ catalunya )
=> ( c @ X3 @ paris ) )
=> ~ sP25 ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( a @ X1 @ X2 )
=> ( ! [X3: reg] :
( ( c @ X3 @ catalunya )
=> ( c @ X3 @ paris ) )
=> ~ sP25 ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( a @ eigen__0 @ X1 )
=> ( ! [X2: reg] :
( ( c @ X2 @ catalunya )
=> ( c @ X2 @ paris ) )
=> ~ sP25 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP22
=> ( ! [X1: reg] :
( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) )
=> ~ sP25 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP22,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ! [X1: reg] :
( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) )
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: reg] :
( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP16
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| ~ sP17
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP25
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP26
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP12
| ~ sP9
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( sP13
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP13
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP11
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(10,plain,
( ~ sP3
| ~ sP11
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP4
| sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__6]) ).
thf(12,plain,
( sP8
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP30
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( sP28
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP27
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( sP19
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP24
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP23
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP14
| ~ sP22
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP2
| ~ sP22
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP18
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP10
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP29
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(t_axiom_for_fool,axiom,
sP18 ).
thf(ax1,axiom,
sP10 ).
thf(ax2,axiom,
sP5 ).
thf(ax3,axiom,
sP29 ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,t_axiom_for_fool,ax1,ax2,ax3,h5,h8]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,27,h7,h8]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,28,h5,h6]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,29,h4]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,30,h3]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[31,h1]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[32,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( a @ X1 @ X2 )
=> ( ! [X3: reg] :
( ( c @ X3 @ catalunya )
=> ( c @ X3 @ paris ) )
=> ~ sP25 ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[31,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEG007^1 : TPTP v9.2.0. Released v4.1.0.
% 0.10/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 8 12:30:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 20.24/20.56 % SZS status Theorem
% 20.24/20.56 % Mode: cade22grackle2x798d
% 20.24/20.56 % Steps: 1927
% 20.24/20.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------