TSTP Solution File: LCL706^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL706^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:04:39 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 71
% Syntax : Number of formulae : 83 ( 46 unt; 5 typ; 32 def)
% Number of atoms : 193 ( 37 equ; 4 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 373 ( 39 ~; 17 |; 8 &; 235 @)
% ( 13 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 51 usr; 52 con; 0-2 aty)
% Number of variables : 156 ( 66 ^; 84 !; 6 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ~ ( eigen__0 @ eigen__7 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ! [X1: $i] :
( ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__7 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
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(conj,conjecture,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) )
=> ! [X2: $i,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) )
=> ! [X2: $i,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ( sP12
=> ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP12,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ! [X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ! [X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP10
=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP10,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| ~ sP7
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(8,plain,
( ~ sP9
| ~ sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h3,h7,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,11,h10,h11]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,12,h9]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,15,h5]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,17,h2]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) )
=> ! [X2: $i,X3: $i > $o] :
( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL706^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 22:38:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22grackle2xfee4
% 0.19/0.43 % Steps: 385
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------