TSTP Solution File: SWV427^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWV427^2 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 22:49:10 EDT 2023
% Result : Theorem 20.20s 20.46s
% Output : Proof 20.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_a,type,
a: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_rel,type,
rel: $i > $i > $o ).
thf(ty_s,type,
s: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( rel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( rel @ eigen__1 @ eigen__2 )
=> ( ~ ( a @ eigen__2 )
=> ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( a @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( s @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( a @ eigen__2 )
=> ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( rel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( rel @ eigen__2 @ X2 ) )
=> ( rel @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( s @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( a @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( s @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP8
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( rel @ eigen__3 @ X1 )
=> ( s @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $o,X2: $i] :
( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ( s @ X1 ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( rel @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP11
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP15
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( rel @ eigen__2 @ X1 )
=> ( s @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) )
=> ( s @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(def_mfalse,definition,
( mfalse
= ( ^ [X1: $i] : $false ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
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,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimpl,definition,
( mimpl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_miff,definition,
( miff
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i] :
( ( X1 @ X3 @ X4 )
& ( X2 @ X4 ) ) ) ) ).
thf(def_mall,definition,
( mall
= ( ^ [X1: individuals > $i > $o,X2: $i] :
! [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists,definition,
( mexists
= ( ^ [X1: individuals > $i > $o,X2: $i] :
? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [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_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_icl_atom,definition,
( icl_atom
= ( ^ [X1: $i > $o] : ( mbox @ rel @ X1 ) ) ) ).
thf(def_icl_princ,definition,
( icl_princ
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_icl_and,definition,
( icl_and
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_icl_or,definition,
( icl_or
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).
thf(def_icl_impl,definition,
( icl_impl
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mimpl @ X1 @ X2 ) ) ) ) ).
thf(def_icl_true,definition,
icl_true = mtrue ).
thf(def_icl_false,definition,
icl_false = mfalse ).
thf(def_icl_says,definition,
( icl_says
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mor @ X1 @ X2 ) ) ) ) ).
thf(def_iclval,definition,
( iclval
= ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).
thf(idem,conjecture,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( ~ ( a @ X4 )
=> ! [X5: $i] :
( ( rel @ X4 @ X5 )
=> ( s @ X5 ) ) ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( s @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( ~ ( a @ X4 )
=> ! [X5: $i] :
( ( rel @ X4 @ X5 )
=> ( s @ X5 ) ) ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( s @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[idem]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( rel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( a @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( s @ X4 ) ) ) ) ) )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ~ ( a @ X2 )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( s @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ( rel @ eigen__0 @ eigen__1 )
=> ( sP4
=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
rel @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( rel @ eigen__1 @ X1 )
=> ( ~ ( a @ X1 )
=> ! [X2: $i] :
( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP18
=> sP7 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP18,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP1
=> sP12 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP11
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP1
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| ~ sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP20
| ~ sP15
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| ~ sP21
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP19
| sP11
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP22
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP3
| ~ sP18
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(refl_axiom,axiom,
sP16 ).
thf(trans_axiom,axiom,
sP2 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,refl_axiom,trans_axiom,h5,h8,h10,h13,h14]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,17,h13,h14]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,18,h12]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,19,h10,h11]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,24,h2]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,25,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( ~ ( a @ X4 )
=> ! [X5: $i] :
( ( rel @ X4 @ X5 )
=> ( s @ X5 ) ) ) ) ) )
=> ! [X3: $i] :
( ( rel @ X2 @ X3 )
=> ( ~ ( a @ X3 )
=> ! [X4: $i] :
( ( rel @ X3 @ X4 )
=> ( s @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV427^2 : TPTP v8.1.2. Released v3.6.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 : Tue Aug 29 07:16:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.20/20.46 % SZS status Theorem
% 20.20/20.46 % Mode: cade22grackle2x798d
% 20.20/20.46 % Steps: 383
% 20.20/20.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------