TSTP Solution File: SEV222^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 19:33:01 EDT 2023
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cZ,type,
cZ: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a > $o ).
thf(ty_cW,type,
cW: ( a > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__1
= ( ^ [X1: a] :
( ~ ( cZ @ X1 )
=> ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cW @ eigen__2 )
=> ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cZ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( ~ ( cZ @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ( ( ^ [X2: a] :
( ~ ( cZ @ X2 )
=> ( eigen__5 @ X2 ) ) )
!= ( ^ [X2: a] :
( ~ ( cZ @ X2 )
=> ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> ( eigen__5 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> ( eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cW @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1 @ eigen__0 )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cW @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP5
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
( ~ ( cZ @ X3 )
=> ( X2 @ X3 ) ) ) ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM60_pme,conjecture,
! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X2 @ X1 ) )
=> ( cZ @ X1 ) )
= ( ! [X2: a > $o] :
( ~ ! [X3: a > $o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
( ~ ( cZ @ X4 )
=> ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X2 @ X1 ) )
=> ( cZ @ X1 ) )
= ( ! [X2: a > $o] :
( ~ ! [X3: a > $o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
( ~ ( cZ @ X4 )
=> ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM60_pme]) ).
thf(h1,assumption,
sP16 != sP15,
introduced(assumption,[]) ).
thf(h2,assumption,
sP16,
introduced(assumption,[]) ).
thf(h3,assumption,
sP15,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
( ~ ( cZ @ X2 )
=> ( X1 @ X2 ) ) ) ) )
=> sP12 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__1
!= ( ^ [X2: a] :
( ~ ( cZ @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP11
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP11,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP11
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP8
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP16
| sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h2,h10,h11,h8]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,9,h10,h11]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,10,h9]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,11,h7,h8]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,12,h6]) ).
thf(h12,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP9
=> sP13 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP9,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(14,plain,
( ~ sP5
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP6
| sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP14
| sP5
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP15
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h4,h5,h1,h0])],[14,15,16,17,h15,h16,h13,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,18,h15,h16]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h12,19,h14]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,20,h12,h13]) ).
thf(22,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,13,21,h2,h3,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).
thf(0,theorem,
! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X2 @ X1 ) )
=> ( cZ @ X1 ) )
= ( ! [X2: a > $o] :
( ~ ! [X3: a > $o] :
( ( cW @ X3 )
=> ( X2
!= ( ^ [X4: a] :
( ~ ( cZ @ X4 )
=> ( X3 @ X4 ) ) ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 02:35:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 % Mode: cade22grackle2xfee4
% 0.20/0.55 % Steps: 3393
% 0.20/0.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------