TSTP Solution File: SEV221^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV221^5 : 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 : n014.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 0.19s 0.43s
% Output : Proof 0.19s
% 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__12,type,
eigen__12: a > $o ).
thf(ty_cW,type,
cW: ( a > $o ) > $o ).
thf(ty_eigen__11,type,
eigen__11: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(sP1,plain,
( sP1
<=> ( cZ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ( ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( eigen__1 @ X2 ) ) )
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__12 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ~ ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cW @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__11 @ eigen__0 )
= ( ~ ( sP1
=> ~ sP3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
( ( cW @ X1 )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__11 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o] :
( ~ ! [X2: a > $o] :
( ( cW @ X2 )
=> ( X1
!= ( ^ [X3: a] :
~ ( ( cZ @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) )
=> ~ ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( eigen__11 @ X1 )
= ( ~ ( ( cZ @ X1 )
=> ~ ( eigen__12 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cW @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__11
= ( ^ [X1: a] :
~ ( ( cZ @ X1 )
=> ~ ( eigen__12 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM61_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)],[cTHM61_pme]) ).
thf(h1,assumption,
( ~ sP5 != ~ sP13 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h4,assumption,
sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP16
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP16,
introduced(assumption,[]) ).
thf(h10,assumption,
sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP1
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h2,h3,h1,h0])],[1,2,3,4,h9,h10,h7,h3]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,5,h9,h10]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,6,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h2,7,h6,h7]) ).
thf(h11,assumption,
~ ( ~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__11
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: a > $o] :
( ( cW @ X1 )
=> ( eigen__11
!= ( ^ [X2: a] :
~ ( ( cZ @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP7
=> ~ sP17 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP7,
introduced(assumption,[]) ).
thf(h16,assumption,
sP17,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP9
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP15
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP15
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| ~ sP11
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h4,h5,h1,h0])],[9,10,11,12,13,14,15,16,h4,h15,h16,h13]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,17,h15,h16]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__12)],[h12,18,h14]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h4,h5,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,19,h12,h13]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__11)],[h5,20,h11]) ).
thf(22,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,8,21,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
% 0.00/0.12 % Problem : SEV221^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 03:04:19 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: 581
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------