TSTP Solution File: SEV067^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV067^5 : 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 : n028.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 19:32:30 EDT 2023
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cS,type,
cS: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_cT,type,
cT: a > $o ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(sP1,plain,
( sP1
<=> ( cT @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cR @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a] :
( ~ ( cR @ X1 @ X2 )
=> ( cR @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cR @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ~ ( cS @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ~ ( ( cR @ eigen__0 @ X1 )
=> ~ ( cT @ X1 ) )
=> ( cT @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cT @ X2 ) )
=> ( cT @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cS @ X2 ) )
=> ( cS @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cT @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cS @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP5
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ~ ( ( cR @ eigen__1 @ X1 )
=> ~ ( cS @ X1 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ~ ( cR @ eigen__1 @ X1 )
=> ( cR @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cS @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP8
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM553_pme,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ sP7 )
=> ( ~ ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) )
=> ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ sP7 )
=> ( ~ ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) )
=> ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM553_pme]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) )
=> ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP9,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP3,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a] : ( cR @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP16
=> sP11 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP16,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP1
=> sP12 ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP1,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| sP8
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,h8,h6,h4,h16,h17,h19,h20]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,12,h19,h20]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__1)],[h14,13,h18]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,14,h16,h17]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__0)],[h13,15,h15]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h2,16,h13,h14]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,17,h11,h12]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,19,h7,h8]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,20,h5,h6]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,21,h3,h4]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,22,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X3 ) )
=> ( cR @ X1 @ X3 ) )
=> ~ ! [X1: a] : ( cR @ X1 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
=> ~ sP3 )
=> ~ sP9 )
=> ~ sP7 )
=> ( ~ ! [X1: a] :
( ( cS @ X1 )
=> ( cT @ X1 ) )
=> ! [X1: a] :
( ( cT @ X1 )
=> ( cS @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV067^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 04:16:04 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22grackle2xfee4
% 0.20/0.42 % Steps: 68
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------