TSTP Solution File: SEV061^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV061^5 : 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 : n023.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 19:32:29 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_eigen__2,type,
eigen__2: b > a > $o ).
thf(ty_eigen__3,type,
eigen__3: b > a > $o ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__4 = eigen__0 )
=> ( eigen__5 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__3 @ eigen__4 @ X1 )
=> ( ~ ( eigen__2 @ eigen__4 @ X1 )
=> ~ ( ( eigen__4 = eigen__0 )
=> ( X1 != eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( eigen__2 @ eigen__4 @ eigen__5 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__3 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: b,X2: a] :
( ( eigen__3 @ X1 @ X2 )
=> ( ~ ( eigen__2 @ X1 @ X2 )
=> ~ ( ( X1 = eigen__0 )
=> ( X2 != eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cTHM176_pme,conjecture,
! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ! [X5: b,X6: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) )
=> ( X3 @ X5 @ X6 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ! [X5: b,X6: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) )
=> ( X3 @ X5 @ X6 ) ) ),
inference(assume_negation,[status(cth)],[cTHM176_pme]) ).
thf(h1,assumption,
~ ! [X1: a,X2: b > a > $o,X3: b > a > $o] :
( ! [X4: b,X5: a] :
( ( X3 @ X4 @ X5 )
=> ( ~ ( X2 @ X4 @ X5 )
=> ~ ( ( X4 = eigen__0 )
=> ( X5 != X1 ) ) ) )
=> ! [X4: b,X5: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( ( X4 = eigen__0 )
=> ( X5 != X1 ) ) )
=> ( X2 @ X4 @ X5 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: b > a > $o,X2: b > a > $o] :
( ! [X3: b,X4: a] :
( ( X2 @ X3 @ X4 )
=> ( ~ ( X1 @ X3 @ X4 )
=> ~ ( ( X3 = eigen__0 )
=> ( X4 != eigen__1 ) ) ) )
=> ! [X3: b,X4: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( ( X3 = eigen__0 )
=> ( X4 != eigen__1 ) ) )
=> ( X1 @ X3 @ X4 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: b > a > $o] :
( ! [X2: b,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( ~ ( eigen__2 @ X2 @ X3 )
=> ~ ( ( X2 = eigen__0 )
=> ( X3 != eigen__1 ) ) ) )
=> ! [X2: b,X3: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( ( X2 = eigen__0 )
=> ( X3 != eigen__1 ) ) )
=> ( eigen__2 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP7
=> ! [X1: b,X2: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( ( X1 = eigen__0 )
=> ( X2 != eigen__1 ) ) )
=> ( eigen__2 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP7,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b,X2: a] :
( ~ ( ( eigen__3 @ X1 @ X2 )
=> ~ ( ( X1 = eigen__0 )
=> ( X2 != eigen__1 ) ) )
=> ( eigen__2 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a] :
( ~ ( ( eigen__3 @ eigen__4 @ X1 )
=> ~ ( ( eigen__4 = eigen__0 )
=> ( X1 != eigen__1 ) ) )
=> ( eigen__2 @ eigen__4 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP4
=> ~ sP1 )
=> sP5 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP4
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
sP4,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,h5,h11,h12,h10]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,5,h11,h12]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,6,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__5)],[h7,7,h8]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__4)],[h6,8,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,9,h5,h6]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,10,h4]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1]) ).
thf(0,theorem,
! [X1: b,X2: a,X3: b > a > $o,X4: b > a > $o] :
( ! [X5: b,X6: a] :
( ( X4 @ X5 @ X6 )
=> ( ~ ( X3 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) ) )
=> ! [X5: b,X6: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( ( X5 = X1 )
=> ( X6 != X2 ) ) )
=> ( X3 @ X5 @ X6 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n023.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
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 02:18:42 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % Mode: cade22grackle2xfee4
% 0.21/0.42 % Steps: 13
% 0.21/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------