TSTP Solution File: SYO003^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO003^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : Fri Sep 1 04:44:39 EDT 2023
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_leibeq,definition,
( leibeq
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X3 @ X1 )
@ ( X3 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i,X3: $i > $o] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ( X3 @ X1 ) )
=> ( X3 @ X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i > $o] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ( X3 @ X1 ) )
=> ( X3 @ X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i > $o] :
( ~ ( ! [X3: $i > $o] :
( ( X3 @ eigen__0 )
=> ( X3 @ X1 ) )
=> ~ ( X2 @ eigen__0 ) )
=> ( X2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o] :
( ~ ( sP2
=> ~ ( X1 @ eigen__0 ) )
=> ( X1 @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP2
=> ~ sP1 )
=> sP3 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP2
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h6,assumption,
sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,h6,h7,h5]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,3,h6,h7]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,4,h4,h5]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,5,h3]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,6,h2]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i > $o] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ( X3 @ X1 ) )
=> ( X3 @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO003^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n004.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Aug 26 06:08:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % Mode: cade22grackle2xfee4
% 0.20/0.38 % Steps: 6
% 0.20/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------