TSTP Solution File: SYO001^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO001^1 : 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 : n029.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 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
=> ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o] :
( ( X1 @ eigen__1 )
=> ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
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] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ! [X4: $i > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X3 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ! [X4: $i > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ! [X3: $i > $o] :
( ( X3 @ eigen__0 )
=> ( X3 @ X1 ) )
=> ~ ! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ! [X3: $i > $o] :
( ( X3 @ eigen__0 )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ~ ( sP7
=> ~ ! [X2: $i > $o] :
( ( X2 @ eigen__1 )
=> ( X2 @ X1 ) ) )
=> ! [X2: $i > $o] :
( ( X2 @ eigen__0 )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP7
=> ~ sP5 )
=> ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP7
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,h6,h7,h9,h10]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,5,h9,h10]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,6,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,7,h6,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,9,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,10,h2]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ~ ! [X4: $i > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) )
=> ! [X4: $i > $o] :
( ( X4 @ X1 )
=> ( X4 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO001^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 06:19:09 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % Mode: cade22grackle2xfee4
% 0.17/0.39 % Steps: 10
% 0.17/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------