TSTP Solution File: SYO277^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO277^5 : 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 : 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 04:46:07 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] : ( eigen__2 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $i > $o] :
( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ( X1 @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__2 @ eigen__0 @ eigen__0 )
=> ( eigen__2 @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM47D,conjecture,
! [X1: $i,X2: $i] :
( ( ! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
= ( ! [X3: $i > $i > $o] :
( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ( X3 @ X1 @ X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( ! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
= ( ! [X3: $i > $i > $o] :
( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ( X3 @ X1 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM47D]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ( ! [X2: $i > $o] :
( ( X2 @ eigen__0 )
=> ( X2 @ X1 ) ) )
= ( ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP6 != sP3,
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h3,h4,h2,h1,h0])],[1,2,3,h3,h8,h9]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,4,h8,h9]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h4,5,h7]) ).
thf(h10,assumption,
~ ( sP8
=> sP5 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP8,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP5
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h5,h6,h2,h1,h0])],[7,8,h11,h12,h6]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,9,h11,h12]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h5,10,h10]) ).
thf(12,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,6,11,h3,h4,h5,h6]) ).
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: $i,X2: $i] :
( ( ! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
= ( ! [X3: $i > $i > $o] :
( ! [X4: $i] : ( X3 @ X4 @ X4 )
=> ( X3 @ X1 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO277^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 04:43:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: cade22grackle2xfee4
% 0.20/0.40 % Steps: 423
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------