TSTP Solution File: SYO006^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO006^1 : 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 04:44:40 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(sP1,plain,
( sP1
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP1
=> ~ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o] :
( ( X1 @ sP1 )
=> ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_leibeq,definition,
( leibeq
= ( ^ [X1: $o,X2: $o] :
! [X3: $o > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X3 @ X1 )
@ ( X3 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $o,X2: $o] :
( ! [X3: $o > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ( X1 = X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $o,X2: $o] :
( ! [X3: $o > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ( X1 = X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $o] :
( ! [X2: $o > $o] :
( ( X2 @ sP1 )
=> ( X2 @ X1 ) )
=> ( sP1 = X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP4
=> ( sP1 = sP5 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1 != sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP5,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0])],[1,2,h3,h5,h6]) ).
thf(4,plain,
( ~ sP3
| sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0])],[4,5,h3,h7,h8]) ).
thf(7,plain,
$false,
inference(tab_be,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,3,6,h5,h6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: $o,X2: $o] :
( ! [X3: $o > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ( X1 = X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO006^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.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 08:21:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 64
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------