TSTP Solution File: SEV282^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 19:33:13 EDT 2023
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: ( ( $i > $o ) > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
( (~)
@ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ( X1
@ ^ [X4: $i] :
( ( (~) @ ( X4 = X3 ) )
& ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cNAT,definition,
( cNAT
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( ( X2 @ cZERO )
& ! [X3: ( $i > $o ) > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( X2 @ ( cSUCC @ X3 ) ) ) )
@ ( X2 @ X1 ) ) ) ) ).
thf(cTTTP6100,conjecture,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTTTP6100]) ).
thf(h1,assumption,
~ ( ~ ( sP1
=> ~ ! [X1: ( $i > $o ) > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP1
=> ~ ! [X1: ( $i > $o ) > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: ( $i > $o ) > $o] :
( ( eigen__0 @ X1 )
=> ( eigen__0
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[h4,h3]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,1,h4,h5]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,2,h2,h3]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).
thf(0,theorem,
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:13:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % Mode: cade22grackle2xfee4
% 0.21/0.40 % Steps: 0
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------