TSTP Solution File: PUZ103^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PUZ103^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : 600s
% DateTime : Mon Jul 18 18:26:03 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c1,type,
c1: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ( eigen__1 @ ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( eigen__1 @ c1 )
=> ~ sP1 )
=> ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( eigen__1 @ ( s @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 @ c1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ c1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 @ ( s @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] :
( ~ ( ( X1 @ c1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_cCKB6_NUM,definition,
( cCKB6_NUM
= ( ^ [X1: $i] :
! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(cCKB6_L3000,conjecture,
! [X1: $i] :
( ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ ( s @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ ( s @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cCKB6_L3000]) ).
thf(h1,assumption,
~ ( sP8
=> ! [X1: $i > $o] :
( ~ ( ( X1 @ c1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ ( s @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP8,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o] :
( ~ ( ( X1 @ c1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( s @ X2 ) ) ) )
=> ( X1 @ ( s @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ sP5
=> sP7 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| ~ sP3
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,h2,h7,h8,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: $i > $o] :
( ~ ( ( X2 @ c1 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ X3 ) ) ) )
=> ( X2 @ ( s @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ103^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.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 : 600
% 0.13/0.34 % DateTime : Sat May 28 21:10:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 4
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------