TSTP Solution File: SEU876^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU876^5 : 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 : 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 17:37:44 EDT 2023
% Result : Theorem 0.21s 0.68s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 32
% Syntax : Number of formulae : 39 ( 8 unt; 5 typ; 2 def)
% Number of atoms : 116 ( 8 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 325 ( 92 ~; 13 |; 0 &; 108 @)
% ( 12 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 71 ( 14 ^; 57 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cE,type,
cE: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_cA,type,
cA: ( a > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( cE @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( cE @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( cE @ X2 )
=> ( X1 @ X2 ) ) )
=> ( cA @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( a > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( cE @ X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1 @ cE ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cA @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cA @ eigen__1 )
=> ~ ! [X1: a] :
( ( cE @ X1 )
=> ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( sP2
=> ~ ! [X1: a] :
( ( cE @ X1 )
=> ( eigen__0 @ X1 ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ~ ! [X1: a] :
( ( cE @ X1 )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( cE @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP3
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( cE @ X3 )
=> ( X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
( ~ ( ! [X2: ( a > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( eigen__1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( cE @ X3 )
=> ( X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( cE @ X2 )
=> ( X1 @ X2 ) ) )
=> ( cA @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( cE @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( cE @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( cE @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( cE @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cDOMLEMMA4_pme,conjecture,
( sP1
=> ~ sP11 ) ).
thf(h1,negated_conjecture,
~ ( sP1
=> ~ sP11 ),
inference(assume_negation,[status(cth)],[cDOMLEMMA4_pme]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP12
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(7,plain,
( sP5
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP9
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(11,plain,
( ~ sP11
| ~ sP9
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,h3]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
( sP1
=> ~ sP11 ),
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU876^5 : TPTP v8.1.2. Released v4.0.0.
% 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 : Wed Aug 23 17:05:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.68 % SZS status Theorem
% 0.21/0.68 % Mode: cade22grackle2xfee4
% 0.21/0.68 % Steps: 9090
% 0.21/0.68 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------