TSTP Solution File: SYO378^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO378^5 : 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 : n022.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 : Thu Jul 21 19:31:44 EDT 2022
% Result : Theorem 9.75s 10.00s
% Output : Proof 9.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 32 ( 13 unt; 2 typ; 4 def)
% Number of atoms : 98 ( 54 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 120 ( 54 ~; 9 |; 0 &; 24 @)
% ( 10 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 16 con; 0-2 aty)
% Number of variables : 60 ( 30 ^ 30 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_c,type,
c: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i > $o] :
( ( ~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) )
!= ( ~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ( ^ [X1: $i > $o] :
~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) )
= ( ^ [X1: $i > $o] :
~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) )
=> ! [X1: $i > $o] :
( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ( ~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) )
= ( ~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ( ( eigen__2
= ( ^ [X1: $i] : ( X1 = c ) ) )
=> ! [X1: $i] :
~ ( eigen__2 @ X1 ) ) )
= ( ~ ( ( eigen__2
= ( ^ [X1: $i] : ( X1 = c ) ) )
=> ! [X1: $i] :
~ ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( ^ [X1: $i] : ( X1 = c ) )
= ( ^ [X1: $i] : ( X1 = c ) ) )
=> ! [X1: $i] : ( X1 != c ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] : ( X1 != c ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( c = c ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( $i > $o ) > $o] :
( ( X1
= ( ^ [X2: $i > $o] :
~ ( ( X2
= ( ^ [X3: $i] : ( X3 = c ) ) )
=> ! [X3: $i] :
~ ( X2 @ X3 ) ) ) )
=> ! [X2: $i > $o] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ^ [X1: $i > $o] :
~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) )
= ( ^ [X1: $i > $o] :
~ ( ( X1
= ( ^ [X2: $i] : ( X2 = c ) ) )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: $i] : ( X1 = c ) )
= ( ^ [X1: $i] : ( X1 = c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_cQDP0,definition,
( cQDP0
= ( ^ [X1: $i] : ( X1 = c ) ) ) ).
thf(def_cQDP1,definition,
( cQDP1
= ( ^ [X1: $i > $o] :
~ ( ( X1 = cQDP0 )
=> ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ).
thf(def_cQDP2,definition,
( cQDP2
= ( ^ [X1: ( $i > $o ) > $o] :
~ ( ( X1 = cQDP1 )
=> ! [X2: $i > $o] :
~ ( X1 @ X2 ) ) ) ) ).
thf(cQDTHM2,conjecture,
~ ! [X1: ( $i > $o ) > $o] :
~ ~ ( ( X1
= ( ^ [X2: $i > $o] :
~ ( ( X2
= ( ^ [X3: $i] : ( X3 = c ) ) )
=> ! [X3: $i] :
~ ( X2 @ X3 ) ) ) )
=> ! [X2: $i > $o] :
~ ( X1 @ X2 ) ) ).
thf(h1,negated_conjecture,
sP8,
inference(assume_negation,[status(cth)],[cQDTHM2]) ).
thf(1,plain,
sP10,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP10
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(8,plain,
( sP9
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,h1]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
~ ! [X1: ( $i > $o ) > $o] :
~ ~ ( ( X1
= ( ^ [X2: $i > $o] :
~ ( ( X2
= ( ^ [X3: $i] : ( X3 = c ) ) )
=> ! [X3: $i] :
~ ( X2 @ X3 ) ) ) )
=> ! [X2: $i > $o] :
~ ( X1 @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO378^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.12/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 08:50:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 9.75/10.00 % SZS status Theorem
% 9.75/10.00 % Mode: mode495
% 9.75/10.00 % Inferences: 36
% 9.75/10.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------