%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO034^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 Oct 9 03:24:43 PM UTC 2025
% Result : Theorem 1.08s 1.29s
% Output : Proof 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 23 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 2 |; 0 &; 5 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 6 ( 1 ^; 5 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] : ( X1 != X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $o] : ( X1 = X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o > $o] :
~ ! [X2: $o] :
( ( X1 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(conj,conjecture,
~ sP2 ).
thf(h1,negated_conjecture,
sP2,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP1
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(3,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,h1]) ).
thf(5,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[4,h0]) ).
thf(0,theorem,
~ sP2,
inference(contra,[status(thm),contra(discharge,[h1])],[4,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO034^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n006.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 : 300
% 0.13/0.35 % DateTime : Thu Oct 9 00:45:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.08/1.29 % SZS status Theorem
% 1.08/1.29 % Mode: mode506
% 1.08/1.29 % Inferences: 19443
% 1.08/1.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------