%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO032^1 : 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 03:24:42 PM UTC 2025
% Result : Theorem 32.14s 32.11s
% Output : Proof 32.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 37 ( 8 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 46 ( 20 ~; 3 |; 0 &; 7 @)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 11 ( 2 ^; 9 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__499,type,
eigen__499: $o ).
thf(ty_eigen__788,type,
eigen__788: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__499,definition,
( eigen__499
= ( eps__0
@ ^ [X1: $o] :
~ ! [X2: $o] :
( ( ~ X1
=> X2 )
= ( ~ X1
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__499])]) ).
thf(eigendef_eigen__788,definition,
( eigen__788
= ( eps__0
@ ^ [X1: $o] :
( ( ~ eigen__499
=> X1 )
!= ( ~ eigen__499
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__788])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $o] :
( ( ~ eigen__499
=> X1 )
= ( ~ eigen__499
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ eigen__499
=> eigen__788 )
= ( ~ eigen__499
=> eigen__788 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o,X2: $o] :
( ( ~ X1
=> X2 )
= ( ~ X1
=> X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o > $o] :
~ ! [X2: $o,X3: $o] :
( ( X1 @ X2 @ X3 )
= ( ~ X2
=> X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(conj,conjecture,
~ sP4 ).
thf(h1,negated_conjecture,
sP4,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP1
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__788]) ).
thf(3,plain,
( sP3
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__499]) ).
thf(4,plain,
( ~ sP4
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1]) ).
thf(6,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).
thf(0,theorem,
~ sP4,
inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO032^1 : TPTP v9.2.0. Released v3.7.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Oct 9 00:29:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 32.14/32.11 % SZS status Theorem
% 32.14/32.11 % Mode: mode510
% 32.14/32.11 % Inferences: 3472
% 32.14/32.11 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------