%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN998^1 : 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 : n012.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 03:19:01 PM UTC 2025
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(def_leibeq,definition,
( leibeq
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ( X2 @ X1 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ( X2 @ X1 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ! [X1: $i > $o] :
( ( X1 @ eigen__0 )
=> ( X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP1
=> sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h4,h2,h1,h0])],[h3,h4]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,1,h3,h4]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,2,h2]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ( X2 @ X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN998^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 15:17:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------