%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO139^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 03:24:59 PM UTC 2025
% Result : Theorem 0.13s 0.34s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( ( ~ ! [X1: $i] :
~ ( ~ ( cP @ X1 )
=> ~ ( cP @ X1 ) )
=> ~ ( cQ @ eigen__0 ) )
=> ~ ( cQ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
~ ( ~ ( cP @ X1 )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP2
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP3
=> ~ ( cQ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ( ( ~ sP3
=> ~ ( cQ @ X1 ) )
=> ~ ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cCOUNTER1,conjecture,
~ sP6 ).
thf(h0,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[cCOUNTER1]) ).
thf(1,plain,
( sP4
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP4
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP1
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP6
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO139^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Thu Oct 9 01:17:23 EDT 2025
% 0.13/0.32 % CPUTime :
% 0.13/0.34 % SZS status Theorem
% 0.13/0.34 % Mode: mode213
% 0.13/0.34 % Inferences: 10
% 0.13/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------