%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO087^5 : 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 : n003.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 03:24:53 PM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cP,type,
cP: $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $o ).
thf(ty_cQ,type,
cQ: $o ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ cP
=> ~ ( ( cQ
=> cR )
=> ~ ( ~ cQ
=> ~ cR ) ) )
=> ( ( ( cP
=> ~ cQ )
=> ~ ( ~ cP
=> cQ ) )
=> cR ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cP
=> ~ cQ )
=> ~ ( ~ cP
=> cQ ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ cQ
=> ~ cR ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> cP ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cQ
=> cR )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> cQ ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP6
=> cR ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP4
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP4
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] : ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> cR ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP4
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP2
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cTHM50_13,conjecture,
~ sP10 ).
thf(h0,negated_conjecture,
sP10,
inference(assume_negation,[status(cth)],[cTHM50_13]) ).
thf(1,plain,
( ~ sP10
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( sP12
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP8
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP3
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP7
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP13
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP13
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP9
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP1
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP1
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h0]) ).
thf(0,theorem,
~ sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO087^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Oct 9 00:20:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 22
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------