%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO099^5 : 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 : n025.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 03:24:55 PM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cM,type,
cM: $i > $o ).
thf(ty_cN,type,
cN: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( !! @ cM ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cN @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cG @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( !! @ cG ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ( cN @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cM @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cTHM78,conjecture,
( ~ ( ~ ( ~ sP1
=> ~ sP4 )
=> ~ ( ~ sP1
=> ~ sP5 ) )
=> ~ ( ~ sP5
=> ~ sP4 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ sP1
=> ~ sP4 )
=> ~ ( ~ sP1
=> ~ sP5 ) )
=> ~ ( ~ sP5
=> ~ sP4 ) ),
inference(assume_negation,[status(cth)],[cTHM78]) ).
thf(h1,assumption,
~ ( ~ ( ~ sP1
=> ~ sP4 )
=> ~ ( ~ sP1
=> ~ sP5 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ~ sP5
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ sP1
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ sP1
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
sP5,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,h7,h8]) ).
thf(h12,assumption,
~ ( cG @ eigen__2 ),
introduced(assumption,[]) ).
thf(3,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[3,h7,h8]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h11,4,h12]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h2,2,5,h10,h11]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP5
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h13,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[7,h13,h10]) ).
thf(h14,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h11,h13,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[9,h6,h14]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h13,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h11,10,h14]) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h2,8,11,h10,h11]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h9,12,h13]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h4,6,13,h8,h9]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h5,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ sP1
=> ~ sP4 )
=> ~ ( ~ sP1
=> ~ sP5 ) )
=> ~ ( ~ sP5
=> ~ sP4 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO099^5 : TPTP v9.2.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n025.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 00:56:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % Mode: mode213
% 0.20/0.39 % Inferences: 29
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------