%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN377^5 : 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 : n005.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 03:18:09 PM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
= ( !! @ cP ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( !! @ cP ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ eigen__1 )
= sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( cP @ X1 )
= sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cX2128,conjecture,
( sP7
= ( ( ~ sP9 ) = sP5 ) ) ).
thf(h0,negated_conjecture,
( sP7
!= ( ( ~ sP9 ) = sP5 ) ),
inference(assume_negation,[status(cth)],[cX2128]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ~ sP9 ) = sP5 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ~ sP9 ) != sP5 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
sP5,
introduced(assumption,[]) ).
thf(h7,assumption,
sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,h5,h6,h1,h2,h0])],[1,2,3,4,h1,h9,h10]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h5,h6,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h6,5,h10]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h5,6,h9]) ).
thf(8,plain,
( ~ sP9
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h1,h2,h0])],[8,9,h7,h8]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h2,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h2,7,10,h5,h6,h7,h8]) ).
thf(h11,assumption,
sP3 != sP5,
introduced(assumption,[]) ).
thf(h12,assumption,
sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h15,assumption,
cP @ eigen__5,
introduced(assumption,[]) ).
thf(12,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h5,h6,h14,h12,h6,h11,h3,h4,h0])],[12,h14,h6]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h14,h12,h6,h11,h3,h4,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__5)],[h5,13,h15]) ).
thf(h16,assumption,
~ ( cP @ eigen__6 ),
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP9
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h7,h8,h14,h12,h6,h11,h3,h4,h0])],[15,h12,h7]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h14,h12,h6,h11,h3,h4,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h8,16,h16]) ).
thf(18,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h12,h6,h11,h3,h4,h0]),tab_bq(discharge,[h5,h6]),tab_bq(discharge,[h7,h8])],[h4,14,17,h5,h6,h7,h8]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h6,h11,h3,h4,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h6,18,h14]) ).
thf(h17,assumption,
cP @ eigen__7,
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h5,h6,h13,h8,h11,h3,h4,h0])],[20,h13,h6]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h13,h8,h11,h3,h4,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__7)],[h5,21,h17]) ).
thf(h18,assumption,
~ ( cP @ eigen__8 ),
introduced(assumption,[]) ).
thf(23,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h7,h8,h13,h8,h11,h3,h4,h0])],[23,h13,h8]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h13,h8,h11,h3,h4,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__8)],[h8,24,h18]) ).
thf(26,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h13,h8,h11,h3,h4,h0]),tab_bq(discharge,[h5,h6]),tab_bq(discharge,[h7,h8])],[h4,22,25,h5,h6,h7,h8]) ).
thf(27,plain,
$false,
inference(tab_be,[status(thm),assumptions([h11,h3,h4,h0]),tab_be(discharge,[h12,h6]),tab_be(discharge,[h13,h8])],[h11,19,26,h12,h6,h13,h8]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h3,27,h11]) ).
thf(29,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,11,28,h1,h2,h3,h4]) ).
thf(0,theorem,
( sP7
= ( ( ~ sP9 ) = sP5 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN377^5 : TPTP v9.2.0. Released v4.0.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n005.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 : Wed Oct 8 15:01:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % Mode: mode213
% 0.13/0.40 % Inferences: 48
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------