%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU841^5 : 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 02:52:48 PM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
= ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
= ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cGAZING_THM7,conjecture,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ),
inference(assume_negation,[status(cth)],[cGAZING_THM7]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ~ ( ( eigen__0 = X1 )
=> ( X1 != X2 ) )
=> ( eigen__0 = X2 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ~ ( sP9
=> ( eigen__1 != X1 ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP9
=> ~ sP7 )
=> ( eigen__0 = eigen__2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP9
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h5,assumption,
eigen__0 != eigen__2,
introduced(assumption,[]) ).
thf(h6,assumption,
sP9,
introduced(assumption,[]) ).
thf(h7,assumption,
sP7,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
= ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1 != sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
sP8,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP3
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,h6,h7,h10,h11]) ).
thf(8,plain,
( ~ sP2
| sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP4
| sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP9
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h9,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[8,9,10,11,12,13,h6,h7,h12,h13]) ).
thf(15,plain,
$false,
inference(tab_be,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h9,7,14,h10,h11,h12,h13]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,15,h9]) ).
thf(17,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_fe(discharge,[h8])],[h5,16,h8]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,17,h6,h7]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,18,h4,h5]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,19,h3]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,20,h2]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU841^5 : 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
% 0.13/0.34 % Computer : n004.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 20:53:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: mode213
% 0.13/0.38 % Inferences: 36
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------