%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN374^5 : 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 : n024.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 03:18:08 PM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 46
% Syntax : Number of formulae : 63 ( 32 unt; 0 typ; 2 def)
% Number of atoms : 139 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 108 ( 42 ~; 20 |; 0 &; 29 @)
% ( 15 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 25 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 10 ( 2 ^; 8 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
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__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__5 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__2 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cP @ eigen__0 )
= sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( sP3
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ eigen__2 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( cP @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( cP @ eigen__2 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP @ eigen__0 )
= ( cP @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( cP @ eigen__0 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( !! @ cP ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cX2125,conjecture,
( ( ~ sP5 )
= ( ( ~ sP14 ) = sP15 ) ) ).
thf(h1,negated_conjecture,
( ( ~ sP5 )
!= ( ( ~ sP14 ) = sP15 ) ),
inference(assume_negation,[status(cth)],[cX2125]) ).
thf(h2,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
( ( ~ sP14 ) = sP15 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
( ( ~ sP14 ) != sP15 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
sP14,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP13
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP13
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h7,h8,h6,h2,h3,h1,h0])],[1,2,3,4,h6,h11,h12]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h8,5,h12]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h7,6,h11]) ).
thf(8,plain,
( ~ sP14
| ~ sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP15
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h6,h2,h3,h1,h0])],[8,9,h9,h10]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h3,7,10,h7,h8,h9,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h2,11,h6]) ).
thf(h13,assumption,
cP @ eigen__4,
introduced(assumption,[]) ).
thf(13,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( sP6
| ~ sP12
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP8
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(16,plain,
( ~ sP5
| ~ sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP15
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h7,h8,h4,h5,h1,h0])],[13,14,15,16,17,h4,h8]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h4,h5,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h7,18,h13]) ).
thf(h14,assumption,
~ ( cP @ eigen__8 ),
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP14
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( sP9
| sP3
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP4
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(23,plain,
( ~ sP5
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP14
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h9,h10,h4,h5,h1,h0])],[20,21,22,23,24,h4,h9]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__8)],[h10,25,h14]) ).
thf(27,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h4,h5,h1,h0]),tab_bq(discharge,[h7,h8]),tab_bq(discharge,[h9,h10])],[h5,19,26,h7,h8,h9,h10]) ).
thf(28,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,12,27,h2,h3,h4,h5]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
( ( ~ sP5 )
= ( ( ~ sP14 ) = sP15 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[28,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN374^5 : TPTP v9.2.0. Released v4.0.0.
% 0.14/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 15:24:38 EDT 2025
% 0.21/0.36 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: mode213
% 0.21/0.41 % Inferences: 98
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------