%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO224^5 : 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 : n011.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 03:25:10 PM UTC 2025
% Result : Theorem 16.88s 17.09s
% Output : Proof 16.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 101
% Syntax : Number of formulae : 110 ( 20 unt; 0 typ; 1 def)
% Number of atoms : 305 ( 35 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 395 ( 157 ~; 64 |; 0 &; 65 @)
% ( 46 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 55 usr; 52 con; 0-2 aty)
% Number of variables : 18 ( 1 ^; 15 !; 0 ?; 18 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i ).
thf(ty_cWRH,type,
cWRH: $i > $o ).
thf(ty_cP,type,
cP: $i ).
thf(ty_cUNIQUE,type,
cUNIQUE: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cJ,type,
cJ: $i ).
thf(ty_cW,type,
cW: $i > $o ).
thf(ty_cLIKE,type,
cLIKE: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( cUNIQUE @ X1 )
=> ~ ( cW @ X1 ) )
=> ~ ( cWRH @ X1 ) )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( cWRH @ cS ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( cUNIQUE @ eigen__1 )
=> ~ ( cW @ eigen__1 ) )
=> ~ ( cWRH @ eigen__1 ) )
=> ~ ( cLIKE @ cJ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( @+[X1: $o] : X1 )
= ( cLIKE @ cP @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( cUNIQUE @ cS )
=> ~ ( cW @ cS ) )
=> ~ sP1 )
=> ~ ( cLIKE @ cJ @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( cP = cP )
= ( cLIKE @ cP @ cS ) )
=> ( ( cJ = cP )
!= ( ~ ! [X1: $i] :
( ~ ( ~ ( ( cUNIQUE @ X1 )
=> ~ ( cW @ X1 ) )
=> ~ ( cWRH @ X1 ) )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cLIKE @ cP @ cS ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cUNIQUE @ eigen__1 )
=> ~ ( cW @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> $false ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] : ~ X1 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> @+[X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cP = cJ )
=> ( cJ = cP ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cJ = cJ ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ! [X2: $i] :
( ~ ( ( cWRH @ X2 )
=> ~ ( cW @ X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP7
=> ~ ( cWRH @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP3
=> ( sP10
!= ( ~ ! [X1: $i] :
( ~ ( ~ ( ( cUNIQUE @ X1 )
=> ~ ( cW @ X1 ) )
=> ~ ( cWRH @ X1 ) )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( cP = cJ )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( cP = X1 )
=> ( X1 = cP ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( sP1
=> ~ ( cW @ cS ) )
=> ( eigen__1 = cS ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( ~ ( ( cUNIQUE @ X1 )
=> ~ ( cW @ X1 ) )
=> ~ ( cWRH @ X1 ) )
=> ~ ( cLIKE @ cJ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ~ sP10 ) = ( ~ sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP1
=> ~ ( cW @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ( cUNIQUE @ cS )
=> ~ ( cW @ cS ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cUNIQUE @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP12 = ( ~ sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ~ sP10 ) = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP23
=> ! [X1: $i] :
( ~ ( ( cWRH @ X1 )
=> ~ ( cW @ X1 ) )
=> ( eigen__1 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cJ = cP ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP16
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( cUNIQUE @ cS )
=> ~ ( cW @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP25
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ( ( cWRH @ X1 )
=> ~ ( cW @ X1 ) )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cP = cP ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( cP = cJ ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP32 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( cW @ cS ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP27
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( cS = cS ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i > $o] :
( ( ( X1 @ cP )
= sP6 )
=> ( ( X1 @ cJ )
!= ( ~ sP19 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( cLIKE @ cJ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( cJ = X1 )
=> ( X1 = cJ ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__1 = cS ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( cLIKE @ cJ @ cS ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP27 = ( ~ sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP10 = ( ~ sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( cUNIQUE @ cS ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(cLING1,conjecture,
( ~ ( ~ ( ~ ( sP13
=> ~ sP46 )
=> ~ sP35 )
=> ~ sP1 )
=> ~ sP38 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP13
=> ~ sP46 )
=> ~ sP35 )
=> ~ sP1 )
=> ~ sP38 ),
inference(assume_negation,[status(cth)],[cLING1]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( sP13
=> ~ sP46 )
=> ~ sP35 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP38,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP13
=> ~ sP46 )
=> ~ sP35 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP13
=> ~ sP46 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP35,
introduced(assumption,[]) ).
thf(h8,assumption,
sP13,
introduced(assumption,[]) ).
thf(h9,assumption,
sP46,
introduced(assumption,[]) ).
thf(1,plain,
( sP34
| ~ sP32
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP44
| sP27
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP16
| sP33
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP24
| ~ sP12
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP28
| ~ sP16
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| ~ sP34
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP38
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP38
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( sP25
| ~ sP10
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP20
| ~ sP10
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP30
| ~ sP25
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP38
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP29
| ~ sP46
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP22
| sP29
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP6
| sP43
| ~ sP33
| ~ sP37 ),
inference(mating_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP4
| sP22
| ~ sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
~ sP8,
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP18
| sP21
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP31
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP26
| ~ sP23
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
sP32,
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP11
| ~ sP33
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP41
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP36
| ~ sP27
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP40
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP41
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP39
| sP6
| ~ sP27
| ~ sP42 ),
inference(mating_rule,[status(thm)],[]) ).
thf(30,plain,
( sP3
| ~ sP10
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP7
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP13
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( sP14
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP2
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP2
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP19
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(37,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( sP10
| sP9 ),
inference(choice_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP19
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( sP45
| ~ sP10
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP15
| ~ sP3
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP38
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP21
| ~ sP1
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
sP37,
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
sP41,
inference(eq_sym,[status(thm)],[]) ).
thf(46,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,h8,h9,h7,h5,h3]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,46,h8,h9]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,47,h6,h7]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,48,h4,h5]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,49,h2,h3]) ).
thf(51,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[50,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP13
=> ~ sP46 )
=> ~ sP35 )
=> ~ sP1 )
=> ~ sP38 ),
inference(contra,[status(thm),contra(discharge,[h1])],[50,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO224^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.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 01:00:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 16.88/17.09 % SZS status Theorem
% 16.88/17.09 % Mode: mode473
% 16.88/17.09 % Inferences: 1470
% 16.88/17.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------