%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU811^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 02:51:33 PM UTC 2025
% Result : Theorem 101.70s 101.63s
% Output : Proof 101.70s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_omega,type,
omega: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( ( setadjoin @ eigen__0 @ eigen__0 )
= ( setadjoin @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__0 ) )
=> ! [X2: $o] :
( ( ( X1 = eigen__0 )
=> X2 )
=> ( ( ( in @ X1 @ eigen__0 )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ eigen__0 ) )
=> ! [X1: $o] :
( ( ( eigen__1 = eigen__0 )
=> X1 )
=> ( ( ( in @ eigen__1 @ eigen__0 )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $o] :
( ( ( eigen__1 = eigen__0 )
=> X1 )
=> ( ( ( in @ eigen__1 @ eigen__0 )
=> X1 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ~ ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ eigen__0 @ X1 )
=> ~ ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 != eigen__1 )
=> ( in @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP6
=> ! [X1: $o] :
( ( ( eigen__0 = eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__0 @ eigen__1 )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ eigen__0 @ eigen__1 )
=> ~ ( in @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] : ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( setadjoin @ eigen__1 @ eigen__1 )
= ( setadjoin @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__1 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = eigen__1 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP1
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP20
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__1 @ eigen__1 ) )
=> ! [X2: $o] :
( ( ( X1 = eigen__1 )
=> X2 )
=> ( ( ( in @ X1 @ eigen__1 )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP20
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( ( setadjoin @ eigen__0 @ eigen__0 )
= X1 )
=> ( X1
= ( setadjoin @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = eigen__0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $o] :
( ( sP26
=> X1 )
=> ( ( sP18
=> X1 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP28 ).
thf(def_setadjoinE,definition,
setadjoinE = sP3 ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(def_notinself2,definition,
notinself2 = sP8 ).
thf(def_omegaS,definition,
( omegaS
= ( ^ [X1: $i] : ( setadjoin @ X1 @ X1 ) ) ) ).
thf(peanoSinj,conjecture,
( sP28
=> ( sP3
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP28
=> ( sP3
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[peanoSinj]) ).
thf(h1,assumption,
sP28,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( in @ eigen__0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( setadjoin @ eigen__0 @ eigen__0 )
= ( setadjoin @ X1 @ X1 ) )
=> ( eigen__0 = X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
in @ eigen__0 @ omega,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( setadjoin @ eigen__0 @ eigen__0 )
= ( setadjoin @ X1 @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( in @ eigen__1 @ omega )
=> ( sP1
=> sP26 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
in @ eigen__1 @ omega,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP26 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP26
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP27
| sP20
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP33
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP19
| sP6
| ~ sP5
| ~ sP1 ),
inference(mating_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP7
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP34
| sP9
| ~ sP12
| ~ sP21 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| ~ sP6
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP15
| ~ sP18
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP25
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP22
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP16
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP10
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP32
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP29
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP28
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP3
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP28
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP3
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP24
| ~ sP20
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP11
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP31
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP23
| ~ sP1
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP30
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP31
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
sP31,
inference(eq_sym,[status(thm)],[]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,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,h1,h3,h7,h15,h16]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,31,h15,h16]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,32,h13,h14]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,33,h12]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,34,h10,h11]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,35,h9]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,36,h7,h8]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,37,h5,h6]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,38,h3,h4]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,39,h1,h2]) ).
thf(0,theorem,
( sP28
=> ( sP3
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP8
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[40,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU811^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 8 21:08:08 EDT 2025
% 0.12/0.32 % CPUTime :
% 101.70/101.63 % SZS status Theorem
% 101.70/101.63 % Mode: mode492
% 101.70/101.63 % Inferences: 7214
% 101.70/101.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------