%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU810^2 : 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 02:51:28 PM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $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
<=> ( ( in @ eigen__0 @ emptyset )
=> ! [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 = eigen__0 )
=> ( sP2
= ( in @ eigen__0 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] : ( in @ eigen__0 @ ( setadjoin @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__0 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> $false ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( setadjoin @ eigen__0 @ eigen__0 )
= emptyset )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__0 ) )
= ( in @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( setadjoin @ eigen__0 @ eigen__0 )
= emptyset ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP2 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__0 ) )
= ( in @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( sP2
= ( in @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( ( setadjoin @ eigen__0 @ eigen__0 )
= X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ ( setadjoin @ eigen__0 @ eigen__0 ) )
= ( in @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(def_emptysetE,definition,
emptysetE = sP4 ).
thf(def_setadjoinIL,definition,
setadjoinIL = sP16 ).
thf(def_in__Cong,definition,
in__Cong = sP9 ).
thf(def_omegaS,definition,
( omegaS
= ( ^ [X1: $i] : ( setadjoin @ X1 @ X1 ) ) ) ).
thf(peano0notS,conjecture,
( sP4
=> ( sP16
=> ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP4
=> ( sP16
=> ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ) ) ) ),
inference(assume_negation,[status(cth)],[peano0notS]) ).
thf(h1,assumption,
sP4,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP16
=> ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP16,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( in @ eigen__0 @ omega )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
in @ eigen__0 @ omega,
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP12
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| ~ sP6
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP16
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
~ sP7,
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP17
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP9
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP15
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP8
| ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1,h3,h5,h9]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,15,h8,h9]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,16,h7]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( sP4
=> ( sP16
=> ( sP9
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( setadjoin @ X1 @ X1 )
!= emptyset ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU810^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 21:34:08 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % Mode: mode213
% 0.14/0.38 % Inferences: 103
% 0.14/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------