%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO868^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 03:26:23 PM UTC 2025
% Result : Theorem 271.50s 271.48s
% Output : Proof 271.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_c_atleast5,type,
c_atleast5: $i > $o ).
thf(ty_c_and,type,
c_and: $o > $o > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_c_ordinal,type,
c_ordinal: $i > $o ).
thf(ty_c_SNoLt,type,
c_SNoLt: $i > $i > $o ).
thf(ty_c_nat_p,type,
c_nat_p: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_c_atleast3,type,
c_atleast3: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c_TransSet,type,
c_TransSet: $i > $o ).
thf(ty_c_not,type,
c_not: $o > $o ).
thf(ty_c_Power,type,
c_Power: $i > $i ).
thf(ty_c_Empty,type,
c_Empty: $i ).
thf(ty_c_False,type,
c_False: $o ).
thf(ty_c_exactly1of2,type,
c_exactly1of2: $o > $o > $o ).
thf(ty_c_In,type,
c_In: $i > $i > $o ).
thf(ty_c_binrep,type,
c_binrep: $i > $i > $i ).
thf(ty_c_atleast2,type,
c_atleast2: $i > $o ).
thf(ty_c_exactly2,type,
c_exactly2: $i > $o ).
thf(ty_c_exactly5,type,
c_exactly5: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( c_not
@ ~ ! [X1: $i] :
~ ( c_In @ X1 @ c_Empty ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ ! [X1: $i] :
~ ( c_In @ X1 @ c_Empty ) )
= ( c_not @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( c_not @ ( c_not @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( c_In @ eigen__0 @ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( c_not @ $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( $false
=> c_False ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ( c_In @ X1 @ c_Empty ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> $false ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( c_not
= ( ^ [X1: $o] :
( X1
=> c_False ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP5 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o] :
( ( c_not @ X1 )
= ( X1
=> c_False ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o] :
( ( c_not @ ( c_not @ X1 ) )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(conj,conjecture,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( c_In @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( ( c_ordinal @ X3 )
=> ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
=> ( ( ( ( c_ordinal @ X3 )
=> ( c_exactly2 @ X3 ) )
=> ( ( c_atleast2 @ X3 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X3 = X4 ) )
=> ( c_atleast3 @ X3 ) )
=> ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
=> ( c_nat_p @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( c_In @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( ( c_ordinal @ X3 )
=> ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
=> ( ( ( ( c_ordinal @ X3 )
=> ( c_exactly2 @ X3 ) )
=> ( ( c_atleast2 @ X3 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X3 = X4 ) )
=> ( c_atleast3 @ X3 ) )
=> ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
=> ( c_nat_p @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( c_In @ eigen__1 @ eigen__0 )
=> ! [X1: $i] :
( ( c_In @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( ( c_ordinal @ X2 )
=> ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
=> ( ( ( ( c_ordinal @ X2 )
=> ( c_exactly2 @ X2 ) )
=> ( ( c_atleast2 @ X2 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X2 = X3 ) )
=> ( c_atleast3 @ X2 ) )
=> ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
=> ( c_nat_p @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
c_In @ eigen__1 @ eigen__0,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( c_In @ X1 @ eigen__1 )
=> ~ ! [X2: $i] :
~ ! [X3: $i] :
( ( ( c_ordinal @ X2 )
=> ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
=> ( ( ( ( c_ordinal @ X2 )
=> ( c_exactly2 @ X2 ) )
=> ( ( c_atleast2 @ X2 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X2 = X3 ) )
=> ( c_atleast3 @ X2 ) )
=> ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
=> ( c_nat_p @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( c_In @ eigen__2 @ eigen__1 )
=> ~ ! [X1: $i] :
~ ! [X2: $i] :
( ( ( c_ordinal @ X1 )
=> ( c_and @ ( c_exactly2 @ X1 ) @ ( c_not @ ( c_exactly5 @ X2 ) ) ) )
=> ( ( ( ( c_ordinal @ X1 )
=> ( c_exactly2 @ X1 ) )
=> ( ( c_atleast2 @ X1 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X1 = X2 ) )
=> ( c_atleast3 @ X1 ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X2 ) ) ) ) ) ) )
=> ( c_nat_p @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
c_In @ eigen__2 @ eigen__1,
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: $i] :
~ ! [X2: $i] :
( ( ( c_ordinal @ X1 )
=> ( c_and @ ( c_exactly2 @ X1 ) @ ( c_not @ ( c_exactly5 @ X2 ) ) ) )
=> ( ( ( ( c_ordinal @ X1 )
=> ( c_exactly2 @ X1 ) )
=> ( ( c_atleast2 @ X1 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X1 = X2 ) )
=> ( c_atleast3 @ X1 ) )
=> ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X2 ) ) ) ) ) ) )
=> ( c_nat_p @ X1 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP6
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP7
| ~ sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
~ sP8,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP2
| sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP3
| ~ sP2 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP12
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(ax13,axiom,
sP9 ).
thf(ax5,axiom,
sP1 ).
thf(ax2,axiom,
sP12 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,ax13,ax5,ax2]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,10,h8,h9]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,11,h7]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,12,h5,h6]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,13,h4]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,14,h2,h3]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,15,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ( c_In @ X1 @ c_Empty )
=> ! [X2: $i] :
( ( c_In @ X2 @ X1 )
=> ! [X3: $i] :
( ( c_In @ X3 @ X2 )
=> ~ ! [X4: $i] :
~ ! [X5: $i] :
( ( ( c_ordinal @ X4 )
=> ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
=> ( ( ( ( c_ordinal @ X4 )
=> ( c_exactly2 @ X4 ) )
=> ( ( c_atleast2 @ X4 )
=> ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
=> ( X4 = X5 ) )
=> ( c_atleast3 @ X4 ) )
=> ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
=> ( c_nat_p @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO868^1 : TPTP v9.2.0. Released v7.5.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.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 00:34:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 271.50/271.48 % SZS status Theorem
% 271.50/271.48 % Mode: mode8a:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 271.50/271.48 % Inferences: 5097
% 271.50/271.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------