TSTP Solution File: SEU779^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU779^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : 600s
% DateTime : Tue Jul 19 14:04:37 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ ( kpair @ eigen__5 @ eigen__4 ) @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( in @ eigen__5 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ eigen__5 ) @ eigen__1 ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ( in @ X1 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__5 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ eigen__5 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( dpsetconstr @ eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__0 )
=> ~ ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 ) )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X2: $i,X3: $i] :
~ ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__0 )
=> ~ ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X4 @ X3 ) @ eigen__2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP3
=> ( in @ ( kpair @ eigen__3 @ eigen__4 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__0 )
=> ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( X1 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ eigen__0 @ eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ ( kpair @ eigen__3 @ eigen__5 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__0 )
=> ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__0 )
=> ~ ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 ) )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] :
~ ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__0 )
=> ~ ( in @ ( kpair @ X3 @ X5 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X5 @ X4 ) @ eigen__2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP6
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_dpsetconstrI,definition,
dpsetconstrI = sP9 ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).
thf(def_breln1compset,definition,
( breln1compset
= ( ^ [X1: $i,X2: $i,X3: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) ) ) ) ).
thf(breln1compI,conjecture,
( sP9
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X7: $i,X8: $i] :
~ ! [X9: $i] :
( ~ ( ( in @ X9 @ X1 )
=> ~ ( in @ ( kpair @ X7 @ X9 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X9 @ X8 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP9
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X7: $i,X8: $i] :
~ ! [X9: $i] :
( ~ ( ( in @ X9 @ X1 )
=> ~ ( in @ ( kpair @ X7 @ X9 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X9 @ X8 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compI]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X7: $i,X8: $i] :
~ ! [X9: $i] :
( ~ ( ( in @ X9 @ X1 )
=> ~ ( in @ ( kpair @ X7 @ X9 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X9 @ X8 ) @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X6: $i,X7: $i] :
~ ! [X8: $i] :
( ~ ( ( in @ X8 @ eigen__0 )
=> ~ ( in @ ( kpair @ X6 @ X8 ) @ X1 ) )
=> ~ ( in @ ( kpair @ X8 @ X7 ) @ X2 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X4 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X5: $i,X6: $i] :
~ ! [X7: $i] :
( ~ ( ( in @ X7 @ eigen__0 )
=> ~ ( in @ ( kpair @ X5 @ X7 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X7 @ X6 ) @ X1 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X4 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X4 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X2 @ X3 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X5: $i,X6: $i] :
~ ! [X7: $i] :
( ~ ( ( in @ X7 @ eigen__0 )
=> ~ ( in @ ( kpair @ X5 @ X7 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X7 @ X6 ) @ X1 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ eigen__0 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ eigen__2 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X3 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ eigen__2 )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ eigen__0 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ eigen__2 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP6
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] :
~ ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__0 )
=> ~ ( in @ ( kpair @ X3 @ X5 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X5 @ X4 ) @ eigen__2 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X2 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X1 ) @ eigen__2 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] :
~ ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__0 )
=> ~ ( in @ ( kpair @ X3 @ X5 ) @ eigen__1 ) )
=> ~ ( in @ ( kpair @ X5 @ X4 ) @ eigen__2 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP4
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 )
=> sP13 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP4,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 ) @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ eigen__4 ) @ eigen__2 )
=> sP13 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP17
=> ( sP12
=> ( sP1
=> sP13 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP17,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP12
=> ( sP1
=> sP13 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP12,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP1
=> sP13 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP1,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP17
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| ~ sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| ~ sP4
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1,h11,h14,h17,h19,h21,h22]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,12,h21,h22]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,13,h19,h20]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,14,h17,h18]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,15,h16]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,16,h14,h15]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,17,h13]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,19,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,23,h4]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,24,h3]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).
thf(0,theorem,
( sP9
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( kpair @ X6 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X7: $i,X8: $i] :
~ ! [X9: $i] :
( ~ ( ( in @ X9 @ X1 )
=> ~ ( in @ ( kpair @ X7 @ X9 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X9 @ X8 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU779^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : 600
% 0.13/0.34 % DateTime : Sun Jun 19 10:39:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % Mode: mode213
% 0.19/0.45 % Inferences: 16
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------