TSTP Solution File: SEU778^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU778^2 : 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 : n021.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 14:04:30 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% 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_kpair,type,
kpair: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $i > $o] : ( subset @ ( dpsetconstr @ eigen__0 @ eigen__0 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset
@ ( 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 ) ) )
@ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X1 @ X2 ) @ ( cartprod @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).
thf(def_setOfPairsIsBReln1,definition,
( setOfPairsIsBReln1
= ( ! [X1: $i,X2: $i > $i > $o] : ( breln1 @ X1 @ ( dpsetconstr @ X1 @ X1 @ X2 ) ) ) ) ).
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(breln1compprop,conjecture,
( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) )
@ ( cartprod @ X1 @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) )
@ ( cartprod @ X1 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compprop]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) )
@ ( cartprod @ X1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( subset
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] :
~ ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__0 )
=> ~ ( in @ ( kpair @ X3 @ X5 ) @ X1 ) )
=> ~ ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
@ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( subset
@ ( 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 ) @ X1 ) ) )
@ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
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 ) )
=> ( subset
@ ( 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 ) @ X1 ) ) )
@ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,h1,h9]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,3,h8,h9]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,4,h7]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,5,h5,h6]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,6,h4]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,7,h3]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,8,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [X4: $i,X5: $i] :
~ ! [X6: $i] :
( ~ ( ( in @ X6 @ X1 )
=> ~ ( in @ ( kpair @ X4 @ X6 ) @ X2 ) )
=> ~ ( in @ ( kpair @ X6 @ X5 ) @ X3 ) ) )
@ ( cartprod @ X1 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU778^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 : Mon Jun 20 10:43:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 4
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------