TSTP Solution File: SEU669^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU669^2 : 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 : n027.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 13:56:07 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $i > $o ).
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_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__1 )
=> ~ ( eigen__2 @ X2 @ X3 ) )
=> ( X1
!= ( kpair @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__1 )
=> ~ ( eigen__2 @ X3 @ X4 ) )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 ) @ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( in @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ( in @ X2 @ ( cartprod @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( in @ ( kpair @ eigen__3 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ eigen__0 @ X1 ) )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_dsetconstrEL,definition,
dsetconstrEL = sP12 ).
thf(def_cartprodpairmemEL,definition,
cartprodpairmemEL = sP7 ).
thf(def_dpsetconstr,definition,
( dpsetconstr
= ( ^ [X1: $i,X2: $i,X3: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ~ ( ( in @ X6 @ X2 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X4
!= ( kpair @ X5 @ X6 ) ) ) ) ) ) ) ).
thf(dpsetconstrEL1,conjecture,
( sP12
=> ( sP7
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( in @ X4 @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP12
=> ( sP7
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( in @ X4 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrEL1]) ).
thf(h1,assumption,
sP12,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP7
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( in @ X4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( in @ X4 @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ X1 )
@ ^ [X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ eigen__0 )
=> ! [X7: $i] :
( ~ ( ( in @ X7 @ X1 )
=> ~ ( X2 @ X6 @ X7 ) )
=> ( X5
!= ( kpair @ X6 @ X7 ) ) ) ) ) )
=> ( in @ X3 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ! [X6: $i] :
( ~ ( ( in @ X6 @ eigen__1 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X4
!= ( kpair @ X5 @ X6 ) ) ) ) ) )
=> ( in @ X2 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__1 )
=> ~ ( eigen__2 @ X4 @ X5 ) )
=> ( X3
!= ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ( in @ X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__1 )
=> ~ ( eigen__2 @ X3 @ X4 ) )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) )
=> sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| ~ sP3
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,h1,h3,h10,h11]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,10,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h8,11,h9]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,12,h8]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,13,h7]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,15,h5]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( sP12
=> ( sP7
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( in @ X4 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU669^2 : 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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 04:28:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 8
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------