TSTP Solution File: SEU769^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU769^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 Aug 31 17:27:52 EDT 2023
% Result : Theorem 3.54s 3.72s
% Output : Proof 3.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__1
@ ( dsetconstr @ ( powerset @ ( cartprod @ eigen__0 @ eigen__0 ) )
@ ^ [X1: $i] : ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( powerset @ ( cartprod @ eigen__0 @ eigen__0 ) )
@ ^ [X2: $i] : ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) )
=> ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ ( powerset @ ( cartprod @ eigen__0 @ eigen__0 ) ) @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_dsetconstrER,definition,
( dsetconstrER
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i,X2: $i] : ( breln @ X1 @ X1 @ X2 ) ) ) ).
thf(def_breln1Set,definition,
( breln1Set
= ( ^ [X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X2: $i] : ( breln1 @ X1 @ X2 ) ) ) ) ).
thf(breln1SetBreln1,conjecture,
( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X1 ) ) ) )
=> ( subset @ X2 @ ( cartprod @ X1 @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X1 ) ) ) )
=> ( subset @ X2 @ ( cartprod @ X1 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[breln1SetBreln1]) ).
thf(h1,assumption,
sP5,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X1 ) ) ) )
=> ( subset @ X2 @ ( cartprod @ X1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,h1,h5,h6]) ).
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,
( sP5
=> ! [X1: $i,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X1 ) ) ) )
=> ( subset @ X2 @ ( cartprod @ X1 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU769^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 16:33:47 EDT 2023
% 0.21/0.36 % CPUTime :
% 3.54/3.72 % SZS status Theorem
% 3.54/3.72 % Mode: cade22grackle2xfee4
% 3.54/3.72 % Steps: 24425
% 3.54/3.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------