TSTP Solution File: SEU599^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU599^2 : 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 : n010.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 17:19:26 EDT 2023
% Result : Theorem 20.24s 20.45s
% Output : Proof 20.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_binintersect,type,
binintersect: $i > $i > $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ( ( binintersect @ eigen__0 @ eigen__1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ( subset @ ( binintersect @ eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( subset @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( binintersect @ eigen__0 @ eigen__1 ) )
=> ( in @ X2 @ X1 ) )
=> ( subset @ ( binintersect @ eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( subset @ ( binintersect @ eigen__0 @ eigen__1 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_in__Cong,definition,
( in__Cong
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 = X4 )
@ ( ( in @ X3 @ X1 )
<=> ( in @ X4 @ X2 ) ) ) ) ) ) ).
thf(def_subsetI1,definition,
( subsetI1
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( subset @ X1 @ X2 ) ) ) ) ).
thf(def_binintersectER,definition,
( binintersectER
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
@ ( in @ X3 @ X2 ) ) ) ) ).
thf(binintersectSubset1,conjecture,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP10
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP10
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[binintersectSubset1]) ).
thf(h1,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP6
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( ( binintersect @ eigen__0 @ X1 )
= eigen__0 )
=> ( subset @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP7
| sP3
| ~ sP1 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h3,h5,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,9,h8]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,10,h7]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,11,h5,h6]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,12,h3,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP10
=> ( sP6
=> ! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= X1 )
=> ( subset @ X1 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU599^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 23 21:13:21 EDT 2023
% 0.13/0.33 % CPUTime :
% 20.24/20.45 % SZS status Theorem
% 20.24/20.45 % Mode: cade22grackle2x798d
% 20.24/20.45 % Steps: 195
% 20.24/20.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------