TSTP Solution File: SEU706^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU706^2 : 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 : n005.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 17:22:42 EDT 2023
% Result : Theorem 20.58s 20.76s
% Output : Proof 20.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ eigen__2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( setadjoin @ eigen__1 @ emptyset )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( setunion @ ( setadjoin @ eigen__1 @ emptyset ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0
= ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( setunion @ eigen__0 )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( setunion @ ( setadjoin @ eigen__1 @ emptyset ) )
= ( setunion @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> $false ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_uniqinunit,definition,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
@ ( X1 = X2 ) ) ) ) ).
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_setadjoin__Cong,definition,
( setadjoin__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 )
@ ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) ) ) ) ).
thf(def_setunion__Cong,definition,
( setunion__Cong
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( X1 = X2 )
@ ( ( setunion @ X1 )
= ( setunion @ X2 ) ) ) ) ) ).
thf(def_setunionsingleton,definition,
setunionsingleton = sP3 ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(theeq,conjecture,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[theeq]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP3,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__0
!= ( setadjoin @ X1 @ emptyset ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( setunion @ eigen__0 )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__0
!= ( setadjoin @ X1 @ emptyset ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( setunion @ eigen__0 )
= X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( in @ eigen__1 @ eigen__0 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h15,assumption,
in @ eigen__1 @ eigen__0,
introduced(assumption,[]) ).
thf(h16,assumption,
sP10,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP5
| ~ sP10
| sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP2 ),
inference(symeq,[status(thm)],]) ).
thf(3,plain,
( sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
~ sP14,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| ~ sP5
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP11
| ~ sP12
| ~ sP2 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP8 ),
inference(symeq,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,h1,h9,h16,h18,h19]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,11,h18,h19]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__2)],[h13,12,h17]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,13,h15,h16]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h12,14,h14]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,15,h12,h13]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h10,16,h11]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,17,h9,h10]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,18,h7,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,19,h5,h6]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,20,h3,h4]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,21,h1,h2]) ).
thf(0,theorem,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setadjoin @ X1 @ X3 )
= ( setadjoin @ X2 @ X4 ) ) ) )
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setunion @ X1 )
= ( setunion @ X2 ) ) )
=> ( sP3
=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU706^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 20:23:39 EDT 2023
% 0.15/0.37 % CPUTime :
% 20.58/20.76 % SZS status Theorem
% 20.58/20.76 % Mode: cade22grackle2x798d
% 20.58/20.76 % Steps: 1462
% 20.58/20.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------