TSTP Solution File: SEU795^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU795^2 : 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 : n026.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 17:31:13 EDT 2023
% Result : Theorem 20.19s 20.50s
% Output : Proof 20.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_descr,type,
descr: ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i > $i] :
~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X4
!= ( X2 @ X5 ) ) ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) )
=> ( X3 = X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( X1 @ X4 ) ) ) ) )
=> ~ ! [X3: $i] :
( ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( X4
!= ( X1 @ X5 ) ) ) ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) )
=> ~ ! [X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1
@ ( descr
@ ^ [X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X2 )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( X3
!= ( eigen__1 @ X4 ) ) ) ) ) ) )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__2
@ ( descr
@ ^ [X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X1 )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( eigen__1 @ X3 ) ) ) ) ) ) )
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__2
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP3
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) )
=> ( X1 @ ( descr @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ).
thf(def_descrp,definition,
( descrp
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( X1
@ ( descr
@ ^ [X2: $i] : ( 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_image1Ex1,definition,
( image1Ex1
= ( ! [X1: $i,X2: $i > $i] :
( exu
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
<=> ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( X4
= ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(def_image1,definition,
( image1
= ( ^ [X1: $i,X2: $i > $i] :
( descr
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
<=> ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( X4
= ( X2 @ X5 ) ) ) ) ) ) ) ).
thf(image1Equiv,conjecture,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP1
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP1
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[image1Equiv]) ).
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 ) ) ) )
=> ( sP1
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ),
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,
~ ( sP1
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i > $i,X2: $i] :
( ( in @ X2
@ ( descr
@ ^ [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ( X4
!= ( X1 @ X5 ) ) ) ) ) ) )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP3
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,h1,h5,h9]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,6,h9]) ).
thf(8,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)],[h7,7,h8]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,8,h7]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,9,h5,h6]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,10,h3,h4]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).
thf(0,theorem,
( sP7
=> ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( in @ X3 @ X1 )
= ( in @ X4 @ X2 ) ) ) )
=> ( sP1
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( descr
@ ^ [X4: $i] :
! [X5: $i] :
( ( in @ X5 @ X4 )
= ( ~ ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( X5
!= ( X2 @ X6 ) ) ) ) ) ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU795^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.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 : 300
% 0.13/0.34 % DateTime : Wed Aug 23 13:26:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 20.19/20.50 % SZS status Theorem
% 20.19/20.50 % Mode: cade22grackle2x798d
% 20.19/20.50 % Steps: 61
% 20.19/20.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------