%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU796^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 Oct 9 02:38:48 PM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_image1,type,
image1: $i > ( $i > $i ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ ( image1 @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
= ( ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__2
!= ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( image1 @ eigen__0 @ eigen__1 ) )
= ( ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3 @ ( image1 @ X1 @ X2 ) )
= ( ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__2
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $i,X2: $i] :
( ( in @ X2 @ ( image1 @ eigen__0 @ X1 ) )
= ( ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_image1Equiv,definition,
( image1Equiv
= ( ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3
@ ( image1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
<=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( X3
= ( X2 @ X4 ) ) ) ) ) ) ).
thf(image1E,conjecture,
( sP4
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3 @ ( image1 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP4
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3 @ ( image1 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[image1E]) ).
thf(h1,assumption,
sP4,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3 @ ( image1 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $i,X2: $i] :
( ( in @ X2 @ ( image1 @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X2
!= ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( image1 @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( X1
!= ( eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP1
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h2,h0])],[1,2,3,4,h1,h6,h7]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,5,h6,h7]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,6,h5]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,7,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( sP4
=> ! [X1: $i,X2: $i > $i,X3: $i] :
( ( in @ X3 @ ( image1 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X3
!= ( X2 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU796^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 21:29:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: cade22grackle2xfee4
% 0.20/0.41 % Steps: 48
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------