%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM648^1 : 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 : n003.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 02:09:27 PM UTC 2025
% Result : Theorem 20.25s 20.51s
% Output : Proof 20.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_y,type,
y: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(sP1,plain,
( sP1
<=> ( x
= ( pl @ y @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( ( pl @ y @ eigen__0 )
= ( pl @ y @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( pl @ y @ eigen__0 )
= ( pl @ y @ eigen__1 ) )
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( pl @ y @ eigen__0 )
= ( pl @ y @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( x
= ( pl @ y @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat,X2: nat] :
( ( ( pl @ y @ X1 )
= ( pl @ y @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( ( pl @ X1 @ X2 )
= ( pl @ X1 @ X3 ) )
=> ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(satz8b,conjecture,
! [X1: nat,X2: nat] :
( ( x
= ( pl @ y @ X1 ) )
=> ( ( x
= ( pl @ y @ X2 ) )
=> ( X1 = X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: nat,X2: nat] :
( ( x
= ( pl @ y @ X1 ) )
=> ( ( x
= ( pl @ y @ X2 ) )
=> ( X1 = X2 ) ) ),
inference(assume_negation,[status(cth)],[satz8b]) ).
thf(h1,assumption,
~ ! [X1: nat] :
( sP5
=> ( ( x
= ( pl @ y @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ( sP1
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP4
| ~ sP5
| ~ sP1 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP3
| ~ sP4
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz8a,axiom,
sP8 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,satz8a,h3,h5,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,6,h5,h6]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: nat,X2: nat] :
( ( x
= ( pl @ y @ X1 ) )
=> ( ( x
= ( pl @ y @ X2 ) )
=> ( X1 = X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM648^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 23:10:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 20.25/20.51 % SZS status Theorem
% 20.25/20.51 % Mode: cade22grackle2x798d
% 20.25/20.51 % Steps: 674
% 20.25/20.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------