%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM670^1 : 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 : n017.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 02:09:33 PM UTC 2025
% Result : Theorem 150.87s 150.05s
% Output : Proof 150.87s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( pl @ ( pl @ X1 @ X2 ) @ X3 )
= ( pl @ X1 @ ( pl @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( pl @ y @ X1 )
= ( pl @ X1 @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( pl @ y @ eigen__0 )
= ( pl @ eigen__0 @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( pl @ eigen__0 @ y )
= x ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( pl @ ( pl @ eigen__0 @ y ) @ z )
= ( pl @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( pl @ eigen__0 @ ( pl @ y @ z ) )
= ( pl @ ( pl @ y @ z ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( pl @ x @ z )
= ( pl @ ( pl @ y @ z ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( pl @ ( pl @ eigen__0 @ y ) @ X1 )
= ( pl @ eigen__0 @ ( pl @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( pl @ eigen__0 @ X1 )
= ( pl @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat,X2: nat] :
( ( pl @ ( pl @ eigen__0 @ X1 ) @ X2 )
= ( pl @ eigen__0 @ ( pl @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> $false ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat,X2: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( pl @ ( pl @ eigen__0 @ y ) @ z )
= ( pl @ eigen__0 @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( x
= ( pl @ y @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(satz19a,conjecture,
~ sP13 ).
thf(h0,negated_conjecture,
sP13,
inference(assume_negation,[status(cth)],[satz19a]) ).
thf(h1,assumption,
sP15,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| sP11
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP14
| sP7
| ~ sP5
| ~ sP6 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| sP4
| ~ sP3
| sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
~ sP11,
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP13
| ~ sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz6,axiom,
sP12 ).
thf(satz5,axiom,
sP1 ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1,satz6,satz5,h0]) ).
thf(m,axiom,
~ ! [X1: nat] :
( x
!= ( pl @ y @ X1 ) ) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[m,13,h1]) ).
thf(0,theorem,
~ sP13,
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM670^1 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 22:12:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 150.87/150.05 % SZS status Theorem
% 150.87/150.05 % Mode: cade22grackle2x01b3
% 150.87/150.05 % Steps: 45943
% 150.87/150.05 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------