%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN000^1 : 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 : n028.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 03:16:05 PM UTC 2025
% Result : Theorem 0.47s 0.69s
% Output : Proof 0.47s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_a,type,
a: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_g,type,
g: $i > $i > $i > $i ).
thf(ty_f,type,
f: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( p @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( p @ h ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(role_conjecture,conjecture,
~ sP1 ).
thf(h0,negated_conjecture,
sP1,
inference(assume_negation,[status(cth)],[role_conjecture]) ).
thf(h1,assumption,
! [X1: $i,X2: $i] :
( ~ ( ( ( f @ eigen__0 )
!= ( g @ X1 @ ( f @ eigen__0 ) @ X2 ) )
=> ( ( f @ ( f @ ( f @ b ) ) )
!= a ) )
=> ( X1
= ( f @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(role_hypothesis,axiom,
sP2 ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,h0,role_hypothesis]) ).
thf(equality,axiom,
~ ! [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( ( f @ X1 )
!= ( g @ X2 @ ( f @ X1 ) @ X3 ) )
=> ( ( f @ ( f @ ( f @ b ) ) )
!= a ) )
=> ( X2
= ( f @ X1 ) ) ) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[equality,2,h1]) ).
thf(0,theorem,
~ sP1,
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN000^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Oct 8 15:10:23 EDT 2025
% 0.14/0.33 % CPUTime :
% 0.47/0.69 % SZS status Theorem
% 0.47/0.69 % Mode: cade22grackle2xfee4
% 0.47/0.69 % Steps: 10514
% 0.47/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------