%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG259^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 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 01:11:35 PM UTC 2025
% Result : Theorem 0.22s 0.48s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_id,type,
id: subst ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_eigen__2,type,
eigen__2: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_eigen__0,type,
eigen__0: subst > term > term ).
thf(ty_one,type,
one: term ).
thf(ty_sh,type,
sh: subst ).
thf(ty_ap,type,
ap: term > term > term ).
thf(sP1,plain,
( sP1
<=> ! [X1: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ eigen__1 @ id ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: term,X2: term,X3: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( lam @ ( eigen__0 @ sh @ one ) )
= ( ap @ ( sub @ eigen__1 @ id ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: term,X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_lamnotap,definition,
( lamnotap
= ( ! [X1: term,X2: term,X3: term] :
( (~)
@ ( ( lam @ X1 )
= ( ap @ X2 @ X3 ) ) ) ) ) ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst,X4: term] : ( ap @ ( sub @ X2 @ X3 ) @ X4 ) ) ) ).
thf(def_hoaslam,definition,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).
thf(def_hoaslamnotap,definition,
( hoaslamnotap
= ( ! [X1: subst > term > term] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
@ ! [X2: term,X3: term] :
( (~)
@ ( ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X1 @ X4 @ X5 ) )
= ( hoasap @ id @ X2 @ id @ X3 ) ) ) ) ) ) ).
thf(def_hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ lamnotap
@ hoaslamnotap ) ) ).
thf(thm,conjecture,
( sP2
=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X1: term,X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ X1 @ id ) @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( eigen__0 @ X1 @ X2 ) @ X3 )
= ( eigen__0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: term,X2: term] :
( ( lam @ ( eigen__0 @ sh @ one ) )
!= ( ap @ ( sub @ X1 @ id ) @ X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h6,h4,h5,h3,h1,h2,h0])],[1,2,3,h1,h7]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,4,h7]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,5,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,6,h4,h5]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,7,h3]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,8,h1,h2]) ).
thf(0,theorem,
( sP2
=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ! [X2: term,X3: term] :
( ( lam @ ( X1 @ sh @ one ) )
!= ( ap @ ( sub @ X2 @ id ) @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG259^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 23:26:53 EDT 2025
% 0.22/0.36 % CPUTime :
% 0.22/0.48 % SZS status Theorem
% 0.22/0.48 % Mode: cade22sinegrackle2x6978
% 0.22/0.48 % Steps: 611
% 0.22/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------