%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU774^2 : 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 : n027.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 02:37:24 PM UTC 2025
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 )
=> ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ( eigen__1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ! [X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X4 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 ) ) ) )
=> ( eigen__1 = X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
=> ( in @ ( kpair @ X1 @ X2 ) @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ eigen__1 ) ) ) )
=> ( eigen__1 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( subset @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP11
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ eigen__0 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_eqbreln,definition,
( eqbreln
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( breln @ X1 @ X2 @ X3 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( breln @ X1 @ X2 @ X4 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X1 )
@ ! [X6: $i] :
( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( in @ X6 @ X2 )
@ ( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( in @ ( kpair @ X5 @ X6 ) @ X3 )
@ ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ) ) )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X1 )
@ ! [X6: $i] :
( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( in @ X6 @ X2 )
@ ( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( in @ ( kpair @ X5 @ X6 ) @ X4 )
@ ( in @ ( kpair @ X5 @ X6 ) @ X3 ) ) ) )
@ ( X3 = X4 ) ) ) ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i,X2: $i] : ( breln @ X1 @ X1 @ X2 ) ) ) ).
thf(eqbreln1,conjecture,
( sP4
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP4
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[eqbreln1]) ).
thf(h1,assumption,
sP4,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h10,assumption,
sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP1
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| ~ sP6
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| ~ sP11
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP10
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| ~ sP2
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP13
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,h1,h5,h8,h10,h12,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,10,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,12,h7]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,13,h5,h6]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,14,h4]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,15,h3]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,16,h1,h2]) ).
thf(0,theorem,
( sP4
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU774^2 : TPTP v9.2.0. Released v3.7.0.
% 0.04/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.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 21:44:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % Mode: cade22grackle2xfee4
% 0.19/0.49 % Steps: 1023
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------