TSTP Solution File: SEU663^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU663^2 : TPTP v8.1.2. 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 Aug 31 17:20:52 EDT 2023
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_ksnd,type,
ksnd: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ksnd @ ( kpair @ eigen__2 @ eigen__3 ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(def_ksndpairEq,definition,
ksndpairEq = sP3 ).
thf(def_cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X2 )
@ ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ).
thf(cartprodsndpairEq,conjecture,
( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodsndpairEq]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
in @ eigen__2 @ eigen__0,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( in @ eigen__3 @ eigen__1 )
=> sP2 ),
introduced(assumption,[]) ).
thf(h9,assumption,
in @ eigen__3 @ eigen__1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[1,2,h1,h10]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,3,h9,h10]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,4,h8]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,5,h6,h7]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,6,h5]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,7,h4]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU663^2 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 14:38:03 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % Mode: cade22grackle2xfee4
% 0.22/0.42 % Steps: 8
% 0.22/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------