TSTP Solution File: SEU663^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU663^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n009.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 : 600s
% DateTime : Tue Jul 19 13:55:51 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $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(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ksnd @ ( kpair @ eigen__2 @ eigen__3 ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(def_ksndpairEq,definition,
ksndpairEq = sP1 ).
thf(def_cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ).
thf(cartprodsndpairEq,conjecture,
( sP1
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP1
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) )
=> ! [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,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) )
=> ! [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,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
in @ eigen__2 @ eigen__0,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( ksnd @ ( kpair @ eigen__2 @ X1 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( in @ eigen__3 @ eigen__1 )
=> sP3 ),
introduced(assumption,[]) ).
thf(h11,assumption,
in @ eigen__3 @ eigen__1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,h1,h12]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,3,h11,h12]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,4,h10]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,5,h8,h9]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,6,h7]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,7,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,8,h5]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( sP1
=> ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) )
=> ! [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])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU663^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 04:05:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % Mode: mode213
% 0.13/0.38 % Inferences: 5
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------