TSTP Solution File: SEU661^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU661^2 : 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 : n011.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 13:55:41 EDT 2022
% Result : Theorem 0.16s 0.33s
% Output : Proof 0.16s
% 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_in,type,
in: $i > $i > $o ).
thf(cartprodmempaircEq,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodmempaircEq]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( kpair @ X1 @ X2 )
= ( kpair @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ X1 )
= ( kpair @ eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
in @ eigen__2 @ eigen__0,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ X1 )
= ( kpair @ eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( in @ eigen__3 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
= ( kpair @ eigen__2 @ eigen__3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
in @ eigen__3 @ eigen__1,
introduced(assumption,[]) ).
thf(h8,assumption,
( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ eigen__2 @ eigen__3 ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[h8]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,1,h7,h8]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,2,h6]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( kpair @ X3 @ X4 )
= ( kpair @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU661^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 600
% 0.12/0.31 % DateTime : Mon Jun 20 10:48:24 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.16/0.33 % SZS status Theorem
% 0.16/0.33 % Mode: mode213
% 0.16/0.33 % Inferences: 0
% 0.16/0.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------