%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU697^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 02:45:41 PM UTC 2025
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(def_lam,definition,
( lam
= ( ^ [X1: $i,X2: $i,X3: $i > $i] :
( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ) ).
thf(lam2lamEq,conjecture,
! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
= ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
= ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[lam2lamEq]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( dpsetconstr @ eigen__0 @ X1
@ ^ [X3: $i] : ( (=) @ ( X2 @ X3 ) ) )
= ( dpsetconstr @ eigen__0 @ X1
@ ^ [X3: $i] : ( (=) @ ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ ( X1 @ X2 ) @ eigen__1 ) )
=> ( ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( X1 @ X2 ) ) )
= ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X2: $i] : ( (=) @ ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( eigen__2 @ X1 ) @ eigen__1 ) )
=> ( ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) )
= ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ ( eigen__2 @ X1 ) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) )
!= ( dpsetconstr @ eigen__0 @ eigen__1
@ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[h5]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,1,h4,h5]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,2,h3]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
= ( dpsetconstr @ X1 @ X2
@ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU697^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n012.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 21:06:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------