%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP010^2 : TPTP v9.2.0. Bugfixed v7.5.0.
% 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 : 300s
% DateTime : Thu Oct 9 01:46:28 PM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Derivation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 229 ( 25 ~; 0 |; 0 &; 190 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_del,type,
del: $tType ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_mem,type,
mem: $i > del > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_c_2Ecardinal_2Ecardleq,type,
c_2Ecardinal_2Ecardleq: del > del > $i ).
thf(ty_eigen__1,type,
eigen__1: del ).
thf(ty_eigen__0,type,
eigen__0: del ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_ap,type,
ap: $i > $i > $i ).
thf(ty_bool,type,
bool: del ).
thf(ty_arr,type,
arr: del > del > del ).
thf(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ecardinal_2ECARD__NOT__LE]) ).
thf(h1,assumption,
~ ! [X1: del,X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__0 @ bool ) )
=> ! [X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ X1 ) @ X2 ) @ X3 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ X1 ) @ X2 ) @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__0 @ bool ) )
=> ! [X2: $i] :
( ( mem @ X2 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ X1 ) @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( mem @ eigen__2 @ ( arr @ eigen__0 @ bool ) )
=> ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
mem @ eigen__2 @ ( arr @ eigen__0 @ bool ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( mem @ X1 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( mem @ eigen__3 @ ( arr @ eigen__1 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
mem @ eigen__3 @ ( arr @ eigen__1 @ bool ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ eigen__2 ) @ eigen__3 ) ) )
!= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ eigen__0 @ eigen__1 ) @ 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: del,X2: del,X3: $i] :
( ( mem @ X3 @ ( arr @ X1 @ bool ) )
=> ! [X4: $i] :
( ( mem @ X4 @ ( arr @ X2 @ bool ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) )
= ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ X1 @ X2 ) @ X3 ) @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP010^2 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n011.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 : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:01:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % Mode: mode213
% 0.20/0.37 % Inferences: 0
% 0.20/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------