TSTP Solution File: SEU768^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU768^2 : 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 : n029.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 14:02:45 EDT 2022
% Result : Theorem 1.96s 2.20s
% Output : Proof 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 25 ( 10 unt; 5 typ; 4 def)
% Number of atoms : 63 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 171 ( 6 ~; 5 |; 0 &; 117 @)
% ( 5 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 43 ( 5 ^ 38 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_brelnall2,definition,
( brelnall2
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( breln @ X1 @ X2 @ X3 )
=> ! [X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( X4 @ X5 ) ) ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i] : ( breln @ X1 @ X1 ) ) ) ).
thf(breln1all2,conjecture,
sP4 ).
thf(h1,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[breln1all2]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(4,plain,
( sP4
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU768^2 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 10:48:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.20 % SZS status Theorem
% 1.96/2.20 % Mode: mode506
% 1.96/2.20 % Inferences: 19462
% 1.96/2.20 % SZS output start Proof
% See solution above
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