TSTP Solution File: SEV165^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV165^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 18:05:10 EDT 2022
% Result : Theorem 63.11s 63.50s
% Output : Proof 63.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 19
% Syntax : Number of formulae : 28 ( 13 unt; 4 typ; 4 def)
% Number of atoms : 69 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 136 ( 51 ~; 5 |; 0 &; 53 @)
% ( 6 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 30 ( 5 ^ 25 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__436,type,
eigen__436: $i > $o ).
thf(ty_eigen__35,type,
eigen__35: $i > $o ).
thf(ty_eigen__437,type,
eigen__437: $i ).
thf(ty_eigen__438,type,
eigen__438: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__436,definition,
( eigen__436
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i,X3: $i] :
( ( ~ ( ( eigen__35 @ X2 )
=> ~ ( X1 @ X3 ) ) )
= ( ~ ( ( eigen__35 @ X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__436])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__438,definition,
( eigen__438
= ( eps__1
@ ^ [X1: $i] :
( ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ X1 ) ) )
!= ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__438])]) ).
thf(eigendef_eigen__437,definition,
( eigen__437
= ( eps__1
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( ~ ( ( eigen__35 @ X1 )
=> ~ ( eigen__436 @ X2 ) ) )
= ( ~ ( ( eigen__35 @ X1 )
=> ~ ( eigen__436 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__437])]) ).
thf(eigendef_eigen__35,definition,
( eigen__35
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i,X4: $i] :
( ( ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) )
= ( ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__35])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ~ ( ( eigen__35 @ X1 )
=> ~ ( eigen__436 @ X2 ) ) )
= ( ~ ( ( eigen__35 @ X1 )
=> ~ ( eigen__436 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ( ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) )
= ( ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ( ~ ( ( eigen__35 @ X2 )
=> ~ ( X1 @ X3 ) ) )
= ( ~ ( ( eigen__35 @ X2 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ X1 ) ) )
= ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > ( ( $i > $i > $i ) > $i ) > $o] :
~ ! [X2: $i > $o,X3: $i > $o,X4: $i,X5: $i] :
( ( X1 @ X2 @ X3
@ ^ [X6: $i > $i > $i] : ( X6 @ X4 @ X5 ) )
= ( ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ eigen__438 ) ) )
= ( ~ ( ( eigen__35 @ eigen__437 )
=> ~ ( eigen__436 @ eigen__438 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(cEXISTS_CART_SET_PROD_pme,conjecture,
~ sP5 ).
thf(h2,negated_conjecture,
sP5,
inference(assume_negation,[status(cth)],[cEXISTS_CART_SET_PROD_pme]) ).
thf(1,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__438]) ).
thf(3,plain,
( sP1
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__437]) ).
thf(4,plain,
( sP3
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__436]) ).
thf(5,plain,
( sP2
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__35]) ).
thf(6,plain,
( ~ sP5
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,h2]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[7,h1]) ).
thf(9,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[8,h0]) ).
thf(0,theorem,
~ sP5,
inference(contra,[status(thm),contra(discharge,[h2])],[7,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV165^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 14:50:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 63.11/63.50 % SZS status Theorem
% 63.11/63.50 % Mode: mode510
% 63.11/63.50 % Inferences: 3626
% 63.11/63.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------