TSTP Solution File: SEV181^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV181^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 18:05:14 EDT 2022
% Result : Theorem 1.99s 2.17s
% Output : Proof 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 42
% Syntax : Number of formulae : 49 ( 10 unt; 2 typ; 3 def)
% Number of atoms : 142 ( 61 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 378 ( 125 ~; 21 |; 0 &; 155 @)
% ( 18 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 86 ( 24 ^ 62 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( ( $i > $o ) > $i ) > $o,X2: ( $i > $o ) > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: ( $i > $o ) > $i] :
~ ( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o > $o] :
( ( X1
@ ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( eigen__0 @ X4 ) )
=> ( X3
!= ( eigen__0 @ X4 ) ) ) )
!= ( eigen__0 @ X2 ) ) ) )
=> ! [X2: $o] :
( ( ( ~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( ( eigen__0
@ ^ [X4: $i] :
~ ! [X5: $i > $o] :
( ~ ( X5 @ ( eigen__0 @ X5 ) )
=> ( X4
!= ( eigen__0 @ X5 ) ) ) )
!= ( eigen__0 @ X3 ) ) ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ~ ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) )
= ( eigen__1
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) )
=> ! [X1: $o] :
( ( ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( eigen__0 @ X4 ) )
=> ( X3
!= ( eigen__0 @ X4 ) ) ) )
!= ( eigen__0 @ X2 ) ) ) )
= X1 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] :
( ( ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( eigen__0 @ X4 ) )
=> ( X3
!= ( eigen__0 @ X4 ) ) ) )
!= ( eigen__0 @ X2 ) ) ) )
= X1 )
=> X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( eigen__1 @ ( eigen__0 @ eigen__1 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1
@ ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP4
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] :
( ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP3
=> ( ( ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ~ ( X2 @ ( eigen__0 @ X2 ) )
=> ( X1
!= ( eigen__0 @ X2 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o] :
( ~ ( X1 @ ( eigen__0 @ X1 ) )
=> ( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( eigen__0 @ X3 ) )
=> ( X2
!= ( eigen__0 @ X3 ) ) ) )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(def_cD_FOR_X5309,definition,
( cD_FOR_X5309
= ( ^ [X1: ( $i > $o ) > $i,X2: $i] :
~ ! [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
=> ( X2
!= ( X1 @ X3 ) ) ) ) ) ).
thf(cTHM143C_pme,conjecture,
! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ~ ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ) ).
thf(h2,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[cTHM143C_pme]) ).
thf(1,plain,
( ~ sP9
| sP10
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP18
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
sP8,
inference(eq_ind,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| ~ sP3
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP7
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP18
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(16,plain,
( sP1
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP15
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X3: $i > $o] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ~ ~ ! [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
=> ( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
=> ( X3
!= ( X1 @ X4 ) ) ) )
!= ( X1 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[19,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV181^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.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 17:06:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.17 % SZS status Theorem
% 1.99/2.17 % Mode: mode506
% 1.99/2.17 % Inferences: 14
% 1.99/2.17 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------