TSTP Solution File: SEU974^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU974^5 : 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 : 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 14:11:06 EDT 2022
% Result : Theorem 1.94s 2.21s
% Output : Proof 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 39
% Syntax : Number of formulae : 47 ( 11 unt; 8 typ; 3 def)
% Number of atoms : 121 ( 46 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 531 ( 120 ~; 16 |; 0 &; 286 @)
% ( 14 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 59 ( 3 ^ 56 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_cL,type,
cL: a > a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cR,type,
cR: a > a ).
thf(ty_cZ,type,
cZ: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ! [X2: a > $o] :
( ( X2 @ ( cP @ eigen__0 @ X1 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) )
=> ~ ! [X2: a > $o] :
( ( X2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ! [X3: a > $o] :
( ( X3 @ ( cP @ X1 @ X2 ) )
=> ~ ! [X4: a,X5: a] :
( ( X3 @ ( cP @ X4 @ X5 ) )
=> ~ ( ~ ( ( ( X5 = cZ )
=> ( X4 = cZ ) )
=> ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
=> ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
=> ~ ! [X3: a > $o] :
( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( X3 @ ( cP @ X4 @ X5 ) )
=> ~ ( ~ ( ( ( X5 = cZ )
=> ( X4 = cZ ) )
=> ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
=> ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X3 = cZ )
=> ( X2 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ( X1 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X3 = cZ )
=> ( X2 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a] :
( ( eigen__2 @ ( cP @ X1 @ X2 ) )
=> ~ ( ~ ( ( ( X2 = cZ )
=> ( X1 = cZ ) )
=> ~ ( eigen__2 @ ( cP @ ( cL @ X1 ) @ ( cL @ X2 ) ) ) )
=> ~ ( eigen__2 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ! [X1: a > $o] :
( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X3 = cZ )
=> ( X2 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o] :
( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X3 = cZ )
=> ( X2 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) )
=> ~ ( ~ ( ( ( eigen__1 = cZ )
=> ( eigen__0 = cZ ) )
=> ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ eigen__1 ) ) ) )
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a] :
( ~ ! [X3: a > $o] :
( ( X3 @ ( cP @ X1 @ X2 ) )
=> ~ ! [X4: a,X5: a] :
( ( X3 @ ( cP @ X4 @ X5 ) )
=> ~ ( ~ ( ( ( X5 = cZ )
=> ( X4 = cZ ) )
=> ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
=> ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
=> ~ ! [X3: a > $o] :
( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( X3 @ ( cP @ X4 @ X5 ) )
=> ~ ( ~ ( ( ( X5 = cZ )
=> ( X4 = cZ ) )
=> ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
=> ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
= cZ )
=> ( ( cR @ cZ )
!= cZ ) )
=> ~ ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( ( X1 != cZ ) )
= ( X1
= ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ~ ( ~ ( ( ( X2 = cZ )
= ( X3 = cZ ) )
=> ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
=> ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
=> ! [X2: a,X3: a] :
( ( X1 @ ( cP @ X2 @ X3 ) )
=> ( X2 = X3 ) ) ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP8
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__2 @ ( cP @ eigen__0 @ X1 ) )
=> ~ ( ~ ( ( ( X1 = cZ )
=> ( eigen__0 = cZ ) )
=> ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ X1 ) ) ) )
=> ~ ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( ( eigen__1 = cZ )
=> ( eigen__0 = cZ ) )
=> ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ eigen__1 ) ) ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ~ ! [X2: a > $o] :
( ( X2 @ ( cP @ eigen__0 @ X1 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) )
=> ~ ! [X2: a > $o] :
( ( X2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( cP @ X3 @ X4 ) )
=> ~ ( ~ ( ( ( X4 = cZ )
=> ( X3 = cZ ) )
=> ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
=> ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cPU_LEM2C_pme,conjecture,
sP10 ).
thf(h2,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[cPU_LEM2C_pme]) ).
thf(1,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP8
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| ~ sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP4
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(10,plain,
( sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP14
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(13,plain,
( sP9
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(14,plain,
( sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,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,h2]) ).
thf(16,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[15,h1]) ).
thf(17,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[16,h0]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h2])],[15,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU974^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n024.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 : 600
% 0.12/0.34 % DateTime : Sun Jun 19 02:51:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.94/2.21 % SZS status Theorem
% 1.94/2.21 % Mode: mode506
% 1.94/2.21 % Inferences: 19477
% 1.94/2.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------