TSTP Solution File: SEV190^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV190^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 18:05:17 EDT 2022
% Result : Theorem 25.98s 26.23s
% Output : Proof 25.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 55 ( 7 unt; 6 typ; 3 def)
% Number of atoms : 142 ( 11 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 463 ( 92 ~; 22 |; 0 &; 268 @)
% ( 20 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 27 con; 0-3 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 73 ( 5 ^ 68 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_iS,type,
iS: $tType ).
thf(ty_eigen__2,type,
eigen__2: iS ).
thf(ty_cP,type,
cP: iS > iS > iS ).
thf(ty_eigen__1,type,
eigen__1: iS ).
thf(ty_cJOIN,type,
cJOIN: iS > iS > iS > $o ).
thf(ty_c0,type,
c0: iS ).
thf(h0,assumption,
! [X1: iS > $o,X2: iS] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: iS] :
~ ! [X2: iS] :
( ~ ( ( cJOIN @ X1 @ X1 @ X1 )
=> ~ ( cJOIN @ X2 @ X2 @ X2 ) )
=> ( cJOIN @ ( cP @ X1 @ X2 ) @ ( cP @ X1 @ X2 ) @ ( cP @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: iS] :
~ ( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ X1 @ X1 @ X1 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ( ~ ( ! [X1: iS] : ( cJOIN @ X1 @ c0 @ X1 )
=> ~ ! [X1: iS] : ( cJOIN @ c0 @ X1 @ X1 ) )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS,X5: iS,X6: iS] :
( ~ ( ( cJOIN @ X1 @ X2 @ X3 )
=> ~ ( cJOIN @ X4 @ X5 @ X6 ) )
=> ( cJOIN @ ( cP @ X1 @ X4 ) @ ( cP @ X2 @ X5 ) @ ( cP @ X3 @ X6 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: iS,X2: iS,X3: iS] :
( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ X1 @ X2 @ X3 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X2 ) @ ( cP @ eigen__1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS,X5: iS,X6: iS] :
( ~ ( ( cJOIN @ X1 @ X2 @ X3 )
=> ~ ( cJOIN @ X4 @ X5 @ X6 ) )
=> ( cJOIN @ ( cP @ X1 @ X4 ) @ ( cP @ X2 @ X5 ) @ ( cP @ X3 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: iS] :
( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ eigen__2 @ eigen__2 @ X1 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__2 ) @ ( cP @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS,X5: iS] :
( ~ ( ( cJOIN @ eigen__1 @ X1 @ X2 )
=> ~ ( cJOIN @ X3 @ X4 @ X5 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ X3 ) @ ( cP @ X1 @ X4 ) @ ( cP @ X2 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ! [X1: iS] : ( cJOIN @ X1 @ c0 @ X1 )
=> ~ ! [X1: iS] : ( cJOIN @ c0 @ X1 @ X1 ) )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ eigen__2 @ eigen__2 @ eigen__2 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__2 ) @ ( cP @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: iS,X2: iS] :
( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ eigen__2 @ X1 @ X2 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ eigen__2 ) @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: iS,X2: iS] :
( ~ ( ( cJOIN @ X1 @ X1 @ X1 )
=> ~ ( cJOIN @ X2 @ X2 @ X2 ) )
=> ( cJOIN @ ( cP @ X1 @ X2 ) @ ( cP @ X1 @ X2 ) @ ( cP @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: iS] : ( cJOIN @ X1 @ c0 @ X1 )
=> ~ ! [X1: iS] : ( cJOIN @ c0 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ X1 )
=> ~ ( cJOIN @ X2 @ X3 @ X4 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ X2 ) @ ( cP @ eigen__1 @ X3 ) @ ( cP @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( cJOIN @ c0 @ c0 @ c0 )
=> ~ sP9 )
=> ! [X1: iS] : ( cJOIN @ X1 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: iS] : ( cJOIN @ X1 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: iS] :
( ~ ( ( cJOIN @ eigen__1 @ eigen__1 @ eigen__1 )
=> ~ ( cJOIN @ X1 @ X1 @ X1 ) )
=> ( cJOIN @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X1 ) @ ( cP @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP1
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: iS > $o] :
( ~ ( ( X1 @ c0 )
=> ~ ! [X2: iS,X3: iS] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( cJOIN @ c0 @ c0 @ c0 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cJOIN @ c0 @ c0 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
=> ~ ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: iS] : ( cJOIN @ c0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_cS_JOIN_CLOS,definition,
( cS_JOIN_CLOS
= ( ^ [X1: iS,X2: iS > iS > iS,X3: iS > iS > iS > $o] :
~ ( ~ ( ! [X4: iS] : ( X3 @ X4 @ X1 @ X4 )
=> ~ ! [X4: iS] : ( X3 @ X1 @ X4 @ X4 ) )
=> ~ ! [X4: iS,X5: iS,X6: iS,X7: iS,X8: iS,X9: iS] :
( ~ ( ( X3 @ X4 @ X5 @ X6 )
=> ~ ( X3 @ X7 @ X8 @ X9 ) )
=> ( X3 @ ( X2 @ X4 @ X7 ) @ ( X2 @ X5 @ X8 ) @ ( X2 @ X6 @ X9 ) ) ) ) ) ) ).
thf(cTHM580_pme,conjecture,
( ~ ( ~ sP19
=> ~ ~ sP6 )
=> sP13 ) ).
thf(h1,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[cTHM580_pme]) ).
thf(1,plain,
( ~ sP20
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP14
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(9,plain,
( sP9
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(10,plain,
( sP10
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| sP17
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP17
| ~ sP18
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP6
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP19
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP1
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP15
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h1]) ).
thf(22,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[21,h0]) ).
thf(0,theorem,
( ~ ( ~ sP19
=> ~ ~ sP6 )
=> sP13 ),
inference(contra,[status(thm),contra(discharge,[h1])],[21,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV190^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.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 07:59:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 25.98/26.23 % SZS status Theorem
% 25.98/26.23 % Mode: mode454
% 25.98/26.23 % Inferences: 27
% 25.98/26.23 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------