TSTP Solution File: SEV079^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV079^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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
% DateTime : Tue Mar 30 22:04:55 EDT 2021
% Result : Theorem 0.12s
% Output : Proof 0.12s
% Verified :
% SZS Type : None (MakeTreeStats fails)
% Syntax : Number of formulae : 31
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ( eigen__1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(cTRANS_ID_pme,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ),
inference(assume_negation,[status(cth)],[cTRANS_ID_pme]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 = X1 )
=> ( X1 != X2 ) )
=> ( eigen__0 = X2 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ~ ( sP4
=> ( eigen__1 != X1 ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP4
=> ~ sP1 )
=> sP5 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP4
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP5
| ~ sP7
| ~ sP1 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
sP2,
inference(eq_sym,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,h6,h7,h5]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,6,h6,h7]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,7,h4,h5]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,8,h3]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,9,h2]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( X1 = X2 )
=> ( X2 != X3 ) )
=> ( X1 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV079^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.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 : Fri Mar 26 14:27:01 EDT 2021
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 4
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.12/0.36 % SZS output end Proof
%------------------------------------------------------------------------------