TSTP Solution File: SEU620^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU620^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 13:54:27 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(def_iskpair,definition,
( iskpair
= ( ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(def_kpairiskpair,definition,
( kpairiskpair
= ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ).
thf(def_kpair,definition,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(kpairp,conjecture,
( sP1
=> sP1 ) ).
thf(h0,negated_conjecture,
~ ( sP1
=> sP1 ),
inference(assume_negation,[status(cth)],[kpairp]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h3,h1,h2,h0])],[1,2,h1,h4]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,3,h4]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,4,h3]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).
thf(0,theorem,
( sP1
=> sP1 ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU620^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 06:29:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 2
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------