TSTP Solution File: SEU828^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU828^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : 300s
% DateTime : Thu Aug 31 17:37:35 EDT 2023
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
~ ( eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0
= ( ^ [X1: $i] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_seteq,definition,
( seteq
= ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
! [X3: $i > $o] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ) ) ).
thf(def_subseteq,definition,
( subseteq
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_powerset,definition,
( powerset
= ( ^ [X1: $i > $o,X2: $i > $o] : ( subseteq @ X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(conj,conjecture,
! [X1: $i > $o] :
( ( ! [X2: $i] :
~ ( X1 @ X2 ) )
= ( X1
= ( ^ [X2: $i] : $false ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o] :
( ( ! [X2: $i] :
~ ( X1 @ X2 ) )
= ( X1
= ( ^ [X2: $i] : $false ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
sP1 != sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
= $false ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP3,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h6,h2,h3,h1,h0])],[1,h2,h7]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,2,h7]) ).
thf(4,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h3,h1,h0]),tab_fe(discharge,[h6])],[h3,3,h6]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP1
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h4,h5,h1,h0])],[5,6,h8,h5]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h4,7,h8]) ).
thf(9,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,4,8,h2,h3,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).
thf(0,theorem,
! [X1: $i > $o] :
( ( ! [X2: $i] :
~ ( X1 @ X2 ) )
= ( X1
= ( ^ [X2: $i] : $false ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU828^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 12:22:23 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % Mode: cade22grackle2xfee4
% 0.19/0.39 % Steps: 12
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------