TSTP Solution File: SEV258^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV258^5 : 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 : n008.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 18:05:36 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__2,type,
eigen__2: ( a > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__5,type,
eigen__5: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a > $o ).
thf(cDISCRETE_TOPOLOGY_pme,conjecture,
~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ $false )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ~ $false ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ $false
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ~ $false ) ) ).
thf(h0,negated_conjecture,
( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ $false )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ~ $false ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ $false
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ~ $false ) ),
inference(assume_negation,[status(cth)],[cDISCRETE_TOPOLOGY_pme]) ).
thf(h1,assumption,
( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ $false )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ~ $false ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ $false
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ $false )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( eigen__0
= ( ^ [X1: a] : $false ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h8,assumption,
( eigen__0
= ( ^ [X1: a] : $false ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
$false,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h8,h9,h7,h5,h3,h1,h0])],[h9]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,1,h8,h9]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h5,2,h7]) ).
thf(h10,assumption,
~ ( ( eigen__1
= ( ^ [X1: a] : ~ $false ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h11,assumption,
( eigen__1
= ( ^ [X1: a] : ~ $false ) ),
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_false,[status(thm),assumptions([h11,h9,h10,h6,h3,h1,h0])],[h9]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h6,h3,h1,h0]),tab_negimp(discharge,[h11,h9])],[h10,4,h11,h9]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h6,5,h10]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h3,3,6,h5,h6]) ).
thf(h12,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a > $o] :
( ( eigen__2 @ X2 )
=> ~ $false )
=> ( X1
!= ( ^ [X2: a] :
~ ! [X3: a > $o] :
( ( eigen__2 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ! [X1: a > $o] :
( ( eigen__2 @ X1 )
=> ~ $false )
=> ( eigen__3
!= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ( eigen__2 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ! [X1: a > $o] :
( ( eigen__2 @ X1 )
=> ~ $false )
=> ( eigen__3
!= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ( eigen__2 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
! [X1: a > $o] :
( ( eigen__2 @ X1 )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h16,assumption,
( eigen__3
= ( ^ [X1: a] :
~ ! [X2: a > $o] :
( ( eigen__2 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(8,plain,
$false,
inference(tab_false,[status(thm),assumptions([h15,h16,h14,h9,h13,h12,h4,h1,h0])],[h9]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h9,h13,h12,h4,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,8,h15,h16]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h4,h1,h0]),tab_negimp(discharge,[h14,h9])],[h13,9,h14,h9]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h4,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,10,h13]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h4,11,h12]) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,7,12,h3,h4]) ).
thf(h17,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ $false
=> ( X2
!= ( ^ [X3: a] :
~ ( ( eigen__4 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ! [X1: a > $o] :
( ~ ( ~ $false
=> ( X1
!= ( ^ [X2: a] :
~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__5 @ X2 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ $false
=> ( eigen__6
!= ( ^ [X1: a] :
~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__5 @ X1 ) ) ) ) )
=> ~ $false ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ $false
=> ( eigen__6
!= ( ^ [X1: a] :
~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__5 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ $false,
introduced(assumption,[]) ).
thf(h22,assumption,
( eigen__6
= ( ^ [X1: a] :
~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__5 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(14,plain,
$false,
inference(tab_false,[status(thm),assumptions([h21,h22,h20,h9,h19,h18,h17,h2,h0])],[h9]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h9,h19,h18,h17,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,14,h21,h22]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h18,h17,h2,h0]),tab_negimp(discharge,[h20,h9])],[h19,15,h20,h9]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h17,h2,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,16,h19]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,17,h18]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h2,18,h17]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,13,19,h1,h2]) ).
thf(0,theorem,
~ ( ~ ( ~ ( ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : $false ) )
=> ~ $false )
=> ~ ! [X1: a > $o] :
( ( X1
= ( ^ [X2: a] : ~ $false ) )
=> ~ $false ) )
=> ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ( X1 @ X3 )
=> ~ $false )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ~ $false ) )
=> ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ~ $false
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ~ $false ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV258^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 14:32:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 0
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------