TSTP Solution File: SEV259^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV259^5 : 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 : 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 18:05:37 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(ty_eigen__1,type,
eigen__1: b > $o ).
thf(ty_eigen__0,type,
eigen__0: ( b > $o ) > $o ).
thf(ty_eigen__3,type,
eigen__3: b > $o ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__1 @ eigen__2 )
=> ( eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
( ( eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(cCLOSURE_THM0_pme,conjecture,
! [X1: ( b > $o ) > $o] :
( ~ ( ~ ( ~ ( ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : $false ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : ~ $false ) )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ~ ( ! [X4: b > $o] :
( ( X2 @ X4 )
=> ( X1 @ X4 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ! [X5: b > $o] :
( ( X2 @ X5 )
=> ~ ( X5 @ X4 ) ) ) ) )
=> ( X1 @ X3 ) ) )
=> ~ ! [X2: b > $o,X3: b > $o,X4: b > $o] :
( ~ ( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X4
!= ( ^ [X5: b] :
~ ( ( X2 @ X5 )
=> ~ ( X3 @ X5 ) ) ) ) )
=> ( X1 @ X4 ) ) )
=> ! [X2: b > $o,X3: b] :
( ( X2 @ X3 )
=> ! [X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X1 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( b > $o ) > $o] :
( ~ ( ~ ( ~ ( ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : $false ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : ~ $false ) )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ~ ( ! [X4: b > $o] :
( ( X2 @ X4 )
=> ( X1 @ X4 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ! [X5: b > $o] :
( ( X2 @ X5 )
=> ~ ( X5 @ X4 ) ) ) ) )
=> ( X1 @ X3 ) ) )
=> ~ ! [X2: b > $o,X3: b > $o,X4: b > $o] :
( ~ ( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X4
!= ( ^ [X5: b] :
~ ( ( X2 @ X5 )
=> ~ ( X3 @ X5 ) ) ) ) )
=> ( X1 @ X4 ) ) )
=> ! [X2: b > $o,X3: b] :
( ( X2 @ X3 )
=> ! [X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X1 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cCLOSURE_THM0_pme]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ! [X3: b > $o] :
( ~ ( ! [X4: b] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] :
~ ( X3 @ X5 ) ) )
=> ( eigen__0 @ X4 ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ~ ! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: b > $o,X2: b] :
( ( X1 @ X2 )
=> ! [X3: b > $o] :
( ~ ( ! [X4: b] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: b > $o] :
( ( X4
= ( ^ [X5: b] :
~ ( X3 @ X5 ) ) )
=> ( eigen__0 @ X4 ) ) )
=> ( X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) )
=> ~ ! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: b > $o,X2: b > $o,X3: b > $o] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( eigen__0 @ X3 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__0 @ X1 ) )
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ~ ( ! [X3: b > $o] :
( ( X1 @ X3 )
=> ( eigen__0 @ X3 ) )
=> ( X2
!= ( ^ [X3: b] :
~ ! [X4: b > $o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( eigen__0 @ X2 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : $false ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] : ~ $false ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: b] :
( ( eigen__1 @ X1 )
=> ! [X2: b > $o] :
( ~ ( ! [X3: b] :
( ( eigen__1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: b > $o] :
( ( X3
= ( ^ [X4: b] :
~ ( X2 @ X4 ) ) )
=> ( eigen__0 @ X3 ) ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP4
=> ! [X1: b > $o] :
( ~ ( ! [X2: b] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] :
~ ( X1 @ X3 ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP4,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: b > $o] :
( ~ ( ! [X2: b] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] :
~ ( X1 @ X3 ) ) )
=> ( eigen__0 @ X2 ) ) )
=> ( X1 @ eigen__2 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP2
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] :
~ ( eigen__3 @ X2 ) ) )
=> ( eigen__0 @ X1 ) ) )
=> sP3 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP2
=> ~ ! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] :
~ ( eigen__3 @ X2 ) ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h17,assumption,
sP2,
introduced(assumption,[]) ).
thf(h18,assumption,
! [X1: b > $o] :
( ( X1
= ( ^ [X2: b] :
~ ( eigen__3 @ X2 ) ) )
=> ( eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| ~ sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,h12,h17,h16]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,3,h17,h18]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,4,h15,h16]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,5,h14]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,6,h12,h13]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,7,h11]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h3,8,h10]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,9,h8,h9]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,10,h6,h7]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,11,h4,h5]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1]) ).
thf(0,theorem,
! [X1: ( b > $o ) > $o] :
( ~ ( ~ ( ~ ( ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : $false ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: b > $o] :
( ( X2
= ( ^ [X3: b] : ~ $false ) )
=> ( X1 @ X2 ) ) )
=> ~ ! [X2: ( b > $o ) > $o,X3: b > $o] :
( ~ ( ! [X4: b > $o] :
( ( X2 @ X4 )
=> ( X1 @ X4 ) )
=> ( X3
!= ( ^ [X4: b] :
~ ! [X5: b > $o] :
( ( X2 @ X5 )
=> ~ ( X5 @ X4 ) ) ) ) )
=> ( X1 @ X3 ) ) )
=> ~ ! [X2: b > $o,X3: b > $o,X4: b > $o] :
( ~ ( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X4
!= ( ^ [X5: b] :
~ ( ( X2 @ X5 )
=> ~ ( X3 @ X5 ) ) ) ) )
=> ( X1 @ X4 ) ) )
=> ! [X2: b > $o,X3: b] :
( ( X2 @ X3 )
=> ! [X4: b > $o] :
( ~ ( ! [X5: b] :
( ( X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: b > $o] :
( ( X5
= ( ^ [X6: b] :
~ ( X4 @ X6 ) ) )
=> ( X1 @ X5 ) ) )
=> ( X4 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV259^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % 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 01:31:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 3
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------