TSTP Solution File: SEV289^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV289^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 18:05:44 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: ( ( $i > $o ) > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( $i > $o ) > $o] :
( ( eigen__1 @ X1 )
=> ( eigen__1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( eigen__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__0
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( eigen__1
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) )
=> ~ sP1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1
@ ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ( eigen__0
@ ^ [X3: $i] :
~ ( ( X3 != X2 )
=> ~ ( X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_cZERO,definition,
( cZERO
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_cNAT,definition,
( cNAT
= ( ^ [X1: ( $i > $o ) > $o] :
! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ cZERO )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2 @ ( cSUCC @ X3 ) ) ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(cTTTP6101,conjecture,
! [X1: ( $i > $o ) > $o] :
( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( $i > $o ) > $o] :
( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTTTP6101]) ).
thf(h1,assumption,
~ ( sP8
=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__0
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP8,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1
@ ^ [X2: $i > $o] :
! [X3: $i] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1
@ ^ [X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( eigen__0
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ sP7
=> sP6 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP7
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,h2,h7,h8,h6]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,6,h7,h8]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).
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 > $o ) > $o] :
( ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2
@ ^ [X3: $i > $o] :
! [X4: $i] :
~ ( X3 @ X4 ) )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X1
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV289^5 : TPTP v8.1.0. Bugfixed v6.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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 : Tue Jun 28 17:05:44 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: 9
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------