TSTP Solution File: SYO256^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO256^5 : 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 : 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 : 600s
% DateTime : Thu Jul 21 19:31:07 EDT 2022
% Result : Theorem 0.11s 0.35s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $o ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ ~ $false )
= ( eigen__0
@ ! [X1: a] :
( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o] :
( ( $false = X1 )
=> ( X1 = $false ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> $false ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP6
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP6 = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP7
=> ( ( ~ sP5 )
= sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP11 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o] :
( ( sP6 = X1 )
=> ( X1 = sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $o] :
( ( eigen__0 @ X1 )
!= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP8
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ~ sP5 )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cTHM121,conjecture,
! [X1: $o > $o,X2: a > $o,X3: a > $o] :
~ ! [X4: $o] :
( ( X1 @ X4 )
!= ( X1
@ ! [X5: a] :
( ~ ( X2 @ X5 )
=> ( X3 @ X5 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $o > $o,X2: a > $o,X3: a > $o] :
~ ! [X4: $o] :
( ( X1 @ X4 )
!= ( X1
@ ! [X5: a] :
( ~ ( X2 @ X5 )
=> ( X3 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM121]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
~ ! [X3: $o] :
( ( eigen__0 @ X3 )
!= ( eigen__0
@ ! [X4: a] :
( ~ ( X1 @ X4 )
=> ( X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
~ ! [X2: $o] :
( ( eigen__0 @ X2 )
!= ( eigen__0
@ ! [X3: a] :
( ~ ( eigen__1 @ X3 )
=> ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP15,
introduced(assumption,[]) ).
thf(1,plain,
( sP8
| ~ sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP5
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP16
| ~ sP8
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP7
| ~ sP6
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| ~ sP7
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP11
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP11
| sP9
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| sP9
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP9
| sP3
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( sP13
| ~ sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP13
| sP11
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| ~ sP3
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP1
| sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
sP4,
inference(eq_sym,[status(thm)],]) ).
thf(20,plain,
( ~ sP15
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP15
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h3]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,22,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,24,h1]) ).
thf(0,theorem,
! [X1: $o > $o,X2: a > $o,X3: a > $o] :
~ ! [X4: $o] :
( ( X1 @ X4 )
!= ( X1
@ ! [X5: a] :
( ~ ( X2 @ X5 )
=> ( X3 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO256^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jul 9 09:52:37 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.35 % SZS status Theorem
% 0.11/0.35 % Mode: mode213
% 0.11/0.35 % Inferences: 21
% 0.11/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------