TSTP Solution File: SYO016^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO016^1 : 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 : n005.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 : Fri Sep 1 04:44:42 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $o > $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ( h
@ ! [X1: $o > $o] :
( ( X1 @ ( h @ ~ $false ) )
=> ( X1 @ ( h @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ! [X1: $o > $o] :
( ( X1 @ ( h @ ~ $false ) )
=> ( X1 @ ( h @ $false ) ) ) )
= ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( h @ $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o] :
( ( X1 @ ( h @ ~ $false ) )
=> ( X1 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ^ [X1: $o] : sP3 )
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( h @ sP4 )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( ^ [X1: $o] : ( h @ ~ sP6 ) )
!= ( ^ [X1: $o] : sP6 ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: $o] : ( h @ ~ sP6 ) )
= ( ^ [X1: $o] : sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( h @ ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( h @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP6 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_leibeq,definition,
( leibeq
= ( ^ [X1: $o,X2: $o] :
! [X3: $o > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X3 @ X1 )
@ ( X3 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $o > $o] :
( ( X1 @ sP13 )
=> ( X1 @ sP3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $o > $o] :
( ( X1 @ sP13 )
=> ( X1 @ sP3 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
~ ( sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP10
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP10
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP14
| sP6
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP13
| ~ sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP3
| sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( sP2
| ~ sP4
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
~ sP6,
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| sP11
| ~ sP2 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| sP13
| sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
( sP7
| ~ sP13
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP7
| sP13
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP8
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h2,h3]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,19,h2,h3]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,20,h1]) ).
thf(0,theorem,
! [X1: $o > $o] :
( ( X1 @ sP13 )
=> ( X1 @ sP3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO016^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.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 : 300
% 0.12/0.33 % DateTime : Sat Aug 26 05:27:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.63 % SZS status Theorem
% 0.19/0.63 % Mode: cade22grackle2xfee4
% 0.19/0.63 % Steps: 15286
% 0.19/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------