TSTP Solution File: SEV384^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV384^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 : Thu Aug 31 19:34:24 EDT 2023
% Result : Theorem 80.43s 80.72s
% Output : Proof 80.43s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $o ).
thf(ty_cR,type,
cR: $i > $i > $o ).
thf(ty_cP,type,
cP: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( s
@ @+[X1: $i] :
~ ( ( s @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( s
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) )
=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( s
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) )
=> ~ ( cR
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) )
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) )
=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( s
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) ) )
=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( s
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ( ~ sP4
=> ~ ! [X2: $i] :
( ( cR
@ @+[X3: $i] :
~ ( ~ ( ( s @ X3 )
=> ( cP @ X3 ) )
=> ~ ! [X4: $i] :
( ( cR @ X3 @ X4 )
=> ( ( s @ X4 )
=> ( cP @ X4 ) ) ) )
@ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ( cP
@ @+[X1: $i] :
~ ( ( s @ X1 )
=> ( cP @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ~ ( ( s
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) ) )
=> ~ ( cR @ X1
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) ) ) )
=> ( cP
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) ) ) )
=> ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 )
=> ( ( s @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP
@ @+[X1: $i] :
~ ( ( s @ X1 )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cR
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) )
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ~ ( cR
@ @+[X2: $i] :
~ ( ~ ( ( s @ X2 )
=> ( cP @ X2 ) )
=> ~ ! [X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( s @ X3 )
=> ( cP @ X3 ) ) ) )
@ X1 ) )
=> ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP13
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP7
=> ~ ( ~ sP4
=> ~ sP11 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ~ ( ( X1
@ @+[X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( cR @ X3 @ X4 )
=> ~ ( X1 @ X4 ) ) ) )
=> ~ ! [X3: $i] :
( ( cR
@ @+[X4: $i] :
~ ( ( X1 @ X4 )
=> ~ ! [X5: $i] :
( ( cR @ X4 @ X5 )
=> ~ ( X1 @ X5 ) ) )
@ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cP
@ @+[X1: $i] :
~ ( ~ ( ( s @ X1 )
=> ( cP @ X1 ) )
=> ~ ! [X2: $i] :
( ( cR @ X1 @ X2 )
=> ( ( s @ X2 )
=> ( cP @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP4
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(cTHM117B,conjecture,
( ~ ( ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( cR @ X3 @ X4 )
=> ~ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) )
=> ( cP @ X1 ) ) )
=> ! [X1: $i] :
( ( s @ X1 )
=> ( cP @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( cR @ X3 @ X4 )
=> ~ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) )
=> ( cP @ X1 ) ) )
=> ! [X1: $i] :
( ( s @ X1 )
=> ( cP @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM117B]) ).
thf(h1,assumption,
~ ( sP17
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
sP17,
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP13
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP5
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP15
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP15
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP3
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| ~ sP3
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP4
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP19
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP19
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| sP7
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h3,h4,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h5,h6])],[h2,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h1,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( ~ ( ! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( cR @ X3 @ X4 )
=> ~ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: $i] :
( ! [X2: $i] :
( ~ ( ( s @ X2 )
=> ~ ( cR @ X1 @ X2 ) )
=> ( cP @ X2 ) )
=> ( cP @ X1 ) ) )
=> ! [X1: $i] :
( ( s @ X1 )
=> ( cP @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV384^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:50:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 80.43/80.72 % SZS status Theorem
% 80.43/80.72 % Mode: cade22grackle2x4fb9
% 80.43/80.72 % Steps: 1291
% 80.43/80.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------