TSTP Solution File: SEV273^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV273^5 : 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 : 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 : 300s
% DateTime : Thu Aug 31 19:33:12 EDT 2023
% Result : Theorem 82.69s 83.01s
% Output : Proof 82.69s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ( ~ ( ( X1
@ @+[X2: a] :
~ ( ~ ( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( cR
@ @+[X3: a] :
~ ( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ~ ! [X4: a] :
( ~ ( ( X1 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( cR @ X4 @ X5 ) ) )
=> ( X4 = X3 ) ) )
@ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ( X1
@ @+[X3: a] :
~ ( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( cR @ X2
@ @+[X3: a] :
~ ( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) ) ) )
=> ( X2
= ( @+[X3: a] :
~ ( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ~ ! [X4: a] :
( ~ ( ( X1 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 )
=> ( cR @ X4 @ X5 ) ) )
=> ( X4 = X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( cR
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) )
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) ) )
=> ( cR
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) )
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cR
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) )
@ @+[X1: a] :
~ ( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ! [X2: a] :
( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ~ ! [X2: a] :
( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ( X2 = X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cR
@ @+[X1: a] :
~ ( cR @ X1 @ X1 )
@ @+[X1: a] :
~ ( cR @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ sP4
=> ~ ! [X1: a] :
( ~ ( cR @ X1 @ X1 )
=> ( cR
@ @+[X2: a] :
~ ( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ~ ( cR @ X3 @ X3 )
=> ~ ! [X4: a] :
( ~ ( cR @ X4 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) )
@ X1 ) ) )
=> ~ ! [X1: a] :
( ~ ( ~ ( cR @ X1 @ X1 )
=> ~ ( ~ ( cR
@ @+[X2: a] :
~ ( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) )
@ @+[X2: a] :
~ ( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) )
=> ( cR @ X1
@ @+[X2: a] :
~ ( ~ ( cR @ X2 @ X2 )
=> ( cR @ X1 @ X2 ) ) ) ) )
=> ( X1
= ( @+[X2: a] :
~ ( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ~ ( cR @ X3 @ X3 )
=> ~ ! [X4: a] :
( ~ ( cR @ X4 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP4
=> ~ ! [X1: a] :
( ~ ( cR @ X1 @ X1 )
=> ( cR
@ @+[X2: a] :
~ ( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ~ ( cR @ X3 @ X3 )
=> ~ ! [X4: a] :
( ~ ( cR @ X4 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP3
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ~ ( cR @ X1 @ X1 )
=> ( cR
@ @+[X2: a] :
~ ( ~ ( ~ ( cR @ X2 @ X2 )
=> ~ ! [X3: a] :
( ~ ( cR @ X3 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ~ ( cR @ X3 @ X3 )
=> ~ ! [X4: a] :
( ~ ( cR @ X4 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cTHM542_pme,conjecture,
( ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) ) )
=> sP3 ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) ) )
=> sP3 ),
inference(assume_negation,[status(cth)],[cTHM542_pme]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP4
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP7
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP3
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,h1,h2]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).
thf(0,theorem,
( ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ! [X2: a] :
( ~ ( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( cR @ X2 @ X3 ) ) )
=> ~ ! [X3: a] :
( ~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( cR @ X3 @ X4 ) ) )
=> ( X3 = X2 ) ) ) )
=> sP3 ),
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV273^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 04:01:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 82.69/83.01 % SZS status Theorem
% 82.69/83.01 % Mode: cade22grackle2x4fb9
% 82.69/83.01 % Steps: 75
% 82.69/83.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------