TSTP Solution File: NUM666^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM666^1 : 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 : n028.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 11:40:18 EDT 2023
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_moreis,type,
moreis: nat > nat > $o ).
thf(ty_some,type,
some: ( nat > $o ) > $o ).
thf(ty_diffprop,type,
diffprop: nat > nat > nat > $o ).
thf(ty_y,type,
y: nat ).
thf(ty_lessis,type,
lessis: nat > nat > $o ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ( moreis @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: nat] :
( ( lessis @ z @ X1 )
=> ( ( some @ ( diffprop @ X2 @ X1 ) )
=> ( some @ ( diffprop @ X2 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( some @ ( diffprop @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: nat] :
( ( lessis @ z @ y )
=> ( ( some @ ( diffprop @ X1 @ y ) )
=> ( some @ ( diffprop @ X1 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ( lessis @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( lessis @ z @ y )
=> ( ( some @ ( diffprop @ x @ y ) )
=> sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( some @ ( diffprop @ x @ y ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( lessis @ z @ y ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( moreis @ y @ X1 )
=> ( lessis @ X1 @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( lessis @ X1 @ X2 )
=> ( ( some @ ( diffprop @ X3 @ X2 ) )
=> ( some @ ( diffprop @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( some @ ( diffprop @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat,X2: nat] :
( ( moreis @ X1 @ X2 )
=> ( lessis @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(satz16d,conjecture,
sP3 ).
thf(h0,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[satz16d]) ).
thf(1,plain,
( ~ sP7
| ~ sP11
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| ~ sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(satz13,axiom,
sP12 ).
thf(satz16a,axiom,
sP10 ).
thf(n,axiom,
sP1 ).
thf(m,axiom,
sP11 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,satz13,satz16a,n,m]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.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 : 300
% 0.13/0.34 % DateTime : Fri Aug 25 14:56:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % Mode: cade22grackle2xfee4
% 0.20/0.43 % Steps: 246
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------