TSTP Solution File: NUM664^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM664^1 : 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 : n007.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 11:40:16 EDT 2023
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_x,type,
x: nat ).
thf(ty_less,type,
less: nat > nat > $o ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ( ~ ( less @ y @ z )
=> ( y = z ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( less @ x @ y )
=> ( ( less @ y @ z )
=> ( less @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( less @ x @ y )
=> ( ( less @ y @ X1 )
=> ( less @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( less @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( y = z ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: nat] :
( ( less @ x @ X1 )
=> ( ( less @ X1 @ X2 )
=> ( less @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP4
=> ( less @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( less @ X1 @ X2 )
=> ( ( less @ X2 @ X3 )
=> ( less @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( less @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> $false ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( less @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(satz16b,conjecture,
sP11 ).
thf(h0,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[satz16b]) ).
thf(1,plain,
( ~ sP7
| ~ sP4
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
~ sP10,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP11
| ~ sP5
| sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(satz15,axiom,
sP8 ).
thf(k,axiom,
sP1 ).
thf(l,axiom,
sP9 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,satz15,k,l]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM664^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n007.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 : Fri Aug 25 11:07:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % Mode: cade22grackle2xfee4
% 0.12/0.39 % Steps: 56
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------