TSTP Solution File: NUM688^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM688^1 : 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 : n021.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 11:40:28 EDT 2023
% Result : Theorem 0.20s 0.46s
% 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_pl,type,
pl: nat > nat > nat ).
thf(ty_u,type,
u: nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_y,type,
y: nat ).
thf(ty_z,type,
z: nat ).
thf(sP1,plain,
( sP1
<=> ( ~ ( more @ z @ u )
=> ( z = u ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( z = u ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( z = X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X2 @ z ) @ ( pl @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ( ( more @ x @ y )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat] :
( ( more @ x @ y )
=> ( ( more @ z @ X1 )
=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( more @ z @ u ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( sP2
=> ( ( more @ x @ X1 )
=> ( more @ ( pl @ x @ z ) @ ( pl @ X1 @ u ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( more @ x @ y )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( X1 = X2 )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( more @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( more @ x @ X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ x @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: nat,X2: nat] :
( sP12
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ x @ X1 ) @ ( pl @ y @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP12
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( more @ X1 @ X2 )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: nat,X2: nat] :
( sP2
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ z ) @ ( pl @ X2 @ u ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(satz22b,conjecture,
sP4 ).
thf(h0,negated_conjecture,
~ sP4,
inference(assume_negation,[status(cth)],[satz22b]) ).
thf(1,plain,
( ~ sP10
| ~ sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP2
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| ~ sP12
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP17
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP1
| sP7
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(satz21,axiom,
sP16 ).
thf(satz19h,axiom,
sP11 ).
thf(n,axiom,
sP1 ).
thf(m,axiom,
sP12 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h0,satz21,satz19h,n,m]) ).
thf(0,theorem,
sP4,
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM688^1 : 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 : n021.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 09:06:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22grackle2xfee4
% 0.20/0.46 % Steps: 1021
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------