TSTP Solution File: NUM756^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM756^1 : 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 : n020.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 11:40:56 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_x,type,
x: frac ).
thf(ty_lessf,type,
lessf: frac > frac > $o ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_y,type,
y: frac ).
thf(ty_moref,type,
moref: frac > frac > $o ).
thf(ty_z,type,
z: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac,X2: frac] :
~ ( ( ( eq @ X1 @ X2 )
=> ~ ( moref @ X1 @ X2 ) )
=> ( ( ( moref @ X1 @ X2 )
=> ~ ( lessf @ X1 @ X2 ) )
=> ~ ( ( lessf @ X1 @ X2 )
=> ~ ( eq @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: frac] :
( ~ ( eq @ x @ X1 )
=> ( ~ ( moref @ x @ X1 )
=> ( lessf @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( eq @ x @ y )
=> ( ~ ( moref @ x @ y )
=> ( lessf @ x @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( moref @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( lessf @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP7
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( sP6
=> ~ sP3 )
=> ~ ( sP3
=> ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: frac,X2: frac] :
( ( moref @ x @ X1 )
=> ( moref @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: frac,X2: frac] :
( ( lessf @ x @ X1 )
=> ( lessf @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: frac] :
( sP9
=> ( lessf @ ( pf @ x @ X1 ) @ ( pf @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP7
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
=> ~ sP6 )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( lessf @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP9
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: frac] :
( sP7
=> ( moref @ ( pf @ x @ X1 ) @ ( pf @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP19
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP3
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: frac,X2: frac] :
( ~ ( eq @ X1 @ X2 )
=> ( ~ ( moref @ X1 @ X2 )
=> ( lessf @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: frac] :
~ ( ( ( eq @ ( pf @ x @ z ) @ X1 )
=> ~ ( moref @ ( pf @ x @ z ) @ X1 ) )
=> ( ( ( moref @ ( pf @ x @ z ) @ X1 )
=> ~ ( lessf @ ( pf @ x @ z ) @ X1 ) )
=> ~ ( ( lessf @ ( pf @ x @ z ) @ X1 )
=> ~ ( eq @ ( pf @ x @ z ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(satz63b,conjecture,
sP8 ).
thf(h0,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[satz63b]) ).
thf(1,plain,
( ~ sP22
| ~ sP3
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP11
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| ~ sP19
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP16
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP24
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| ~ sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP20
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| sP8
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP12
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP23
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(satz62a,axiom,
sP4 ).
thf(satz41a,axiom,
sP23 ).
thf(satz62c,axiom,
sP17 ).
thf(satz41b,axiom,
sP1 ).
thf(e,axiom,
sP19 ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h0,satz62a,satz41a,satz62c,satz41b,e]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM756^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n020.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 : Fri Aug 25 14:43:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % Mode: cade22grackle2xfee4
% 0.20/0.52 % Steps: 1279
% 0.20/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------