%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM760^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 Oct 9 02:09:51 PM UTC 2025
% Result : Theorem 263.72s 260.88s
% Output : Proof 263.72s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_x,type,
x: frac ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_u,type,
u: frac ).
thf(ty_moref,type,
moref: frac > frac > $o ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_y,type,
y: frac ).
thf(ty_lessf,type,
lessf: frac > frac > $o ).
thf(ty_z,type,
z: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac,X2: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( moref @ z @ u )
=> ( moref @ ( pf @ z @ y ) @ ( pf @ u @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( moref @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
=> ( lessf @ ( pf @ y @ z ) @ ( pf @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( moref @ ( pf @ y @ z ) @ ( pf @ y @ u ) )
=> ( lessf @ ( pf @ y @ u ) @ ( pf @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( moref @ ( pf @ z @ y ) @ X1 )
=> ( ( eq @ ( pf @ z @ y ) @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: frac] :
( ( moref @ ( pf @ y @ z ) @ X1 )
=> ( lessf @ X1 @ ( pf @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: frac,X2: frac] :
( ( lessf @ ( pf @ y @ u ) @ X1 )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ ( pf @ y @ u ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( moref @ ( pf @ z @ y ) @ ( pf @ u @ y ) )
=> ( ( eq @ ( pf @ z @ y ) @ ( pf @ y @ z ) )
=> ( ( eq @ ( pf @ u @ y ) @ ( pf @ y @ u ) )
=> ( moref @ ( pf @ y @ z ) @ ( pf @ y @ u ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: frac] :
( ( moref @ x @ y )
=> ( moref @ ( pf @ x @ X1 ) @ ( pf @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: frac,X2: frac] :
( ( moref @ X1 @ X2 )
=> ( lessf @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( lessf @ ( pf @ y @ u ) @ ( pf @ y @ z ) )
=> ( ( lessf @ ( pf @ y @ z ) @ ( pf @ x @ z ) )
=> ( lessf @ ( pf @ y @ u ) @ ( pf @ x @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: frac] :
( ( moref @ ( pf @ z @ y ) @ ( pf @ u @ y ) )
=> ( ( eq @ ( pf @ z @ y ) @ ( pf @ y @ z ) )
=> ( ( eq @ ( pf @ u @ y ) @ X1 )
=> ( moref @ ( pf @ y @ z ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( lessf @ ( pf @ y @ z ) @ ( pf @ x @ z ) )
=> ( lessf @ ( pf @ y @ u ) @ ( pf @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: frac] :
( ( moref @ z @ u )
=> ( moref @ ( pf @ z @ X1 ) @ ( pf @ u @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eq @ ( pf @ u @ y ) @ ( pf @ y @ u ) )
=> ( moref @ ( pf @ y @ z ) @ ( pf @ y @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( moref @ x @ y )
=> ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: frac] : ( eq @ ( pf @ u @ X1 ) @ ( pf @ X1 @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( lessf @ X2 @ X3 )
=> ( lessf @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: frac] : ( eq @ ( pf @ z @ X1 ) @ ( pf @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( lessf @ ( pf @ y @ z ) @ ( pf @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( moref @ ( pf @ z @ y ) @ ( pf @ u @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eq @ ( pf @ z @ y ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( moref @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( lessf @ ( pf @ y @ u ) @ ( pf @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( lessf @ ( pf @ y @ u ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: frac,X2: frac] :
( sP22
=> ( ( eq @ ( pf @ z @ y ) @ X1 )
=> ( ( eq @ ( pf @ u @ y ) @ X2 )
=> ( moref @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eq @ ( pf @ u @ y ) @ ( pf @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: frac,X2: frac] :
( ( moref @ x @ X1 )
=> ( moref @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( moref @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP23
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( moref @ ( pf @ y @ z ) @ ( pf @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: frac] :
( ( lessf @ ( pf @ y @ u ) @ X1 )
=> ( moref @ X1 @ ( pf @ y @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( moref @ z @ u ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP25
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: frac,X2: frac] :
( ( moref @ z @ X1 )
=> ( moref @ ( pf @ z @ X2 ) @ ( pf @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: frac] :
( ( moref @ ( pf @ x @ z ) @ X1 )
=> ( lessf @ X1 @ ( pf @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( moref @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: frac] :
( sP26
=> ( ( lessf @ ( pf @ y @ z ) @ X1 )
=> ( lessf @ ( pf @ y @ u ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(satz64,conjecture,
sP32 ).
thf(h0,negated_conjecture,
~ sP32,
inference(assume_negation,[status(cth)],[satz64]) ).
thf(1,plain,
( ~ sP31
| ~ sP23
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| ~ sP22
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP16
| ~ sP28
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP27
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP6
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| ~ sP21
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP5
| ~ sP33
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP12
| ~ sP26
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP4
| ~ sP39
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP41
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP38
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP8
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP40
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP36
| ~ sP25
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP34
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP3
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP19
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP11
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP2
| ~ sP35
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP15
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP18
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP1
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP37
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP17
| ~ sP24
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP10
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP29
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP20
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP1
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP30
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP30
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(m,axiom,
sP24 ).
thf(n,axiom,
sP35 ).
thf(satz43,axiom,
sP3 ).
thf(satz50,axiom,
sP19 ).
thf(satz42,axiom,
sP11 ).
thf(satz44,axiom,
sP40 ).
thf(satz61,axiom,
sP30 ).
thf(satz58,axiom,
sP1 ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,m,n,satz43,satz50,satz42,satz44,satz61,satz58,h0]) ).
thf(0,theorem,
sP32,
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM760^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n008.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 : Wed Oct 8 22:04:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 263.72/260.88 % SZS status Theorem
% 263.72/260.88 % Mode: cade22grackle2x220a
% 263.72/260.88 % Steps: 165344
% 263.72/260.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------