%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM746^1 : 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 : n023.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 02:09:47 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% 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_y,type,
y: frac ).
thf(ty_z,type,
z: frac ).
thf(sP1,plain,
( sP1
<=> ( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( lessf @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( lessf @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( ( lessf @ X2 @ X3 )
=> ( lessf @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: frac] :
( ( eq @ x @ y )
=> ( ( eq @ y @ X1 )
=> ( eq @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac] :
( ( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) )
=> ( ( lessf @ y @ X1 )
=> ( lessf @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eq @ x @ z ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: frac,X2: frac] :
( ( eq @ x @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eq @ y @ z ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: frac] :
( ( lessf @ x @ y )
=> ( ( ~ ( lessf @ y @ X1 )
=> ( eq @ y @ X1 ) )
=> ( lessf @ x @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP3
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP11
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: frac,X2: frac] :
( ( lessf @ x @ X1 )
=> ( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( lessf @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( lessf @ x @ y )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP17
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( lessf @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP19
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: frac,X2: frac] :
( ( ~ ( lessf @ x @ X1 )
=> ( eq @ x @ X1 ) )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP10
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( ~ ( lessf @ X2 @ X3 )
=> ( eq @ X2 @ X3 ) )
=> ( lessf @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(satz52,conjecture,
( ~ sP2
=> sP7 ) ).
thf(h0,negated_conjecture,
~ ( ~ sP2
=> sP7 ),
inference(assume_negation,[status(cth)],[satz52]) ).
thf(h1,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP1
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP20
| ~ sP19
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP18
| ~ sP17
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| ~ sP11
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP22
| ~ sP10
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP12
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP21
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP15
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP16
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| sP3
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP17
| sP19
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz51a,axiom,
sP4 ).
thf(satz51b,axiom,
sP23 ).
thf(satz39,axiom,
sP16 ).
thf(k,axiom,
sP1 ).
thf(l,axiom,
sP17 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h1,h2,satz51a,satz51b,satz39,k,l]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,18,h1,h2]) ).
thf(0,theorem,
( ~ sP2
=> sP7 ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : NUM746^1 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 22:28:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2xfee4
% 0.21/0.43 % Steps: 170
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------