%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM759^1 : 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 : n012.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 2.18s 2.38s
% Output : Proof 2.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_x,type,
x: frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_y,type,
y: frac ).
thf(ty_z,type,
z: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X3 ) )
=> ( eq @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: frac] :
( ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) )
=> ( ( eq @ ( pf @ z @ y ) @ X1 )
=> ( eq @ ( pf @ x @ z ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: frac] : ( eq @ ( pf @ z @ X1 ) @ ( pf @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eq @ ( pf @ x @ z ) @ ( pf @ z @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: frac] : ( eq @ ( pf @ x @ X1 ) @ ( pf @ X1 @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: frac] :
( ( eq @ ( pf @ x @ X1 ) @ ( pf @ y @ X1 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eq @ ( pf @ z @ y ) @ ( pf @ y @ z ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: frac,X2: frac] :
( ( eq @ ( pf @ x @ z ) @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ ( pf @ x @ z ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: frac,X2: frac] :
( ( eq @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X2 ) )
=> ( eq @ x @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eq @ ( pf @ z @ y ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP4
=> sP7 ) ),
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
<=> ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: frac,X2: frac] : ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eq @ ( pf @ x @ z ) @ ( pf @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: frac] :
( sP4
=> ( ( eq @ ( pf @ z @ x ) @ X1 )
=> ( eq @ ( pf @ x @ z ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(satz63e,conjecture,
sP5 ).
thf(h0,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[satz63e]) ).
thf(1,plain,
( ~ sP11
| ~ sP14
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP18
| ~ sP20
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| ~ sP17
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP15
| ~ sP4
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP21
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| ~ sP6
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP19
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP19
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz58,axiom,
sP19 ).
thf(satz39,axiom,
sP16 ).
thf(satz63b,axiom,
sP1 ).
thf(e,axiom,
sP17 ).
thf(18,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,h0,satz58,satz39,satz63b,e]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM759^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.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 : Wed Oct 8 22:21:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.18/2.38 % SZS status Theorem
% 2.18/2.38 % Mode: cade22grackle2xfee4
% 2.18/2.38 % Steps: 14743
% 2.18/2.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------