%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM771^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 02:12:07 PM UTC 2025
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_num,type,
num: frac > nat ).
thf(ty_y,type,
y: frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_ts,type,
ts: nat > nat > nat ).
thf(ty_den,type,
den: frac > nat ).
thf(ty_fr,type,
fr: nat > nat > frac ).
thf(ty_x,type,
x: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ts @ ( num @ x ) @ ( num @ y ) )
= ( ts @ ( num @ y ) @ ( num @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ts @ ( den @ x ) @ ( den @ y ) )
= ( ts @ ( den @ x ) @ ( den @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac] : ( eq @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( ts @ ( den @ x ) @ X1 )
= ( ts @ X1 @ ( den @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat] :
( ( ts @ ( num @ x ) @ X1 )
= ( ts @ X1 @ ( num @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ts @ ( den @ x ) @ ( den @ y ) )
= ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ts @ ( num @ x ) @ ( num @ y ) )
= ( ts @ ( num @ x ) @ ( num @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(satz69,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[satz69]) ).
thf(1,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
sP12,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP3
| ~ sP2
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP5
| ~ sP12
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP9
| sP7
| ~ sP5
| ~ sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(satz37,axiom,
sP6 ).
thf(satz29,axiom,
sP1 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,satz37,satz29,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM771^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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 : Wed Oct 8 22:33:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 47
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------