TSTP Solution File: SWW600_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Tue May 21 07:27:29 EDT 2024
% Result : Theorem 0.13s 0.41s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 41
% Syntax : Number of formulae : 50 ( 3 unt; 38 typ; 0 def)
% Number of atoms : 98 ( 46 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 140 ( 54 ~; 0 |; 72 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 299 ( 51 atm; 105 fun; 51 num; 92 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 33 ( 18 >; 15 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 29 usr; 17 con; 0-4 aty)
% Number of variables : 92 ( 48 !; 44 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
abs: $int > $int ).
tff(func_def_14,type,
div: ( $int * $int ) > $int ).
tff(func_def_15,type,
mod: ( $int * $int ) > $int ).
tff(func_def_22,type,
gcd: ( $int * $int ) > $int ).
tff(func_def_23,type,
ref: ty > ty ).
tff(func_def_24,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_25,type,
contents: ( ty * uni ) > uni ).
tff(func_def_27,type,
sK1: $int ).
tff(func_def_28,type,
sK2: $int ).
tff(func_def_29,type,
sK3: $int ).
tff(func_def_30,type,
sK4: $int ).
tff(func_def_31,type,
sK5: $int ).
tff(func_def_32,type,
sK6: $int ).
tff(func_def_33,type,
sK7: $int ).
tff(func_def_34,type,
sK8: $int ).
tff(func_def_35,type,
sK9: $int > $int ).
tff(func_def_36,type,
sK10: $int > $int ).
tff(func_def_37,type,
sK11: ( $int * $int ) > $int ).
tff(func_def_38,type,
sK12: ( $int * $int * $int ) > $int ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(pred_def_4,type,
divides: ( $int * $int ) > $o ).
tff(pred_def_5,type,
even: $int > $o ).
tff(pred_def_6,type,
odd: $int > $o ).
tff(pred_def_7,type,
sP0: ( $int * $int * $int ) > $o ).
tff(f415,plain,
$false,
inference(subsumption_resolution,[],[f309,f312]) ).
tff(f312,plain,
! [X8: $int,X9: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 )
& ~ $less(0,sK7)
& ( sK7 = $sum($product(sK4,sK1),$product(sK3,sK2)) )
& ( sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)) )
& ( gcd(sK1,sK2) = gcd(sK8,sK7) )
& ~ $less(sK7,0)
& ~ $less(sK8,0)
& ~ $less(sK2,0)
& ~ $less(sK1,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f205,f282,f281]) ).
tff(f281,plain,
( ? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) )
=> ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK1),$product(X2,sK2)) = X6 )
& ( $sum($product(X5,sK1),$product(X4,sK2)) = X7 )
& ( gcd(X7,X6) = gcd(sK1,sK2) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(sK2,0)
& ~ $less(sK1,0) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK1),$product(X2,sK2)) = X6 )
& ( $sum($product(X5,sK1),$product(X4,sK2)) = X7 )
& ( gcd(X7,X6) = gcd(sK1,sK2) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 )
& ~ $less(0,sK7)
& ( sK7 = $sum($product(sK4,sK1),$product(sK3,sK2)) )
& ( sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)) )
& ( gcd(sK1,sK2) = gcd(sK8,sK7) )
& ~ $less(sK7,0)
& ~ $less(sK8,0) ) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(flattening,[],[f204]) ).
tff(f204,plain,
? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ! [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ( ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ( gcd(X0,X1) = gcd(X7,X6) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ~ $less(0,X6)
=> ? [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,plain,
~ ! [X1: $int,X7: $int] :
( ( ~ $less(X7,0)
& ~ $less(X1,0) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& ~ $less(X14,0)
& ~ $less(X2,0) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(theory_normalization,[],[f84]) ).
tff(f84,negated_conjecture,
~ ! [X1: $int,X7: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& $lesseq(0,X2) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(negated_conjecture,[],[f83]) ).
tff(f83,conjecture,
! [X1: $int,X7: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& $lesseq(0,X2) )
=> ( ~ $less(0,X14)
=> ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_gcd) ).
tff(f309,plain,
sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)),
inference(cnf_transformation,[],[f283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n022.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 : Sat May 18 20:23:23 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % (10988)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39 % (10990)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39 % (10990)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.39 % (10990)Terminated due to inappropriate strategy.
% 0.13/0.39 % (10990)------------------------------
% 0.13/0.39 % (10990)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39 % (10990)Termination reason: Inappropriate
% 0.13/0.39
% 0.13/0.39 % (10990)Memory used [KB]: 921
% 0.13/0.39 % (10990)Time elapsed: 0.006 s
% 0.13/0.39 % (10990)Instructions burned: 8 (million)
% 0.13/0.39 % (10991)WARNING: value z3 for option sas not known
% 0.13/0.39 % (10990)------------------------------
% 0.13/0.39 % (10990)------------------------------
% 0.13/0.39 % (10989)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % (10991)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.39 % (10992)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 % (10993)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.39 % (10994)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.39 % (10995)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.40 % (10989)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.40 % (10989)Terminated due to inappropriate strategy.
% 0.13/0.40 % (10989)------------------------------
% 0.13/0.40 % (10989)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40 % (10989)Termination reason: Inappropriate
% 0.13/0.40
% 0.13/0.40 % (10989)Memory used [KB]: 921
% 0.13/0.40 % (10989)Time elapsed: 0.009 s
% 0.13/0.40 % (10989)Instructions burned: 8 (million)
% 0.13/0.40 % (10992)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.40 % (10992)Terminated due to inappropriate strategy.
% 0.13/0.40 % (10992)------------------------------
% 0.13/0.40 % (10992)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40 % (10989)------------------------------
% 0.13/0.40 % (10989)------------------------------
% 0.13/0.40 % (10992)Termination reason: Inappropriate
% 0.13/0.40
% 0.13/0.40 % (10992)Memory used [KB]: 921
% 0.13/0.40 % (10992)Time elapsed: 0.009 s
% 0.13/0.40 % (10992)Instructions burned: 8 (million)
% 0.13/0.40 % (10992)------------------------------
% 0.13/0.40 % (10992)------------------------------
% 0.13/0.40 % (10995)First to succeed.
% 0.13/0.40 % (10995)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10988"
% 0.13/0.41 % (10995)Refutation found. Thanks to Tanya!
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41 % (10995)------------------------------
% 0.13/0.41 % (10995)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.41 % (10995)Termination reason: Refutation
% 0.13/0.41
% 0.13/0.41 % (10995)Memory used [KB]: 949
% 0.13/0.41 % (10995)Time elapsed: 0.013 s
% 0.13/0.41 % (10995)Instructions burned: 11 (million)
% 0.13/0.41 % (10988)Success in time 0.043 s
%------------------------------------------------------------------------------