TSTP Solution File: SWW600_2 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% 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 : Mon Jun 24 18:53:47 EDT 2024
% Result : Theorem 0.24s 0.44s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 61 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 184 ( 78 ~; 10 |; 72 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 347 ( 61 atm; 123 fun; 61 num; 102 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 32 ( 29 usr; 17 con; 0-4 aty)
% Number of variables : 102 ( 58 !; 44 ?; 102 :)
% 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,
sK0: $int ).
tff(func_def_28,type,
sK1: $int ).
tff(func_def_29,type,
sK2: $int ).
tff(func_def_30,type,
sK3: $int ).
tff(func_def_31,type,
sK4: $int ).
tff(func_def_32,type,
sK5: $int ).
tff(func_def_33,type,
sK6: $int ).
tff(func_def_34,type,
sK7: $int ).
tff(func_def_35,type,
sK8: $int > $int ).
tff(func_def_36,type,
sK9: $int > $int ).
tff(func_def_37,type,
sK10: ( $int * $int ) > $int ).
tff(func_def_38,type,
sK11: ( $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(f467,plain,
$false,
inference(avatar_sat_refutation,[],[f417,f422,f427,f432,f437,f442,f448,f453,f458,f462,f466]) ).
tff(f466,plain,
( ~ spl12_8
| ~ spl12_10 ),
inference(avatar_contradiction_clause,[],[f465]) ).
tff(f465,plain,
( $false
| ~ spl12_8
| ~ spl12_10 ),
inference(trivial_inequality_removal,[],[f463]) ).
tff(f463,plain,
( ( sK7 != sK7 )
| ~ spl12_8
| ~ spl12_10 ),
inference(superposition,[],[f461,f452]) ).
tff(f452,plain,
( ( sK7 = $sum($product(sK5,sK0),$product(sK4,sK1)) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f450]) ).
tff(f450,plain,
( spl12_8
<=> ( sK7 = $sum($product(sK5,sK0),$product(sK4,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
tff(f461,plain,
( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != sK7 )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f460]) ).
tff(f460,plain,
( spl12_10
<=> ! [X9: $int,X8: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
tff(f462,plain,
spl12_10,
inference(avatar_split_clause,[],[f308,f460]) ).
tff(f308,plain,
! [X8: $int,X9: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != sK7 ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != sK7 )
& ~ $less(0,sK6)
& ( sK6 = $sum($product(sK3,sK0),$product(sK2,sK1)) )
& ( sK7 = $sum($product(sK5,sK0),$product(sK4,sK1)) )
& ( gcd(sK0,sK1) = gcd(sK7,sK6) )
& ~ $less(sK6,0)
& ~ $less(sK7,0)
& ~ $less(sK1,0)
& ~ $less(sK0,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f205,f280,f279]) ).
tff(f279,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,sK0),$product(X9,sK1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK0),$product(X2,sK1)) = X6 )
& ( $sum($product(X5,sK0),$product(X4,sK1)) = X7 )
& ( gcd(X7,X6) = gcd(sK0,sK1) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
& ~ $less(sK1,0)
& ~ $less(sK0,0) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != X7 )
& ~ $less(0,X6)
& ( $sum($product(X3,sK0),$product(X2,sK1)) = X6 )
& ( $sum($product(X5,sK0),$product(X4,sK1)) = X7 )
& ( gcd(X7,X6) = gcd(sK0,sK1) )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK0),$product(X9,sK1)) != sK7 )
& ~ $less(0,sK6)
& ( sK6 = $sum($product(sK3,sK0),$product(sK2,sK1)) )
& ( sK7 = $sum($product(sK5,sK0),$product(sK4,sK1)) )
& ( gcd(sK0,sK1) = gcd(sK7,sK6) )
& ~ $less(sK6,0)
& ~ $less(sK7,0) ) ),
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/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f458,plain,
spl12_9,
inference(avatar_split_clause,[],[f306,f455]) ).
tff(f455,plain,
( spl12_9
<=> ( sK6 = $sum($product(sK3,sK0),$product(sK2,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
tff(f306,plain,
sK6 = $sum($product(sK3,sK0),$product(sK2,sK1)),
inference(cnf_transformation,[],[f281]) ).
tff(f453,plain,
spl12_8,
inference(avatar_split_clause,[],[f305,f450]) ).
tff(f305,plain,
sK7 = $sum($product(sK5,sK0),$product(sK4,sK1)),
inference(cnf_transformation,[],[f281]) ).
tff(f448,plain,
( spl12_7
| ~ spl12_6 ),
inference(avatar_split_clause,[],[f443,f439,f445]) ).
tff(f445,plain,
( spl12_7
<=> ( gcd(sK0,sK1) = gcd(sK6,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
tff(f439,plain,
( spl12_6
<=> ( gcd(sK0,sK1) = gcd(sK7,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
tff(f443,plain,
( ( gcd(sK0,sK1) = gcd(sK6,sK7) )
| ~ spl12_6 ),
inference(forward_demodulation,[],[f441,f348]) ).
tff(f348,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X1: $int,X7: $int] : ( gcd(X1,X7) = gcd(X7,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f441,plain,
( ( gcd(sK0,sK1) = gcd(sK7,sK6) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f439]) ).
tff(f442,plain,
spl12_6,
inference(avatar_split_clause,[],[f304,f439]) ).
tff(f304,plain,
gcd(sK0,sK1) = gcd(sK7,sK6),
inference(cnf_transformation,[],[f281]) ).
tff(f437,plain,
~ spl12_5,
inference(avatar_split_clause,[],[f307,f434]) ).
tff(f434,plain,
( spl12_5
<=> $less(0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
tff(f307,plain,
~ $less(0,sK6),
inference(cnf_transformation,[],[f281]) ).
tff(f432,plain,
~ spl12_4,
inference(avatar_split_clause,[],[f303,f429]) ).
tff(f429,plain,
( spl12_4
<=> $less(sK6,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
tff(f303,plain,
~ $less(sK6,0),
inference(cnf_transformation,[],[f281]) ).
tff(f427,plain,
~ spl12_3,
inference(avatar_split_clause,[],[f302,f424]) ).
tff(f424,plain,
( spl12_3
<=> $less(sK7,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
tff(f302,plain,
~ $less(sK7,0),
inference(cnf_transformation,[],[f281]) ).
tff(f422,plain,
~ spl12_2,
inference(avatar_split_clause,[],[f301,f419]) ).
tff(f419,plain,
( spl12_2
<=> $less(sK1,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
tff(f301,plain,
~ $less(sK1,0),
inference(cnf_transformation,[],[f281]) ).
tff(f417,plain,
~ spl12_1,
inference(avatar_split_clause,[],[f300,f414]) ).
tff(f414,plain,
( spl12_1
<=> $less(sK0,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
tff(f300,plain,
~ $less(sK0,0),
inference(cnf_transformation,[],[f281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.07/0.14 % Command : run_vampire %s %d SAT
% 0.14/0.37 % Computer : n023.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Jun 19 08:02:09 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.39 This is a TF0_THM_EQU_ARI problem
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.43 % (10990)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.43 % (10992)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:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.24/0.44 % (10992)First to succeed.
% 0.24/0.44 % (10992)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10990"
% 0.24/0.44 % (10990)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (10992)Refutation found. Thanks to Tanya!
% 0.24/0.44 % SZS status Theorem for theBenchmark
% 0.24/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.44 % (10992)------------------------------
% 0.24/0.44 % (10992)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.24/0.44 % (10992)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.24/0.44 % (10992)Termination reason: Refutation
% 0.24/0.44
% 0.24/0.44 % (10992)Memory used [KB]: 980
% 0.24/0.44 % (10992)Time elapsed: 0.007 s
% 0.24/0.44 % (10992)Instructions burned: 15 (million)
% 0.24/0.44 % (10992)------------------------------
% 0.24/0.44 % (10992)------------------------------
% 0.24/0.44 % (10990)Success in time 0.042 s
%------------------------------------------------------------------------------