TSTP Solution File: SWW600_2 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% 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 : Mon Jun 24 18:35:04 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 50 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 154 ( 60 ~; 0 |; 80 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 13 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 328 ( 56 atm; 114 fun; 56 num; 102 var)
% Number of types : 6 ( 4 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 27 usr; 17 con; 0-4 aty)
% Number of variables : 102 ( 50 !; 52 ?; 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 ) > $int ).
tff(func_def_36,type,
sK9: ( $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(f223,plain,
$false,
inference(subsumption_resolution,[],[f199,f198]) ).
tff(f198,plain,
! [X8: $int,X9: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
( ~ $less(sK0,0)
& ~ $less(sK1,0)
& ( sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)) )
& ! [X8: $int,X9: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 )
& ~ $less(sK3,0)
& ( sK3 = $sum($product(sK7,sK0),$product(sK2,sK1)) )
& ~ $less(0,sK3)
& ~ $less(sK5,0)
& ( gcd(sK0,sK1) = gcd(sK5,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f170,f172,f171]) ).
tff(f171,plain,
( ? [X0: $int,X1: $int] :
( ~ $less(X0,0)
& ~ $less(X1,0)
& ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ( $sum($product(X6,X0),$product(X4,X1)) = X5 )
& ! [X8: $int,X9: $int] : ( $sum($product(X9,X0),$product(X8,X1)) != X5 )
& ~ $less(X3,0)
& ( $sum($product(X7,X0),$product(X2,X1)) = X3 )
& ~ $less(0,X3)
& ~ $less(X5,0)
& ( gcd(X0,X1) = gcd(X5,X3) ) ) )
=> ( ~ $less(sK0,0)
& ~ $less(sK1,0)
& ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ( $sum($product(X6,sK0),$product(X4,sK1)) = X5 )
& ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != X5 )
& ~ $less(X3,0)
& ( $sum($product(X7,sK0),$product(X2,sK1)) = X3 )
& ~ $less(0,X3)
& ~ $less(X5,0)
& ( gcd(X5,X3) = gcd(sK0,sK1) ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f172,plain,
( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
( ( $sum($product(X6,sK0),$product(X4,sK1)) = X5 )
& ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != X5 )
& ~ $less(X3,0)
& ( $sum($product(X7,sK0),$product(X2,sK1)) = X3 )
& ~ $less(0,X3)
& ~ $less(X5,0)
& ( gcd(X5,X3) = gcd(sK0,sK1) ) )
=> ( ( sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)) )
& ! [X9: $int,X8: $int] : ( $sum($product(X9,sK0),$product(X8,sK1)) != sK5 )
& ~ $less(sK3,0)
& ( sK3 = $sum($product(sK7,sK0),$product(sK2,sK1)) )
& ~ $less(0,sK3)
& ~ $less(sK5,0)
& ( gcd(sK0,sK1) = gcd(sK5,sK3) ) ) ),
introduced(choice_axiom,[]) ).
tff(f170,plain,
? [X0: $int,X1: $int] :
( ~ $less(X0,0)
& ~ $less(X1,0)
& ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
( ( $sum($product(X6,X0),$product(X4,X1)) = X5 )
& ! [X8: $int,X9: $int] : ( $sum($product(X9,X0),$product(X8,X1)) != X5 )
& ~ $less(X3,0)
& ( $sum($product(X7,X0),$product(X2,X1)) = X3 )
& ~ $less(0,X3)
& ~ $less(X5,0)
& ( gcd(X0,X1) = gcd(X5,X3) ) ) ),
inference(rectify,[],[f154]) ).
tff(f154,plain,
? [X1: $int,X0: $int] :
( ~ $less(X1,0)
& ~ $less(X0,0)
& ? [X3: $int,X7: $int,X5: $int,X6: $int,X4: $int,X2: $int] :
( ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
& ! [X8: $int,X9: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X6 )
& ~ $less(X7,0)
& ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
& ~ $less(0,X7)
& ~ $less(X6,0)
& ( gcd(X1,X0) = gcd(X6,X7) ) ) ),
inference(flattening,[],[f153]) ).
tff(f153,plain,
? [X0: $int,X1: $int] :
( ? [X5: $int,X6: $int,X2: $int,X3: $int,X7: $int,X4: $int] :
( ! [X8: $int,X9: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X6 )
& ~ $less(0,X7)
& ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
& ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
& ~ $less(X7,0)
& ( gcd(X1,X0) = gcd(X6,X7) )
& ~ $less(X6,0) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ! [X5: $int,X6: $int,X2: $int,X3: $int,X7: $int,X4: $int] :
( ( ( $sum($product(X4,X1),$product(X5,X0)) = X6 )
& ( $sum($product(X2,X1),$product(X3,X0)) = X7 )
& ~ $less(X7,0)
& ( gcd(X1,X0) = gcd(X6,X7) )
& ~ $less(X6,0) )
=> ( ~ $less(0,X7)
=> ? [X9: $int,X8: $int] : ( $sum($product(X9,X1),$product(X8,X0)) = X6 ) ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,plain,
~ ! [X7: $int,X1: $int] :
( ( ~ $less(X7,0)
& ~ $less(X1,0) )
=> ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
( ( ~ $less(X2,0)
& ( gcd(X1,X7) = gcd(X2,X14) )
& ~ $less(X14,0)
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
=> ( ~ $less(0,X14)
=> ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(theory_normalization,[],[f84]) ).
tff(f84,negated_conjecture,
~ ! [X7: $int,X1: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
( ( $lesseq(0,X2)
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
=> ( ~ $less(0,X14)
=> ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
inference(negated_conjecture,[],[f83]) ).
tff(f83,conjecture,
! [X7: $int,X1: $int] :
( ( $lesseq(0,X7)
& $lesseq(0,X1) )
=> ! [X12: $int,X8: $int,X0: $int,X11: $int,X2: $int,X14: $int] :
( ( $lesseq(0,X2)
& ( gcd(X1,X7) = gcd(X2,X14) )
& $lesseq(0,X14)
& ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
& ( $sum($product(X12,X1),$product(X8,X7)) = X14 ) )
=> ( ~ $less(0,X14)
=> ? [X16: $int,X15: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f199,plain,
sK5 = $sum($product(sK6,sK0),$product(sK4,sK1)),
inference(cnf_transformation,[],[f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.12 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 08:02:09 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a TF0_THM_EQU_ARI problem
% 0.12/0.36 Running first-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20720)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/15Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20719)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20718)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20715)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59848Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20721)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/32Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20716)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/34Mi)
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20717)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/8Mi)
% 0.22/0.43 % (20718)Instruction limit reached!
% 0.22/0.43 % (20718)------------------------------
% 0.22/0.43 % (20718)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43 % (20718)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43 % (20718)Termination reason: Time limit
% 0.22/0.43 % (20718)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (20718)Memory used [KB]: 825
% 0.22/0.43 % (20718)Time elapsed: 0.003 s
% 0.22/0.43 % (20718)Instructions burned: 3 (million)
% 0.22/0.43 % (20717)Instruction limit reached!
% 0.22/0.43 % (20717)------------------------------
% 0.22/0.43 % (20717)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43 % (20717)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43 % (20717)Termination reason: Time limit
% 0.22/0.43 % (20717)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (20717)Memory used [KB]: 1143
% 0.22/0.43 % (20717)Time elapsed: 0.007 s
% 0.22/0.43 % (20717)Instructions burned: 8 (million)
% 0.22/0.43 % (20721)First to succeed.
% 0.22/0.43 % (20720)Also succeeded, but the first one will report.
% 0.22/0.43 % (20721)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20712"
% 0.22/0.43 % (20719)Also succeeded, but the first one will report.
% 0.22/0.43 % (20712)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (20721)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (20721)------------------------------
% 0.22/0.44 % (20721)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.44 % (20721)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.44 % (20721)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (20721)Memory used [KB]: 895
% 0.22/0.44 % (20721)Time elapsed: 0.008 s
% 0.22/0.44 % (20721)Instructions burned: 9 (million)
% 0.22/0.44 % (20721)------------------------------
% 0.22/0.44 % (20721)------------------------------
% 0.22/0.44 % (20712)Success in time 0.065 s
%------------------------------------------------------------------------------