%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW600_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:30:54 PM UTC 2026
% Result : Theorem 0.20s 1.03s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 34 equ)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 104 ( 40 ~; 0 |; 52 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 232 ( 40 atm; 78 fun; 40 num; 74 var)
% Number of types : 6 ( 4 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 29 usr; 17 con; 0-4 aty)
% Number of variables : 74 ( 42 !; 32 ?; 74 :)
% 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_26,type,
sK0: $int > $int ).
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 ) > $int ).
tff(func_def_36,type,
sK10: $int > $int ).
tff(func_def_37,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(f83,conjecture,
! [X1: $int,X0: $int] :
( ( $lesseq(0,X0)
& $lesseq(0,X1) )
=> ! [X2: $int,X7: $int,X6: $int,X3: $int,X4: $int,X5: $int] :
( ( ( gcd(X7,X6) = gcd(X0,X1) )
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& $lesseq(0,X6)
& $lesseq(0,X7) )
=> ( ~ $less(0,X6)
=> ? [X9: $int,X8: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_gcd) ).
tff(f84,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( ( $lesseq(0,X0)
& $lesseq(0,X1) )
=> ! [X2: $int,X7: $int,X6: $int,X3: $int,X4: $int,X5: $int] :
( ( ( gcd(X7,X6) = gcd(X0,X1) )
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& $lesseq(0,X6)
& $lesseq(0,X7) )
=> ( ~ $less(0,X6)
=> ? [X9: $int,X8: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f83]) ).
tff(f101,plain,
~ ! [X1: $int,X0: $int] :
( ( ~ $less(X0,0)
& ~ $less(X1,0) )
=> ! [X2: $int,X7: $int,X6: $int,X3: $int,X4: $int,X5: $int] :
( ( ( gcd(X7,X6) = gcd(X0,X1) )
& ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
& ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
& ~ $less(X6,0)
& ~ $less(X7,0) )
=> ( ~ $less(0,X6)
=> ? [X9: $int,X8: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
inference(theory_normalization,[],[f84]) ).
tff(f133,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ! [X5: $int,X4: $int,X3: $int,X6: $int,X2: $int,X7: $int] :
( ( ~ $less(X3,0)
& ( $sum($product(X5,X1),$product(X2,X0)) = X4 )
& ~ $less(X4,0)
& ( $sum($product(X7,X1),$product(X6,X0)) = X3 )
& ( gcd(X1,X0) = gcd(X3,X4) ) )
=> ( ~ $less(0,X4)
=> ? [X8: $int,X9: $int] : ( $sum($product(X9,X1),$product(X8,X0)) = X3 ) ) ) ),
inference(rectify,[],[f101]) ).
tff(f161,plain,
? [X0: $int,X1: $int] :
( ? [X5: $int,X4: $int,X3: $int,X6: $int,X2: $int,X7: $int] :
( ! [X9: $int,X8: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X3 )
& ~ $less(0,X4)
& ~ $less(X3,0)
& ( $sum($product(X5,X1),$product(X2,X0)) = X4 )
& ~ $less(X4,0)
& ( $sum($product(X7,X1),$product(X6,X0)) = X3 )
& ( gcd(X1,X0) = gcd(X3,X4) ) )
& ~ $less(X1,0)
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f162,plain,
? [X0: $int,X1: $int] :
( ~ $less(X1,0)
& ~ $less(X0,0)
& ? [X2: $int,X4: $int,X3: $int,X7: $int,X5: $int,X6: $int] :
( ( $sum($product(X7,X1),$product(X6,X0)) = X3 )
& ( gcd(X1,X0) = gcd(X3,X4) )
& ~ $less(X3,0)
& ! [X9: $int,X8: $int] : ( $sum($product(X9,X1),$product(X8,X0)) != X3 )
& ( $sum($product(X5,X1),$product(X2,X0)) = X4 )
& ~ $less(0,X4)
& ~ $less(X4,0) ) ),
inference(flattening,[],[f161]) ).
tff(f249,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(X5,X1),$product(X7,X0)) = X4 )
& ( gcd(X1,X0) = gcd(X4,X3) )
& ~ $less(X4,0)
& ! [X8: $int,X9: $int] : ( $sum($product(X8,X1),$product(X9,X0)) != X4 )
& ( $sum($product(X6,X1),$product(X2,X0)) = X3 )
& ~ $less(0,X3)
& ~ $less(X3,0) ) ),
inference(rectify,[],[f162]) ).
tff(f250,plain,
( ~ $less(sK2,0)
& ~ $less(sK1,0)
& ( $sum($product(sK6,sK2),$product(sK8,sK1)) = sK5 )
& ( gcd(sK5,sK4) = gcd(sK2,sK1) )
& ~ $less(sK5,0)
& ! [X8: $int,X9: $int] : ( sK5 != $sum($product(X8,sK2),$product(X9,sK1)) )
& ( $sum($product(sK7,sK2),$product(sK3,sK1)) = sK4 )
& ~ $less(0,sK4)
& ~ $less(sK4,0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6),skolemize(X6,sK7),skolemize(X7,sK8)],[f249]) ).
tff(f327,plain,
! [X8: $int,X9: $int] : ( sK5 != $sum($product(X8,sK2),$product(X9,sK1)) ),
inference(cnf_transformation,[],[f250]) ).
tff(f330,plain,
$sum($product(sK6,sK2),$product(sK8,sK1)) = sK5,
inference(cnf_transformation,[],[f250]) ).
tff(f421,plain,
$false,
inference(forward_subsumption_resolution,[],[f330,f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW600_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 14:27:36 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.53/0.87 % (3657249)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.53/0.87 % (3657260)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2211494107:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.53/0.87 % (3657260)Instruction limit reached!
% 2.53/0.87 % (3657260)------------------------------
% 2.53/0.87 % (3657260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.87 % (3657260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.87 % (3657260)CaDiCaL version: 2.1.3
% 2.53/0.87 % (3657260)Termination reason: Instruction limit
% 2.53/0.87 % (3657260)Termination phase: Saturation
% 2.53/0.87 % (3657260)Time elapsed: 0.027 s
% 2.53/0.87 % (3657260)Peak memory usage: 117 MB
% 2.53/0.87 % (3657260)Instructions burned: 34 (million)
% 2.53/0.87 % (3657255)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1936173810:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.53/0.87 % (3657258)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=283390259:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.53/0.87 % (3657254)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1077892505:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.53/0.87 % (3657257)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=854562303:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.53/0.87 % (3657259)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3992744711:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.53/0.87 % (3657256)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1110311464:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.53/0.87 % (3657258)Instruction limit reached!
% 2.53/0.87 % (3657258)------------------------------
% 2.53/0.87 % (3657258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.87 % (3657258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.87 % (3657258)CaDiCaL version: 2.1.3
% 2.53/0.87 % (3657258)Termination reason: Instruction limit
% 2.53/0.87 % (3657258)Termination phase: Saturation
% 2.53/0.87 % (3657258)Time elapsed: 0.003 s
% 2.53/0.87 % (3657258)Peak memory usage: 87 MB
% 2.53/0.87 % (3657258)Instructions burned: 5 (million)
% 2.53/0.87 % (3657257)Instruction limit reached!
% 2.53/0.87 % (3657257)------------------------------
% 2.53/0.87 % (3657257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.87 % (3657257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.87 % (3657257)CaDiCaL version: 2.1.3
% 2.53/0.87 % (3657257)Termination reason: Instruction limit
% 2.53/0.87 % (3657257)Termination phase: Saturation
% 2.53/0.87 % (3657257)Time elapsed: 0.005 s
% 2.53/0.87 % (3657257)Peak memory usage: 88 MB
% 2.53/0.87 % (3657257)Instructions burned: 8 (million)
% 2.53/0.87 % (3657254)Instruction limit reached!
% 2.53/0.87 % (3657254)------------------------------
% 2.53/0.87 % (3657254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.87 % (3657254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.87 % (3657254)CaDiCaL version: 2.1.3
% 2.53/0.87 % (3657254)Termination reason: Instruction limit
% 2.53/0.87 % (3657254)Termination phase: Saturation
% 2.53/0.87 % (3657254)Time elapsed: 0.030 s
% 2.53/0.87 % (3657254)Peak memory usage: 116 MB
% 2.53/0.87 % (3657254)Instructions burned: 13 (million)
% 2.53/0.87 % (3657259)First to succeed.
% 2.53/0.87 % (3657259)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3657249"
% 2.53/0.87 % (3657256)Also succeeded, but the first one will report.
% 2.53/0.87 % (3657255)Also succeeded, but the first one will report.
% 2.53/0.87 % (3657262)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=110315017:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.53/0.87 % (3657262)Also succeeded, but the first one will report.
% 2.53/0.87 % (3657269)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=4051111424:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.53/0.87 % (3657270)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2634326427:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 0.20/1.03 % (3657270)Instruction limit reached!
% 0.20/1.03 % (3657270)------------------------------
% 0.20/1.03 % (3657270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.03 % (3657270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.03 % (3657270)CaDiCaL version: 2.1.3
% 0.20/1.03 % (3657270)Termination reason: Instruction limit
% 0.20/1.03 % (3657270)Termination phase: Saturation
% 0.20/1.03 % (3657270)Time elapsed: 0.011 s
% 0.20/1.03 % (3657270)Peak memory usage: 88 MB
% 0.20/1.03 % (3657270)Instructions burned: 18 (million)
% 0.20/1.03 % (3657269)Instruction limit reached!
% 0.20/1.03 % (3657269)------------------------------
% 0.20/1.03 % (3657269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.03 % (3657269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.03 % (3657269)CaDiCaL version: 2.1.3
% 0.20/1.03 % (3657269)Termination reason: Instruction limit
% 0.20/1.03 % (3657269)Termination phase: Saturation
% 0.20/1.03 % (3657269)Time elapsed: 0.023 s
% 0.20/1.03 % (3657269)Peak memory usage: 89 MB
% 0.20/1.03 % (3657269)Instructions burned: 30 (million)
% 0.20/1.03 % (3657271)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1973506935:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 0.20/1.03 % (3657271)Also succeeded, but the first one will report.
% 0.20/1.03 % (3657275)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1174722531:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 0.20/1.03 % (3657277)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=3893726992:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 0.20/1.03 % (3657275)Instruction limit reached!
% 0.20/1.03 % (3657275)------------------------------
% 0.20/1.03 % (3657275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.03 % (3657275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.03 % (3657275)CaDiCaL version: 2.1.3
% 0.20/1.03 % (3657275)Termination reason: Instruction limit
% 0.20/1.03 % (3657275)Termination phase: Saturation
% 0.20/1.03 % (3657275)Time elapsed: 0.017 s
% 0.20/1.03 % (3657275)Peak memory usage: 89 MB
% 0.20/1.03 % (3657275)Instructions burned: 27 (million)
% 0.20/1.03 % (3657277)Also succeeded, but the first one will report.
% 0.20/1.03 % (3657259)Refutation found. Thanks to Tanya!
% 0.20/1.03 % SZS status Theorem for theBenchmark
% 0.20/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.03 % (3657259)------------------------------
% 0.20/1.03 % (3657259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.03 % (3657259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.03 % (3657259)CaDiCaL version: 2.1.3
% 0.20/1.03 % (3657259)Termination reason: Refutation
% 0.20/1.03 % (3657259)Time elapsed: 0.033 s
% 0.20/1.03 % (3657259)Peak memory usage: 112 MB
% 0.20/1.03 % (3657259)Instructions burned: 13 (million)
% 0.20/1.03 % (3657259)------------------------------
% 0.20/1.03 % (3657259)------------------------------
% 0.20/1.03 % (3657249)Success in time 0.446 s
% 0.20/1.03 % Vampire exiting
%------------------------------------------------------------------------------