%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW652_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:31:03 PM UTC 2026
% Result : Theorem 4.01s 1.34s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 0 |; 28 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 167 ( 60 atm; 49 fun; 37 num; 21 var)
% Number of types : 9 ( 7 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 28 ( 23 usr; 16 con; 0-4 aty)
% Number of variables : 21 ( 12 !; 9 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(type_def_9,type,
uf_pure1: $tType ).
tff(type_def_10,type,
uf1: $tType ).
tff(type_def_11,type,
graph1: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
ref: ty > ty ).
tff(func_def_13,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_14,type,
contents: ( ty * uni ) > uni ).
tff(func_def_15,type,
uf_pure: ty ).
tff(func_def_16,type,
size1: uf_pure1 > $int ).
tff(func_def_17,type,
num1: uf_pure1 > $int ).
tff(func_def_19,type,
uf: ty ).
tff(func_def_20,type,
mk_uf1: uf_pure1 > uf1 ).
tff(func_def_21,type,
state1: uf1 > uf_pure1 ).
tff(func_def_22,type,
graph: ty ).
tff(func_def_25,type,
sK0: $int ).
tff(func_def_26,type,
sK1: $int ).
tff(func_def_27,type,
sK2: $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
repr1: ( uf_pure1 * $int * $int ) > $o ).
tff(pred_def_5,type,
same1: ( uf_pure1 * $int * $int ) > $o ).
tff(pred_def_6,type,
same_reprs1: ( uf_pure1 * uf_pure1 ) > $o ).
tff(pred_def_7,type,
path1: ( graph1 * $int * $int ) > $o ).
tff(f24,conjecture,
! [X2: $int,X1: $int,X0: $int] :
( $lesseq(0,X0)
=> ( ( $lesseq(0,X1)
& $less(X1,X0) )
=> ( ( $lesseq(0,X2)
& $less(X2,X0) )
=> $less($sum($product(X1,X0),X2),$product(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ineq1) ).
tff(f25,negated_conjecture,
~ ! [X2: $int,X1: $int,X0: $int] :
( $lesseq(0,X0)
=> ( ( $lesseq(0,X1)
& $less(X1,X0) )
=> ( ( $lesseq(0,X2)
& $less(X2,X0) )
=> $less($sum($product(X1,X0),X2),$product(X0,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
tff(f26,plain,
~ ! [X2: $int,X1: $int,X0: $int] :
( ~ $less(X0,0)
=> ( ( ~ $less(X1,0)
& $less(X1,X0) )
=> ( ( ~ $less(X2,0)
& $less(X2,X0) )
=> $less($sum($product(X1,X0),X2),$product(X0,X0)) ) ) ),
inference(theory_normalization,[],[f25]) ).
tff(f49,plain,
~ ! [X2: $int,X1: $int,X0: $int] :
( ~ $less(X2,0)
=> ( ( $less(X1,X2)
& ~ $less(X1,0) )
=> ( ( $less(X0,X2)
& ~ $less(X0,0) )
=> $less($sum($product(X1,X2),X0),$product(X2,X2)) ) ) ),
inference(rectify,[],[f26]) ).
tff(f51,plain,
? [X2: $int,X1: $int,X0: $int] :
( ~ $less($sum($product(X1,X2),X0),$product(X2,X2))
& $less(X0,X2)
& ~ $less(X0,0)
& $less(X1,X2)
& ~ $less(X1,0)
& ~ $less(X2,0) ),
inference(ennf_transformation,[],[f49]) ).
tff(f52,plain,
? [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
& ~ $less(X1,0)
& ~ $less(X2,0)
& $less(X1,X2)
& ~ $less(X0,0)
& ~ $less($sum($product(X1,X2),X0),$product(X2,X2)) ),
inference(flattening,[],[f51]) ).
tff(f55,plain,
? [X0: $int,X1: $int,X2: $int] :
( $less(X1,X0)
& ~ $less(X2,0)
& ~ $less(X0,0)
& $less(X2,X0)
& ~ $less(X1,0)
& ~ $less($sum($product(X2,X0),X1),$product(X0,X0)) ),
inference(rectify,[],[f52]) ).
tff(f56,plain,
( $less(sK1,sK0)
& ~ $less(sK2,0)
& ~ $less(sK0,0)
& $less(sK2,sK0)
& ~ $less(sK1,0)
& ~ $less($sum($product(sK2,sK0),sK1),$product(sK0,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f55]) ).
tff(f58,plain,
~ $less($sum($product(sK2,sK0),sK1),$product(sK0,sK0)),
inference(cnf_transformation,[],[f56]) ).
tff(f59,plain,
~ $less(sK1,0),
inference(cnf_transformation,[],[f56]) ).
tff(f60,plain,
$less(sK2,sK0),
inference(cnf_transformation,[],[f56]) ).
tff(f63,plain,
$less(sK1,sK0),
inference(cnf_transformation,[],[f56]) ).
tff(f67,plain,
$less(0,$sum(sK0,$uminus(sK1))),
inference(evaluation,[],[f63]) ).
tff(f68,plain,
$less(0,$sum($sum($sum($product(sK2,sK0),sK1),1),$uminus($product(sK0,sK0)))),
inference(evaluation,[],[f58]) ).
tff(f69,plain,
$less(0,$sum(sK1,1)),
inference(evaluation,[],[f59]) ).
tff(f71,plain,
$less(0,$sum(sK0,$uminus(sK2))),
inference(evaluation,[],[f60]) ).
tff(f79,definition,
( spl3_2
<=> $less(0,$sum(sK0,$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f82,plain,
spl3_2,
inference(avatar_split_clause,[],[f67,f79]) ).
tff(f84,definition,
( spl3_3
<=> $less(0,$sum($sum($sum($product(sK2,sK0),sK1),1),$uminus($product(sK0,sK0)))) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f87,plain,
spl3_3,
inference(avatar_split_clause,[],[f68,f84]) ).
tff(f89,definition,
( spl3_4
<=> $less(0,$sum(sK1,1)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f92,plain,
spl3_4,
inference(avatar_split_clause,[],[f69,f89]) ).
tff(f99,definition,
( spl3_6
<=> $less(0,$sum(sK0,$uminus(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f102,plain,
spl3_6,
inference(avatar_split_clause,[],[f71,f99]) ).
tff(f103,plain,
$false,
inference(avatar_smt_refutation,[],[f102,f92,f87,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW652_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:21:55 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.34 % (2416958)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.01/1.34 % (2417056)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4026356635:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.01/1.34 % (2417056)Instruction limit reached!
% 4.01/1.34 % (2417056)------------------------------
% 4.01/1.34 % (2417056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417056)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417056)Termination reason: Instruction limit
% 4.01/1.34 % (2417056)Termination phase: Saturation
% 4.01/1.34 % (2417056)Time elapsed: 0.003 s
% 4.01/1.34 % (2417056)Peak memory usage: 89 MB
% 4.01/1.34 % (2417056)Instructions burned: 6 (million)
% 4.01/1.34 % (2417057)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3869524218:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.01/1.34 % (2417055)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1689446218:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.01/1.34 % (2417053)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4212764791:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.01/1.34 % (2417054)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2785931109:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.01/1.34 % (2417058)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4011298858:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.01/1.34 % (2417052)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=900013596:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.01/1.34 % (2417055)Instruction limit reached!
% 4.01/1.34 % (2417055)------------------------------
% 4.01/1.34 % (2417055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417055)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417055)Termination reason: Instruction limit
% 4.01/1.34 % (2417055)Termination phase: Saturation
% 4.01/1.34 % (2417055)Time elapsed: 0.005 s
% 4.01/1.34 % (2417055)Peak memory usage: 88 MB
% 4.01/1.34 % (2417055)Instructions burned: 7 (million)
% 4.01/1.34 % (2417052)First to succeed.
% 4.01/1.34 % (2417057)Also succeeded, but the first one will report.
% 4.01/1.34 % (2417052)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2416958"
% 4.01/1.34 % (2417053)Also succeeded, but the first one will report.
% 4.01/1.34 % (2417058)Also succeeded, but the first one will report.
% 4.01/1.34 % (2417060)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=756514512:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.01/1.34 % (2417060)Instruction limit reached!
% 4.01/1.34 % (2417060)------------------------------
% 4.01/1.34 % (2417060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417060)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417060)Termination reason: Instruction limit
% 4.01/1.34 % (2417060)Termination phase: Saturation
% 4.01/1.34 % (2417060)Time elapsed: 0.006 s
% 4.01/1.34 % (2417060)Peak memory usage: 88 MB
% 4.01/1.34 % (2417060)Instructions burned: 18 (million)
% 4.01/1.34 % (2417054)Instruction limit reached!
% 4.01/1.34 % (2417054)------------------------------
% 4.01/1.34 % (2417054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417054)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417054)Termination reason: Instruction limit
% 4.01/1.34 % (2417054)Termination phase: Saturation
% 4.01/1.34 % (2417054)Time elapsed: 0.114 s
% 4.01/1.34 % (2417054)Peak memory usage: 115 MB
% 4.01/1.34 % (2417054)Instructions burned: 201 (million)
% 4.01/1.34 % (2417067)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=3174496116:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.01/1.34 % (2417067)Instruction limit reached!
% 4.01/1.34 % (2417067)------------------------------
% 4.01/1.34 % (2417067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417067)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417067)Termination reason: Instruction limit
% 4.01/1.34 % (2417067)Termination phase: Saturation
% 4.01/1.34 % (2417067)Time elapsed: 0.021 s
% 4.01/1.34 % (2417067)Peak memory usage: 88 MB
% 4.01/1.34 % (2417067)Instructions burned: 30 (million)
% 4.01/1.34 % (2417069)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1253943383:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.01/1.34 % (2417069)Instruction limit reached!
% 4.01/1.34 % (2417069)------------------------------
% 4.01/1.34 % (2417069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417069)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417069)Termination reason: Instruction limit
% 4.01/1.34 % (2417069)Termination phase: Saturation
% 4.01/1.34 % (2417069)Time elapsed: 0.006 s
% 4.01/1.34 % (2417069)Peak memory usage: 90 MB
% 4.01/1.34 % (2417069)Instructions burned: 17 (million)
% 4.01/1.34 % (2417070)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3546218457:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.01/1.34 % (2417070)Instruction limit reached!
% 4.01/1.34 % (2417070)------------------------------
% 4.01/1.34 % (2417070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417070)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417070)Termination reason: Instruction limit
% 4.01/1.34 % (2417070)Termination phase: Saturation
% 4.01/1.34 % (2417070)Time elapsed: 0.020 s
% 4.01/1.34 % (2417070)Peak memory usage: 89 MB
% 4.01/1.34 % (2417070)Instructions burned: 25 (million)
% 4.01/1.34 % (2417052)Refutation found. Thanks to Tanya!
% 4.01/1.34 % SZS status Theorem for theBenchmark
% 4.01/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.01/1.34 % (2417052)------------------------------
% 4.01/1.34 % (2417052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.01/1.34 % (2417052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.01/1.34 % (2417052)CaDiCaL version: 2.1.3
% 4.01/1.34 % (2417052)Termination reason: Refutation
% 4.01/1.34 % (2417052)Time elapsed: 0.037 s
% 4.01/1.34 % (2417052)Peak memory usage: 117 MB
% 4.01/1.34 % (2417052)Instructions burned: 14 (million)
% 4.01/1.34 % (2417052)------------------------------
% 4.01/1.34 % (2417052)------------------------------
% 4.01/1.34 % (2416958)Success in time 0.475 s
% 4.01/1.34 % Vampire exiting
%------------------------------------------------------------------------------