%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT035_1 : TPTP v9.3.1. Released v5.0.0.
% 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 09:47:09 AM UTC 2026
% Result : Theorem 3.80s 1.34s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 59 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 17 ~; 14 |; 6 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 83 ( 21 atm; 22 fun; 19 num; 21 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(func_def_11,type,
sK2: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f8,axiom,
! [X1: collection,X0: $int] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f9,axiom,
! [X0: $int,X1: collection] :
( in(X0,X1)
<=> ( count(add(X0,X1)) = count(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f13,conjecture,
! [X2: $int,X1: $int,X0: collection] :
( $greater(X2,0)
=> $greatereq($sum(count(X0),X2),count(add(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ! [X2: $int,X1: $int,X0: collection] :
( $greater(X2,0)
=> $greatereq($sum(count(X0),X2),count(add(X1,X0))) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f15,plain,
~ ! [X2: $int,X1: $int,X0: collection] :
( $less(0,X2)
=> ~ $less($sum(count(X0),X2),count(add(X1,X0))) ),
inference(theory_normalization,[],[f14]) ).
tff(f20,plain,
! [X1: $int,X0: collection] :
( ( count(add(X1,X0)) = $sum(count(X0),1) )
<=> ~ in(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f21,plain,
~ ! [X1: $int,X2: collection,X0: $int] :
( $less(0,X0)
=> ~ $less($sum(count(X2),X0),count(add(X1,X2))) ),
inference(rectify,[],[f15]) ).
tff(f26,plain,
? [X2: collection,X1: $int,X0: $int] :
( $less($sum(count(X2),X0),count(add(X1,X2)))
& $less(0,X0) ),
inference(ennf_transformation,[],[f21]) ).
tff(f35,plain,
? [X0: collection,X1: $int,X2: $int] :
( $less($sum(count(X0),X2),count(add(X1,X0)))
& $less(0,X2) ),
inference(rectify,[],[f26]) ).
tff(f36,plain,
( $less($sum(count(sK0),sK2),count(add(sK1,sK0)))
& $less(0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f35]) ).
tff(f41,plain,
! [X1: $int,X0: collection] :
( ( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) )
& ( ~ in(X1,X0)
| ( count(add(X1,X0)) != $sum(count(X0),1) ) ) ),
inference(nnf_transformation,[],[f20]) ).
tff(f42,plain,
! [X0: $int,X1: collection] :
( ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) )
& ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ) ),
inference(rectify,[],[f41]) ).
tff(f43,plain,
! [X0: $int,X1: collection] :
( ( in(X0,X1)
| ( count(add(X0,X1)) != count(X1) ) )
& ( ( count(add(X0,X1)) = count(X1) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f51,plain,
$less(0,sK2),
inference(cnf_transformation,[],[f36]) ).
tff(f52,plain,
$less($sum(count(sK0),sK2),count(add(sK1,sK0))),
inference(cnf_transformation,[],[f36]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( in(X0,X1)
| ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f64,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( count(add(X0,X1)) = count(X1) ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f73,definition,
( spl3_1
<=> $less($sum(count(sK0),sK2),count(add(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f75,plain,
( $less($sum(count(sK0),sK2),count(add(sK1,sK0)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f73]) ).
tff(f76,plain,
spl3_1,
inference(avatar_split_clause,[],[f52,f73]) ).
tff(f78,definition,
( spl3_2
<=> $less(0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f81,plain,
spl3_2,
inference(avatar_split_clause,[],[f51,f78]) ).
tff(f121,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| ( count(add(X0,X1)) = count(X1) ) ),
inference(resolution,[],[f62,f64]) ).
tff(f265,plain,
( $less($sum(count(sK0),sK2),$sum(count(sK0),1))
| ( count(add(sK1,sK0)) = count(sK0) )
| ~ spl3_1 ),
inference(superposition,[],[f75,f121]) ).
tff(f281,definition,
( spl3_4
<=> $less($sum(count(sK0),sK2),$sum(count(sK0),1)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f285,definition,
( spl3_5
<=> ( count(add(sK1,sK0)) = count(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f288,plain,
( spl3_4
| spl3_5
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f265,f73,f285,f281]) ).
tff(f292,plain,
$false,
inference(avatar_smt_refutation,[],[f288,f81,f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT035_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 00:10:49 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running first-order theorem proving
% 0.10/0.26 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
% 2.47/1.14 % (4169019)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.47/1.14 % (4169054)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3519207051:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.47/1.14 % (4169054)Refutation not found, incomplete strategy
% 2.47/1.14 % (4169054)------------------------------
% 2.47/1.14 % (4169054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.14 % (4169054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.14 % (4169054)CaDiCaL version: 2.1.3
% 2.47/1.14 % (4169054)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.14 % (4169054)Time elapsed: 0.020 s
% 2.47/1.14 % (4169054)Peak memory usage: 116 MB
% 2.47/1.14 % (4169054)Instructions burned: 12 (million)
% 2.47/1.14 % (4169060)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3727021190:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.47/1.14 % (4169066)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3670757637:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.47/1.14 % (4169063)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3495753600:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.47/1.14 % (4169064)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=227299331:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.47/1.14 % (4169055)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2005396942:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.47/1.14 % (4169058)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3325465916:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.47/1.14 % (4169063)Instruction limit reached!
% 2.47/1.14 % (4169063)------------------------------
% 2.47/1.14 % (4169063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.14 % (4169063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.14 % (4169063)CaDiCaL version: 2.1.3
% 2.47/1.14 % (4169063)Termination reason: Instruction limit
% 2.47/1.14 % (4169063)Termination phase: Saturation
% 2.47/1.14 % (4169063)Time elapsed: 0.004 s
% 2.47/1.14 % (4169063)Peak memory usage: 89 MB
% 2.47/1.14 % (4169063)Instructions burned: 4 (million)
% 2.47/1.14 % (4169060)Instruction limit reached!
% 2.47/1.14 % (4169060)------------------------------
% 2.47/1.14 % (4169060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.14 % (4169060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.14 % (4169060)CaDiCaL version: 2.1.3
% 2.47/1.14 % (4169060)Termination reason: Instruction limit
% 2.47/1.14 % (4169060)Termination phase: Saturation
% 2.47/1.14 % (4169060)Time elapsed: 0.005 s
% 2.47/1.14 % (4169060)Peak memory usage: 88 MB
% 2.47/1.14 % (4169060)Instructions burned: 7 (million)
% 2.47/1.14 % (4169064)First to succeed.
% 2.47/1.14 % (4169064)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4169019"
% 2.47/1.14 % (4169055)Also succeeded, but the first one will report.
% 2.47/1.14 % (4169066)Instruction limit reached!
% 2.47/1.14 % (4169066)------------------------------
% 2.47/1.14 % (4169066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.14 % (4169066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.14 % (4169066)CaDiCaL version: 2.1.3
% 2.47/1.14 % (4169066)Termination reason: Instruction limit
% 2.47/1.14 % (4169066)Termination phase: Saturation
% 2.47/1.14 % (4169066)Time elapsed: 0.048 s
% 2.47/1.14 % (4169066)Peak memory usage: 116 MB
% 2.47/1.14 % (4169066)Instructions burned: 33 (million)
% 2.47/1.14 % (4169054)------------------------------
% 2.47/1.14 % (4169054)------------------------------
% 2.47/1.14 % (4169116)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2454389864:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.47/1.14 % (4169117)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=3726250519:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.47/1.14 % (4169116)Instruction limit reached!
% 2.47/1.14 % (4169116)------------------------------
% 2.47/1.14 % (4169116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169116)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169116)Termination reason: Instruction limit
% 3.80/1.34 % (4169116)Termination phase: Saturation
% 3.80/1.34 % (4169116)Time elapsed: 0.011 s
% 3.80/1.34 % (4169116)Peak memory usage: 88 MB
% 3.80/1.34 % (4169116)Instructions burned: 14 (million)
% 3.80/1.34 % (4169117)Instruction limit reached!
% 3.80/1.34 % (4169117)------------------------------
% 3.80/1.34 % (4169117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169117)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169117)Termination reason: Instruction limit
% 3.80/1.34 % (4169117)Termination phase: Saturation
% 3.80/1.34 % (4169117)Time elapsed: 0.022 s
% 3.80/1.34 % (4169117)Peak memory usage: 89 MB
% 3.80/1.34 % (4169117)Instructions burned: 29 (million)
% 3.80/1.34 % (4169058)Instruction limit reached!
% 3.80/1.34 % (4169058)------------------------------
% 3.80/1.34 % (4169058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169058)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169058)Termination reason: Instruction limit
% 3.80/1.34 % (4169058)Termination phase: Saturation
% 3.80/1.34 % (4169058)Time elapsed: 0.179 s
% 3.80/1.34 % (4169058)Peak memory usage: 117 MB
% 3.80/1.34 % (4169058)Instructions burned: 202 (million)
% 3.80/1.34 % (4169133)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1858002138:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.80/1.34 % (4169133)Instruction limit reached!
% 3.80/1.34 % (4169133)------------------------------
% 3.80/1.34 % (4169133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169133)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169133)Termination reason: Instruction limit
% 3.80/1.34 % (4169133)Termination phase: Saturation
% 3.80/1.34 % (4169133)Time elapsed: 0.011 s
% 3.80/1.34 % (4169133)Peak memory usage: 90 MB
% 3.80/1.34 % (4169133)Instructions burned: 16 (million)
% 3.80/1.34 % (4169148)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1320808170:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.80/1.34 % (4169148)Instruction limit reached!
% 3.80/1.34 % (4169148)------------------------------
% 3.80/1.34 % (4169148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169148)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169148)Termination reason: Instruction limit
% 3.80/1.34 % (4169148)Time elapsed: 0.010 s
% 3.80/1.34 % (4169148)Peak memory usage: 89 MB
% 3.80/1.34 % (4169148)Instructions burned: 24 (million)
% 3.80/1.34 % (4169151)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=2592538208:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.80/1.34 % (4169152)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=434095687:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.80/1.34 % (4169151)Instruction limit reached!
% 3.80/1.34 % (4169151)------------------------------
% 3.80/1.34 % (4169151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169151)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169151)Termination reason: Instruction limit
% 3.80/1.34 % (4169151)Termination phase: Saturation
% 3.80/1.34 % (4169151)Time elapsed: 0.016 s
% 3.80/1.34 % (4169151)Peak memory usage: 89 MB
% 3.80/1.34 % (4169151)Instructions burned: 28 (million)
% 3.80/1.34 % (4169064)Refutation found. Thanks to Tanya!
% 3.80/1.34 % SZS status Theorem for theBenchmark
% 3.80/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.34 % (4169064)------------------------------
% 3.80/1.34 % (4169064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.34 % (4169064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.34 % (4169064)CaDiCaL version: 2.1.3
% 3.80/1.34 % (4169064)Termination reason: Refutation
% 3.80/1.34 % (4169064)Time elapsed: 0.039 s
% 3.80/1.34 % (4169064)Peak memory usage: 116 MB
% 3.80/1.34 % (4169064)Instructions burned: 20 (million)
% 3.80/1.34 % (4169064)------------------------------
% 3.80/1.34 % (4169064)------------------------------
% 3.80/1.34 % (4169019)Success in time 0.433 s
% 3.80/1.34 % Vampire exiting
%------------------------------------------------------------------------------