%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT034_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 2.78s 1.07s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 48 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 16 ~; 14 |; 3 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 69 ( 12 atm; 21 fun; 21 num; 15 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 : 8 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 26 !; 4 ?; 30 :)
% 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(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f8,axiom,
! [X1: collection,X0: $int] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f9,axiom,
! [X1: collection,X0: $int] :
( ( count(add(X0,X1)) = count(X1) )
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f13,conjecture,
! [X1: $int,X0: collection] : $greatereq($sum(count(X0),1),count(add(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ! [X1: $int,X0: collection] : $greatereq($sum(count(X0),1),count(add(X1,X0))),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f16,plain,
~ ! [X1: $int,X0: collection] : ~ $less($sum(count(X0),1),count(add(X1,X0))),
inference(theory_normalization,[],[f14]) ).
tff(f20,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
<=> ( count(X0) = count(add(X1,X0)) ) ),
inference(rectify,[],[f9]) ).
tff(f21,plain,
~ ! [X1: collection,X0: $int] : ~ $less($sum(count(X1),1),count(add(X0,X1))),
inference(rectify,[],[f16]) ).
tff(f25,plain,
? [X1: collection,X0: $int] : $less($sum(count(X1),1),count(add(X0,X1))),
inference(ennf_transformation,[],[f21]) ).
tff(f27,plain,
! [X1: collection,X0: $int] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f28,plain,
! [X0: collection,X1: $int] :
( ( ~ in(X1,X0)
| ( $sum(count(X0),1) != count(add(X1,X0)) ) )
& ( ( $sum(count(X0),1) = count(add(X1,X0)) )
| in(X1,X0) ) ),
inference(rectify,[],[f27]) ).
tff(f29,plain,
! [X0: collection,X1: $int] :
( ( in(X1,X0)
| ( count(X0) != count(add(X1,X0)) ) )
& ( ( count(X0) = count(add(X1,X0)) )
| ~ in(X1,X0) ) ),
inference(nnf_transformation,[],[f20]) ).
tff(f33,plain,
? [X0: collection,X1: $int] : $less($sum(count(X0),1),count(add(X1,X0))),
inference(rectify,[],[f25]) ).
tff(f34,plain,
$less($sum(count(sK0),1),count(add(sK1,sK0))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
tff(f42,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
| ( $sum(count(X0),1) = count(add(X1,X0)) ) ),
inference(cnf_transformation,[],[f28]) ).
tff(f45,plain,
! [X0: collection,X1: $int] :
( ~ in(X1,X0)
| ( count(X0) = count(add(X1,X0)) ) ),
inference(cnf_transformation,[],[f29]) ).
tff(f51,plain,
$less($sum(count(sK0),1),count(add(sK1,sK0))),
inference(cnf_transformation,[],[f34]) ).
tff(f75,definition,
( spl2_2
<=> $less($sum(count(sK0),1),count(add(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f77,plain,
( $less($sum(count(sK0),1),count(add(sK1,sK0)))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f78,plain,
spl2_2,
inference(avatar_split_clause,[],[f51,f75]) ).
tff(f112,plain,
! [X0: collection,X1: $int] :
( ( $sum(count(X0),1) = count(add(X1,X0)) )
| ( count(X0) = count(add(X1,X0)) ) ),
inference(resolution,[],[f42,f45]) ).
tff(f288,plain,
( ( count(add(sK1,sK0)) = count(sK0) )
| $less($sum(count(sK0),1),$sum(count(sK0),1))
| ~ spl2_2 ),
inference(superposition,[],[f77,f112]) ).
tff(f306,definition,
( spl2_3
<=> ( count(add(sK1,sK0)) = count(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f310,definition,
( spl2_4
<=> $less($sum(count(sK0),1),$sum(count(sK0),1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f313,plain,
( spl2_3
| spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f288,f75,f310,f306]) ).
tff(f315,plain,
$false,
inference(avatar_smt_refutation,[],[f313,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT034_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n016.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 00:10:49 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running first-order theorem proving
% 0.10/0.20 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
% 2.78/1.07 % (4168871)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.78/1.07 % (4168970)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2572956282:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.78/1.07 % (4168964)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1284475800:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.78/1.07 % (4168962)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1714377066:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.78/1.07 % (4168961)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=468206249:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.78/1.07 % (4168970)First to succeed.
% 2.78/1.07 % (4168970)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4168871"
% 2.78/1.07 % (4168966)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3853543089:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.78/1.07 % (4168971)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1466805334:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.78/1.07 % (4168966)Instruction limit reached!
% 2.78/1.07 % (4168966)------------------------------
% 2.78/1.07 % (4168966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.07 % (4168966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.07 % (4168966)CaDiCaL version: 2.1.3
% 2.78/1.07 % (4168966)Termination reason: Instruction limit
% 2.78/1.07 % (4168966)Termination phase: Saturation
% 2.78/1.07 % (4168966)Time elapsed: 0.009 s
% 2.78/1.07 % (4168966)Peak memory usage: 88 MB
% 2.78/1.07 % (4168966)Instructions burned: 7 (million)
% 2.78/1.07 % (4168961)Instruction limit reached!
% 2.78/1.07 % (4168961)------------------------------
% 2.78/1.07 % (4168961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.07 % (4168961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.07 % (4168961)CaDiCaL version: 2.1.3
% 2.78/1.07 % (4168961)Termination reason: Instruction limit
% 2.78/1.07 % (4168961)Termination phase: Saturation
% 2.78/1.07 % (4168961)Time elapsed: 0.032 s
% 2.78/1.07 % (4168961)Peak memory usage: 115 MB
% 2.78/1.07 % (4168961)Instructions burned: 12 (million)
% 2.78/1.07 % (4168967)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3287684843:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.78/1.07 % (4168962)Also succeeded, but the first one will report.
% 2.78/1.07 % (4168967)Instruction limit reached!
% 2.78/1.07 % (4168967)------------------------------
% 2.78/1.07 % (4168967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.07 % (4168967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.07 % (4168967)CaDiCaL version: 2.1.3
% 2.78/1.07 % (4168967)Termination reason: Instruction limit
% 2.78/1.07 % (4168967)Termination phase: Saturation
% 2.78/1.07 % (4168967)Time elapsed: 0.004 s
% 2.78/1.07 % (4168967)Peak memory usage: 89 MB
% 2.78/1.07 % (4168967)Instructions burned: 4 (million)
% 2.78/1.07 % (4168971)Instruction limit reached!
% 2.78/1.07 % (4168971)------------------------------
% 2.78/1.07 % (4168971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.07 % (4168971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.07 % (4168971)CaDiCaL version: 2.1.3
% 2.78/1.07 % (4168971)Termination reason: Instruction limit
% 2.78/1.07 % (4168971)Termination phase: Saturation
% 2.78/1.07 % (4168971)Time elapsed: 0.049 s
% 2.78/1.07 % (4168971)Peak memory usage: 116 MB
% 2.78/1.07 % (4168971)Instructions burned: 34 (million)
% 2.78/1.07 % (4168964)Also succeeded, but the first one will report.
% 2.78/1.07 % (4168970)Refutation found. Thanks to Tanya!
% 2.78/1.07 % SZS status Theorem for theBenchmark
% 2.78/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.07 % (4168970)------------------------------
% 2.78/1.07 % (4168970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.07 % (4168970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.07 % (4168970)CaDiCaL version: 2.1.3
% 2.78/1.07 % (4168970)Termination reason: Refutation
% 2.78/1.07 % (4168970)Time elapsed: 0.027 s
% 2.78/1.07 % (4168970)Peak memory usage: 116 MB
% 2.78/1.07 % (4168970)Instructions burned: 21 (million)
% 2.78/1.07 % (4168970)------------------------------
% 2.78/1.07 % (4168970)------------------------------
% 2.78/1.07 % (4168871)Success in time 0.326 s
% 2.78/1.07 % Vampire exiting
%------------------------------------------------------------------------------