%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT081_1 : 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 : n010.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 09:47:15 AM UTC 2026
% Result : Theorem 2.69s 1.10s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 6 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 26 ( 6 atm; 0 fun; 9 num; 11 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 : 7 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( $int * list ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_10,type,
sK0: ( $int * list ) > list ).
tff(func_def_11,type,
sK1: ( $int * list ) > $int ).
tff(func_def_12,type,
sK2: ( $int * list ) > list ).
tff(func_def_13,type,
sK3: ( $int * list ) > $int ).
tff(func_def_14,type,
sK4: $int ).
tff(func_def_15,type,
sK5: ( list * $int ) > list ).
tff(func_def_16,type,
sK6: ( list * $int ) > $int ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f14,axiom,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $greater(count(X0,X1),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8) ).
tff(f15,conjecture,
! [X0: $int] : ~ in(X0,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ! [X0: $int] : ~ in(X0,nil),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f18,plain,
! [X0: $int,X1: list] :
( in(X0,X1)
<=> $less(0,count(X0,X1)) ),
inference(theory_normalization,[],[f14]) ).
tff(f26,plain,
? [X0: $int] : in(X0,nil),
inference(ennf_transformation,[],[f16]) ).
tff(f34,plain,
in(sK4,nil),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f26]) ).
tff(f37,plain,
! [X0: $int,X1: list] :
( ( in(X0,X1)
| ~ $less(0,count(X0,X1)) )
& ( $less(0,count(X0,X1))
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
tff(f53,plain,
in(sK4,nil),
inference(cnf_transformation,[],[f34]) ).
tff(f56,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f57,plain,
! [X0: $int,X1: list] :
( $less(0,count(X0,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tff(f76,definition,
( spl7_1
<=> in(sK4,nil) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f78,plain,
( in(sK4,nil)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f79,plain,
spl7_1,
inference(avatar_split_clause,[],[f53,f76]) ).
tff(f85,plain,
! [X0: $int] :
( $less(0,0)
| ~ in(X0,nil) ),
inference(superposition,[],[f57,f56]) ).
tff(f86,plain,
! [X0: $int] : ~ in(X0,nil),
inference(evaluation,[],[f85]) ).
tff(f87,plain,
( $false
| ~ spl7_1 ),
inference(resolution,[],[f86,f78]) ).
tff(f88,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f87]) ).
tff(f89,plain,
$false,
inference(avatar_smt_refutation,[],[f88,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT081_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:08:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 2.69/1.10 % (2483189)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.69/1.10 % (2483274)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=112029446:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.69/1.10 % (2483274)First to succeed.
% 2.69/1.10 % (2483274)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2483189"
% 2.69/1.10 % (2483275)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1583702529:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.69/1.10 % (2483273)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1493644730:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.69/1.10 % (2483278)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1097627300:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.69/1.10 % (2483278)Instruction limit reached!
% 2.69/1.10 % (2483278)------------------------------
% 2.69/1.10 % (2483278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.10 % (2483278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.10 % (2483278)CaDiCaL version: 2.1.3
% 2.69/1.10 % (2483278)Termination reason: Instruction limit
% 2.69/1.10 % (2483278)Termination phase: Saturation
% 2.69/1.10 % (2483278)Time elapsed: 0.004 s
% 2.69/1.10 % (2483278)Peak memory usage: 88 MB
% 2.69/1.10 % (2483278)Instructions burned: 5 (million)
% 2.69/1.10 % (2483273)Instruction limit reached!
% 2.69/1.10 % (2483273)------------------------------
% 2.69/1.10 % (2483273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.10 % (2483273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.10 % (2483273)CaDiCaL version: 2.1.3
% 2.69/1.10 % (2483273)Termination reason: Instruction limit
% 2.69/1.10 % (2483273)Termination phase: Saturation
% 2.69/1.10 % (2483273)Time elapsed: 0.031 s
% 2.69/1.10 % (2483273)Peak memory usage: 115 MB
% 2.69/1.10 % (2483273)Instructions burned: 12 (million)
% 2.69/1.10 % (2483281)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4196243125:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.69/1.10 % (2483277)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2041455407:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.69/1.10 % (2483275)Also succeeded, but the first one will report.
% 2.69/1.10 % (2483277)Instruction limit reached!
% 2.69/1.10 % (2483277)------------------------------
% 2.69/1.10 % (2483277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.10 % (2483277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.10 % (2483277)CaDiCaL version: 2.1.3
% 2.69/1.10 % (2483277)Termination reason: Instruction limit
% 2.69/1.10 % (2483277)Termination phase: Saturation
% 2.69/1.10 % (2483277)Time elapsed: 0.006 s
% 2.69/1.10 % (2483277)Peak memory usage: 88 MB
% 2.69/1.10 % (2483277)Instructions burned: 7 (million)
% 2.69/1.10 % (2483282)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2400154288:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.69/1.10 % (2483281)Also succeeded, but the first one will report.
% 2.69/1.10 % (2483282)Also succeeded, but the first one will report.
% 2.69/1.10 % (2483274)Refutation found. Thanks to Tanya!
% 2.69/1.10 % SZS status Theorem for theBenchmark
% 2.69/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.10 % (2483274)------------------------------
% 2.69/1.10 % (2483274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.10 % (2483274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.10 % (2483274)CaDiCaL version: 2.1.3
% 2.69/1.10 % (2483274)Termination reason: Refutation
% 2.69/1.10 % (2483274)Time elapsed: 0.021 s
% 2.69/1.10 % (2483274)Peak memory usage: 116 MB
% 2.69/1.10 % (2483274)Instructions burned: 9 (million)
% 2.69/1.10 % (2483274)------------------------------
% 2.69/1.10 % (2483274)------------------------------
% 2.69/1.10 % (2483189)Success in time 0.322 s
% 2.69/1.10 % Vampire exiting
%------------------------------------------------------------------------------