%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT095_1 : 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 : n011.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 09:47:17 AM UTC 2026
% Result : Theorem 3.97s 1.33s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 67 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 113 ( 42 ~; 39 |; 24 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 100 ( 0 atm; 16 fun; 20 num; 64 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 98 !; 20 ?; 118 :)
% 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: ( list * $int ) > $int ).
tff(func_def_11,type,
sK1: ( list * $int ) > list ).
tff(func_def_12,type,
sK2: ( list * $int ) > list ).
tff(func_def_13,type,
sK3: ( list * $int ) > $int ).
tff(func_def_14,type,
sK4: ( list * $int ) > $int ).
tff(func_def_15,type,
sK5: ( list * $int ) > list ).
tff(pred_def_1,type,
in: ( $int * list ) > $o ).
tff(pred_def_2,type,
inRange: ( $int * list ) > $o ).
tff(f5,axiom,
! [X1: list,X0: $int] :
( in(X0,X1)
<=> ( ? [X2: $int,X3: list] :
( in(X0,X3)
& ( X1 = cons(X2,X3) ) )
| ? [X3: list,X2: $int] :
( ( X1 = cons(X2,X3) )
& ( X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).
tff(f9,axiom,
! [X0: $int] : ( count(X0,nil) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(f11,axiom,
! [X1: $int,X2: list,X3: $int,X0: $int] :
( ( X0 = X1 )
=> ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_4) ).
tff(f15,conjecture,
~ ! [X2: list,X3: list,X1: $int,X0: $int] :
( ( ( X3 = cons(X0,X2) )
& in(X1,X2) )
=> ( count(X1,X3) = count(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X2: list,X3: list,X1: $int,X0: $int] :
( ( ( X3 = cons(X0,X2) )
& in(X1,X2) )
=> ( count(X1,X3) = count(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: list,X1: $int] :
( in(X1,X0)
<=> ( ? [X2: $int,X3: list] :
( ( cons(X2,X3) = X0 )
& in(X1,X3) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) ) ) ),
inference(rectify,[],[f5]) ).
tff(f24,plain,
! [X0: $int,X1: list,X3: $int] :
( ( X0 = X3 )
=> ( $sum(count(X3,X1),1) = count(X3,cons(X0,X1)) ) ),
inference(rectify,[],[f11]) ).
tff(f26,plain,
~ ~ ! [X2: $int,X0: list,X3: $int,X1: list] :
( ( in(X2,X0)
& ( cons(X3,X0) = X1 ) )
=> ( count(X2,X1) = count(X2,X0) ) ),
inference(rectify,[],[f16]) ).
tff(f27,plain,
! [X2: $int,X0: list,X3: $int,X1: list] :
( ( in(X2,X0)
& ( cons(X3,X0) = X1 ) )
=> ( count(X2,X1) = count(X2,X0) ) ),
inference(flattening,[],[f26]) ).
tff(f29,plain,
! [X2: $int,X0: list,X3: $int,X1: list] :
( ( count(X2,X1) = count(X2,X0) )
| ~ in(X2,X0)
| ( cons(X3,X0) != X1 ) ),
inference(ennf_transformation,[],[f27]) ).
tff(f30,plain,
! [X0: list,X3: $int,X2: $int,X1: list] :
( ~ in(X2,X0)
| ( cons(X3,X0) != X1 )
| ( count(X2,X1) = count(X2,X0) ) ),
inference(flattening,[],[f29]) ).
tff(f32,plain,
! [X3: $int,X1: list,X0: $int] :
( ( X0 != X3 )
| ( $sum(count(X3,X1),1) = count(X3,cons(X0,X1)) ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f33,plain,
! [X0: list,X1: $int] :
( ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X0 )
| ~ in(X1,X3) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) )
& ( ? [X2: $int,X3: list] :
( ( cons(X2,X3) = X0 )
& in(X1,X3) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) )
| ~ in(X1,X0) ) ),
inference(nnf_transformation,[],[f19]) ).
tff(f34,plain,
! [X0: list,X1: $int] :
( ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X0 )
| ~ in(X1,X3) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) )
& ( ? [X2: $int,X3: list] :
( ( cons(X2,X3) = X0 )
& in(X1,X3) )
| ? [X4: list,X5: $int] :
( ( cons(X5,X4) = X0 )
& ( X1 = X5 ) )
| ~ in(X1,X0) ) ),
inference(flattening,[],[f33]) ).
tff(f35,plain,
! [X0: list,X1: $int] :
( ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X0 )
| ~ in(X1,X3) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) )
& ( ? [X6: $int,X7: list] :
( ( cons(X6,X7) = X0 )
& in(X1,X7) )
| ? [X8: list,X9: $int] :
( ( cons(X9,X8) = X0 )
& ( X1 = X9 ) )
| ~ in(X1,X0) ) ),
inference(rectify,[],[f34]) ).
tff(f36,plain,
! [X0: list,X1: $int] :
( ( in(X1,X0)
| ( ! [X2: $int,X3: list] :
( ( cons(X2,X3) != X0 )
| ~ in(X1,X3) )
& ! [X4: list,X5: $int] :
( ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ) ) )
& ( ( ( cons(sK0(X0,X1),sK1(X0,X1)) = X0 )
& in(X1,sK1(X0,X1)) )
| ( ( cons(sK3(X0,X1),sK2(X0,X1)) = X0 )
& ( sK3(X0,X1) = X1 ) )
| ~ in(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X6,sK0(X0,X1)),skolemize(X7,sK1(X0,X1)),skolemize(X8,sK2(X0,X1)),skolemize(X9,sK3(X0,X1))],[f35]) ).
tff(f38,plain,
! [X0: $int,X1: list,X2: $int] :
( ( X0 != X2 )
| ( $sum(count(X0,X1),1) = count(X0,cons(X2,X1)) ) ),
inference(rectify,[],[f32]) ).
tff(f45,plain,
! [X0: list,X1: $int,X2: $int,X3: list] :
( ~ in(X2,X0)
| ( cons(X1,X0) != X3 )
| ( count(X2,X3) = count(X2,X0) ) ),
inference(rectify,[],[f30]) ).
tff(f50,plain,
! [X0: list,X1: $int,X4: list,X5: $int] :
( in(X1,X0)
| ( cons(X5,X4) != X0 )
| ( X1 != X5 ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f55,plain,
! [X2: $int,X0: $int,X1: list] :
( ( X0 != X2 )
| ( $sum(count(X0,X1),1) = count(X0,cons(X2,X1)) ) ),
inference(cnf_transformation,[],[f38]) ).
tff(f59,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f69,plain,
! [X2: $int,X3: list,X0: list,X1: $int] :
( ~ in(X2,X0)
| ( cons(X1,X0) != X3 )
| ( count(X2,X3) = count(X2,X0) ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f73,plain,
! [X1: $int,X4: list,X5: $int] :
( in(X1,cons(X5,X4))
| ( X1 != X5 ) ),
inference(equality_resolution,[],[f50]) ).
tff(f74,plain,
! [X4: list,X5: $int] : in(X5,cons(X5,X4)),
inference(equality_resolution,[],[f73]) ).
tff(f75,plain,
! [X2: $int,X1: list] : ( count(X2,cons(X2,X1)) = $sum(count(X2,X1),1) ),
inference(equality_resolution,[],[f55]) ).
tff(f78,plain,
! [X2: $int,X0: list,X1: $int] :
( ( count(X2,X0) = count(X2,cons(X1,X0)) )
| ~ in(X2,X0) ),
inference(equality_resolution,[],[f69]) ).
tff(f129,plain,
! [X0: $int,X1: list] :
( ( count(X0,X1) = $sum(count(X0,X1),1) )
| ~ in(X0,X1) ),
inference(superposition,[],[f75,f78]) ).
tff(f266,plain,
! [X0: $int,X1: list] :
( ~ in(X0,cons(X0,X1))
| ( $sum($sum(count(X0,X1),1),1) = $sum(count(X0,X1),1) ) ),
inference(superposition,[],[f129,f75]) ).
tff(f278,plain,
! [X0: $int,X1: list] : ( $sum($sum(count(X0,X1),1),1) = $sum(count(X0,X1),1) ),
inference(forward_subsumption_resolution,[],[f266,f74]) ).
tff(f343,plain,
$sum($sum(0,1),1) = $sum(0,1),
inference(superposition,[],[f278,f59]) ).
tff(f355,plain,
$false,
inference(evaluation,[],[f343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT095_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n011.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 00:08:31 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 2.26/1.13 % (3917419)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.26/1.13 % (3917428)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=579010491:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.26/1.13 % (3917428)Instruction limit reached!
% 2.26/1.13 % (3917428)------------------------------
% 2.26/1.13 % (3917428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/1.13 % (3917428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/1.13 % (3917428)CaDiCaL version: 2.1.3
% 2.26/1.13 % (3917428)Termination reason: Instruction limit
% 2.26/1.13 % (3917428)Termination phase: Saturation
% 2.26/1.13 % (3917428)Time elapsed: 0.003 s
% 2.26/1.13 % (3917428)Peak memory usage: 89 MB
% 2.26/1.13 % (3917428)Instructions burned: 7 (million)
% 2.26/1.13 % (3917425)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=105394956:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.26/1.13 % (3917427)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2804325245:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.26/1.13 % (3917426)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3737506366:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.26/1.13 % (3917424)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1023591782:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.26/1.13 % (3917427)Instruction limit reached!
% 2.26/1.13 % (3917427)------------------------------
% 2.26/1.13 % (3917427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/1.13 % (3917427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/1.13 % (3917427)CaDiCaL version: 2.1.3
% 2.26/1.13 % (3917427)Termination reason: Instruction limit
% 2.26/1.13 % (3917427)Termination phase: Saturation
% 2.26/1.13 % (3917427)Time elapsed: 0.006 s
% 2.26/1.13 % (3917427)Peak memory usage: 88 MB
% 2.26/1.13 % (3917427)Instructions burned: 8 (million)
% 2.26/1.13 % (3917429)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=268964102:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.26/1.13 % (3917430)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1551710106:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.26/1.13 % (3917424)Refutation not found, incomplete strategy
% 2.26/1.13 % (3917424)------------------------------
% 2.26/1.13 % (3917424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/1.13 % (3917424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/1.13 % (3917424)CaDiCaL version: 2.1.3
% 2.26/1.13 % (3917424)Termination reason: Refutation not found, incomplete strategy
% 2.26/1.13 % (3917424)Time elapsed: 0.032 s
% 2.26/1.13 % (3917424)Peak memory usage: 112 MB
% 2.26/1.13 % (3917424)Instructions burned: 11 (million)
% 2.26/1.13 % (3917425)First to succeed.
% 2.26/1.13 % (3917425)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3917419"
% 2.26/1.13 % (3917429)Also succeeded, but the first one will report.
% 2.26/1.13 % (3917430)Also succeeded, but the first one will report.
% 2.26/1.13 % (3917432)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1115030705:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.26/1.13 % (3917432)Instruction limit reached!
% 2.26/1.13 % (3917432)------------------------------
% 2.26/1.13 % (3917432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.26/1.13 % (3917432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/1.13 % (3917432)CaDiCaL version: 2.1.3
% 2.26/1.13 % (3917432)Termination reason: Instruction limit
% 2.26/1.13 % (3917432)Termination phase: Saturation
% 2.26/1.13 % (3917432)Time elapsed: 0.006 s
% 2.26/1.13 % (3917432)Peak memory usage: 88 MB
% 2.26/1.13 % (3917432)Instructions burned: 16 (million)
% 2.26/1.13 % (3917426)Also succeeded, but the first one will report.
% 2.26/1.13 % (3917437)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=2164183109:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.26/1.13 % (3917437)Instruction limit reached!
% 2.26/1.13 % (3917437)------------------------------
% 2.26/1.13 % (3917437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.33 % (3917437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.33 % (3917437)CaDiCaL version: 2.1.3
% 3.97/1.33 % (3917437)Termination reason: Instruction limit
% 3.97/1.33 % (3917437)Termination phase: Saturation
% 3.97/1.33 % (3917437)Time elapsed: 0.022 s
% 3.97/1.33 % (3917437)Peak memory usage: 89 MB
% 3.97/1.33 % (3917437)Instructions burned: 29 (million)
% 3.97/1.33 % (3917441)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1284638863:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.97/1.33 % (3917441)Instruction limit reached!
% 3.97/1.33 % (3917441)------------------------------
% 3.97/1.33 % (3917441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.33 % (3917441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.33 % (3917441)CaDiCaL version: 2.1.3
% 3.97/1.33 % (3917441)Termination reason: Instruction limit
% 3.97/1.33 % (3917441)Termination phase: Saturation
% 3.97/1.33 % (3917441)Time elapsed: 0.006 s
% 3.97/1.33 % (3917441)Peak memory usage: 90 MB
% 3.97/1.33 % (3917441)Instructions burned: 16 (million)
% 3.97/1.33 % (3917424)------------------------------
% 3.97/1.33 % (3917424)------------------------------
% 3.97/1.33 % (3917425)Refutation found. Thanks to Tanya!
% 3.97/1.33 % SZS status Theorem for theBenchmark
% 3.97/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.33 % (3917425)------------------------------
% 3.97/1.33 % (3917425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.33 % (3917425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.33 % (3917425)CaDiCaL version: 2.1.3
% 3.97/1.33 % (3917425)Termination reason: Refutation
% 3.97/1.33 % (3917425)Time elapsed: 0.041 s
% 3.97/1.33 % (3917425)Peak memory usage: 115 MB
% 3.97/1.33 % (3917425)Instructions burned: 23 (million)
% 3.97/1.33 % (3917425)------------------------------
% 3.97/1.33 % (3917425)------------------------------
% 3.97/1.33 % (3917419)Success in time 0.473 s
% 3.97/1.33 % Vampire exiting
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