%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT087_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 : n014.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 09:47:16 AM UTC 2026
% Result : Theorem 2.81s 1.16s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 54 ( 0 atm; 11 fun; 22 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 34 :)
% 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_11,type,
sK0: ( $int * list ) > $int ).
tff(func_def_12,type,
sK1: ( $int * list ) > list ).
tff(func_def_13,type,
sK2: ( $int * list ) > list ).
tff(func_def_14,type,
sK3: ( $int * list ) > $int ).
tff(func_def_15,type,
sK4: ( $int * list ) > list ).
tff(func_def_16,type,
sK5: ( $int * list ) > $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(f11,axiom,
! [X0: $int,X1: $int,X2: list,X3: $int] :
( ( X0 = X1 )
=> ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_4) ).
tff(f15,conjecture,
~ ! [X1: list,X0: $int] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X1: list,X0: $int] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f19,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f31,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 = X1 )
=> ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) ) ),
inference(rectify,[],[f11]) ).
tff(f33,plain,
~ ~ ! [X0: list,X1: $int] : ( count(X1,X0) = count(X1,cons(1,X0)) ),
inference(rectify,[],[f16]) ).
tff(f34,plain,
! [X0: list,X1: $int] : ( count(X1,X0) = count(X1,cons(1,X0)) ),
inference(flattening,[],[f33]) ).
tff(f42,plain,
! [X2: list,X1: $int,X0: $int] :
( ( count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f31]) ).
tff(f55,plain,
! [X0: list,X1: $int,X2: $int] :
( ( count(X2,cons(X1,X0)) = $sum(count(X2,X0),1) )
| ( X1 != X2 ) ),
inference(rectify,[],[f42]) ).
tff(f76,plain,
! [X0: list,X1: $int] : ( count(X1,X0) = count(X1,cons(1,X0)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f79,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f81,plain,
! [X2: $int,X0: list,X1: $int] :
( ( count(X2,cons(X1,X0)) = $sum(count(X2,X0),1) )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f55]) ).
tff(f88,plain,
! [X2: $int,X0: list] : ( count(X2,cons(X2,X0)) = $sum(count(X2,X0),1) ),
inference(equality_resolution,[],[f81]) ).
tff(f134,plain,
! [X0: list] : ( count(1,X0) = $sum(count(1,X0),1) ),
inference(superposition,[],[f76,f88]) ).
tff(f139,plain,
! [X0: list] : ( count(1,X0) = $sum(1,count(1,X0)) ),
inference(forward_demodulation,[],[f134,f19]) ).
tff(f143,plain,
0 = $sum(1,0),
inference(superposition,[],[f139,f79]) ).
tff(f145,plain,
$false,
inference(evaluation,[],[f143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT087_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:08:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.81/1.16 % (2304497)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.81/1.16 % (2304505)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3455573713:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.81/1.16 % (2304505)First to succeed.
% 2.81/1.16 % (2304505)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2304497"
% 2.81/1.16 % (2304502)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=537721333:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.81/1.16 % (2304504)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4065123564:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.81/1.16 % (2304506)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=42181994:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.81/1.16 % (2304503)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3302232236:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.81/1.16 % (2304508)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4218880430:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.81/1.16 % (2304507)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=935125053:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.81/1.16 % (2304506)Instruction limit reached!
% 2.81/1.16 % (2304506)------------------------------
% 2.81/1.16 % (2304506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.16 % (2304506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.16 % (2304506)CaDiCaL version: 2.1.3
% 2.81/1.16 % (2304506)Termination reason: Instruction limit
% 2.81/1.16 % (2304506)Termination phase: Saturation
% 2.81/1.16 % (2304506)Time elapsed: 0.004 s
% 2.81/1.16 % (2304506)Peak memory usage: 88 MB
% 2.81/1.16 % (2304506)Instructions burned: 5 (million)
% 2.81/1.16 % (2304502)Instruction limit reached!
% 2.81/1.16 % (2304502)------------------------------
% 2.81/1.16 % (2304502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.16 % (2304502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.16 % (2304502)CaDiCaL version: 2.1.3
% 2.81/1.16 % (2304502)Termination reason: Instruction limit
% 2.81/1.16 % (2304502)Termination phase: Saturation
% 2.81/1.16 % (2304502)Time elapsed: 0.030 s
% 2.81/1.16 % (2304502)Peak memory usage: 111 MB
% 2.81/1.16 % (2304502)Instructions burned: 12 (million)
% 2.81/1.16 % (2304503)Also succeeded, but the first one will report.
% 2.81/1.16 % (2304507)Also succeeded, but the first one will report.
% 2.81/1.16 % (2304508)Also succeeded, but the first one will report.
% 2.81/1.16 % (2304504)Also succeeded, but the first one will report.
% 2.81/1.16 % (2304505)Refutation found. Thanks to Tanya!
% 2.81/1.16 % SZS status Theorem for theBenchmark
% 2.81/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.16 % (2304505)------------------------------
% 2.81/1.16 % (2304505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.16 % (2304505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.16 % (2304505)CaDiCaL version: 2.1.3
% 2.81/1.16 % (2304505)Termination reason: Refutation
% 2.81/1.16 % (2304505)Time elapsed: 0.003 s
% 2.81/1.16 % (2304505)Peak memory usage: 89 MB
% 2.81/1.16 % (2304505)Instructions burned: 4 (million)
% 2.81/1.16 % (2304505)------------------------------
% 2.81/1.16 % (2304505)------------------------------
% 2.81/1.16 % (2304497)Success in time 0.306 s
% 2.81/1.16 % Vampire exiting
%------------------------------------------------------------------------------