%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT080_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 09:48:05 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 8 ~; 8 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 82 ( 13 atm; 0 fun; 54 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 : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 23 :)
% 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_14,type,
sK0: ( $int * list ) > $int ).
tff(func_def_15,type,
sK1: ( $int * list ) > list ).
tff(func_def_16,type,
sK2: ( $int * list ) > $int ).
tff(func_def_17,type,
sK3: ( $int * list ) > list ).
tff(func_def_18,type,
sK4: ( $int * list ) > $int ).
tff(func_def_19,type,
sK5: ( $int * list ) > list ).
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(f10,axiom,
! [X0: $int,X1: $int,X2: list,X3: $int] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
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,
~ in(4,cons(1,cons(2,cons(3,nil)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ in(4,cons(1,cons(2,cons(3,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(f32,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(rectify,[],[f10]) ).
tff(f34,plain,
in(4,cons(1,cons(2,cons(3,nil)))),
inference(flattening,[],[f16]) ).
tff(f35,plain,
! [X0: $int,X1: $int,X2: list] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f45,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(f64,plain,
! [X0: $int] : ( 0 = count(X0,nil) ),
inference(cnf_transformation,[],[f9]) ).
tff(f65,plain,
! [X2: list,X0: $int,X1: $int] :
( ( count(X0,cons(X1,X2)) = count(X0,X2) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f35]) ).
tff(f69,plain,
! [X0: $int,X1: list] :
( ~ in(X0,X1)
| $less(0,count(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
tff(f71,plain,
in(4,cons(1,cons(2,cons(3,nil)))),
inference(cnf_transformation,[],[f34]) ).
tff(f98,plain,
$less(0,count(4,cons(1,cons(2,cons(3,nil))))),
inference(resolution,[],[f69,f71]) ).
tff(f245,plain,
( $less(0,count(4,cons(2,cons(3,nil))))
| ( 1 = 4 ) ),
inference(superposition,[],[f98,f65]) ).
tff(f260,plain,
$less(0,count(4,cons(2,cons(3,nil)))),
inference(evaluation,[],[f245]) ).
tff(f264,plain,
( $less(0,count(4,cons(3,nil)))
| ( 4 = 2 ) ),
inference(superposition,[],[f260,f65]) ).
tff(f265,plain,
$less(0,count(4,cons(3,nil))),
inference(evaluation,[],[f264]) ).
tff(f274,plain,
( $less(0,count(4,nil))
| ( 4 = 3 ) ),
inference(superposition,[],[f265,f65]) ).
tff(f275,plain,
$less(0,count(4,nil)),
inference(evaluation,[],[f274]) ).
tff(f276,plain,
$less(0,0),
inference(forward_demodulation,[],[f275,f64]) ).
tff(f277,plain,
$false,
inference(evaluation,[],[f276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT080_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:11:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (3168854)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3168865)dis+10_1_sil=32000:sp=arity:random_seed=423882836:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (3168863)% WARNING: option uhcvi not known.
% 0.21/0.28 % (3168865) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3168854-3168865"...
% 0.21/0.28 % (3168865)...printing done.
% 0.21/0.28 % (3168864)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3516685602:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (3168862)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=577179623_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (3168867)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=530445242:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (3168866)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4158849349:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (3168863)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=824274594:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (3168865)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3168865)------------------------------
% 0.21/0.28 % (3168865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3168865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3168865)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3168865)Termination reason: Refutation
% 0.21/0.28 % (3168865)Time elapsed: 0.006 s
% 0.21/0.28 % (3168865)Peak memory usage: 12 MB
% 0.21/0.28 % (3168865)Instructions burned: 13 (million)
% 0.21/0.28 % (3168854)Success in time 0.042 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------