%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM043_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:39:28 AM UTC 2026
% Result : Theorem 4.26s 1.46s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-4 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
atom: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
div_mod:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_8,type,
nDvd: ( int * int * list(int) ) > atom ).
tff(func_def_9,type,
atom_size: atom > nat ).
tff(func_def_10,type,
divisor: atom > int ).
tff(func_def_11,type,
hd_coeff: atom > int ).
tff(func_def_12,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_13,type,
fFalse: bool ).
tff(func_def_14,type,
fTrue: bool ).
tff(func_def_15,type,
a: atom ).
tff(func_def_16,type,
d: int ).
tff(func_def_17,type,
e: list(int) ).
tff(func_def_18,type,
i: int ).
tff(func_def_19,type,
j: int ).
tff(func_def_20,type,
ks1: list(int) ).
tff(func_def_21,type,
ks: list(int) ).
tff(func_def_22,type,
l: int ).
tff(func_def_23,type,
sK0: list(int) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
cl_Groups_Oplus:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
uminus:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_div:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
boolean_algebra:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
nat_is_nat: int > $o ).
tff(pred_def_20,type,
pp: bool > $o ).
tff(f1,axiom,
a = nDvd(d,l,ks),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_NDvd) ).
tff(f2,axiom,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
tff(f64,axiom,
! [X0: list(int),X1: int,X2: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_divisor_Osimps_I3_J) ).
tff(f135,conjecture,
div_mod(int,i,d) = div_mod(int,j,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f136,negated_conjecture,
( ( ~ div_mod(int,i,d) ) = div_mod(int,j,d) ),
inference(negated_conjecture,[status(cth)],[f135]) ).
tff(f137,plain,
div_mod(int,i,d) != div_mod(int,j,d),
inference(flattening,[],[f136]) ).
tff(f172,plain,
div_mod(int,i,d) != div_mod(int,j,d),
inference(cnf_transformation,[],[f137]) ).
tff(f180,plain,
div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)),
inference(cnf_transformation,[],[f2]) ).
tff(f181,plain,
! [X2: int,X0: list(int),X1: int] : ( divisor(nDvd(X2,X1,X0)) = X2 ),
inference(cnf_transformation,[],[f64]) ).
tff(f182,plain,
a = nDvd(d,l,ks),
inference(cnf_transformation,[],[f1]) ).
tff(f239,plain,
d = divisor(a),
inference(superposition,[],[f181,f182]) ).
tff(f248,plain,
div_mod(int,i,d) = div_mod(int,j,d),
inference(forward_demodulation,[],[f180,f239]) ).
tff(f249,plain,
$false,
inference(forward_subsumption_resolution,[],[f248,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM043_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:50:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 4.26/1.46 % (242226)Detected formulas, will run a generic FOF schedule.
% 4.26/1.46 % (242307)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1409717754:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.26/1.46 % (242307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.26/1.46 % (242307)Refutation not found, incomplete strategy
% 4.26/1.46 % (242307)------------------------------
% 4.26/1.46 % (242307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.26/1.46 % (242307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.26/1.46 % (242307)CaDiCaL version: 2.1.3
% 4.26/1.46 % (242307)Termination reason: Refutation not found, incomplete strategy
% 4.26/1.46 % (242307)Time elapsed: 0.001 s
% 4.26/1.46 % (242307)Peak memory usage: 88 MB
% 4.26/1.46 % (242307)Instructions burned: 1 (million)
% 4.26/1.46 % (242305)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3615214239:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.26/1.46 % (242304)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=245976932:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.26/1.46 % (242306)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3287183184:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.26/1.46 % (242306)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.26/1.46 % (242308)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4114810334:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.26/1.46 % (242308)First to succeed.
% 4.26/1.46 % (242308)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-242226"
% 4.26/1.46 % (242309)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2621506367:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.26/1.46 % (242309)Also succeeded, but the first one will report.
% 4.26/1.46 % (242310)dis-21_1_sil=8000:lcm=predicate:random_seed=2929589525:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.26/1.46 % (242310)Refutation not found, incomplete strategy
% 4.26/1.46 % (242310)------------------------------
% 4.26/1.46 % (242310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.26/1.46 % (242310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.26/1.46 % (242310)CaDiCaL version: 2.1.3
% 4.26/1.46 % (242310)Termination reason: Refutation not found, incomplete strategy
% 4.26/1.46 % (242310)Time elapsed: 0.017 s
% 4.26/1.46 % (242310)Peak memory usage: 88 MB
% 4.26/1.46 % (242310)Instructions burned: 24 (million)
% 4.26/1.46 % (242307)------------------------------
% 4.26/1.46 % (242307)------------------------------
% 4.26/1.46 % (242308)Refutation found. Thanks to Tanya!
% 4.26/1.46 % SZS status Theorem for theBenchmark
% 4.26/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 4.26/1.46 % (242308)------------------------------
% 4.26/1.46 % (242308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.26/1.46 % (242308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.26/1.46 % (242308)CaDiCaL version: 2.1.3
% 4.26/1.46 % (242308)Termination reason: Refutation
% 4.26/1.46 % (242308)Time elapsed: 0.005 s
% 4.26/1.46 % (242308)Peak memory usage: 88 MB
% 4.26/1.46 % (242308)Instructions burned: 5 (million)
% 4.26/1.46 % (242308)------------------------------
% 4.26/1.46 % (242308)------------------------------
% 4.26/1.46 % (242226)Success in time 0.53 s
% 4.26/1.46 % Vampire exiting
%------------------------------------------------------------------------------