%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM041_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 0.19s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 19 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 11 con; 0-5 aty)
% Number of variables : 19 ( 19 !; 0 ?; 19 :)
% 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,
atom: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
div_mod:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_4,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_5,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_6,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).
tff(func_def_7,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_8,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_9,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_10,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_11,type,
c_PresArith_Oatom_OLe: ( int * list(int) ) > atom ).
tff(func_def_12,type,
nDvd: ( int * int * list(int) ) > atom ).
tff(func_def_13,type,
atom_case:
!>[X0: $tType] : ( ( fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom ) > X0 ) ).
tff(func_def_14,type,
atom_rec:
!>[X0: $tType] : ( ( fun(int,fun(list(int),X0)) * fun(int,fun(int,fun(list(int),X0))) * fun(int,fun(int,fun(list(int),X0))) * atom ) > X0 ) ).
tff(func_def_15,type,
divisor: atom > int ).
tff(func_def_16,type,
hd_coeff: atom > int ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
a: atom ).
tff(func_def_21,type,
d: int ).
tff(func_def_22,type,
e: list(int) ).
tff(func_def_23,type,
i: int ).
tff(func_def_24,type,
j: int ).
tff(func_def_25,type,
ks: list(int) ).
tff(func_def_26,type,
ks1: list(int) ).
tff(func_def_27,type,
l: int ).
tff(func_def_28,type,
sK0: list(int) ).
tff(func_def_29,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
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,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comm_ring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_21,type,
pp: bool > $o ).
tff(pred_def_22,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f11,axiom,
! [X0: $tType] :
( semiring_div(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_mod__add__eq) ).
tff(f108,axiom,
semiring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f124,conjecture,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f125,negated_conjecture,
( ( ~ div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) ) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d) ),
inference(negated_conjecture,[status(cth)],[f124]) ).
tff(f127,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
inference(flattening,[],[f125]) ).
tff(f139,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f244,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1) )
| ~ semiring_div(X0) ),
inference(cnf_transformation,[],[f139]) ).
tff(f356,plain,
semiring_div(int),
inference(cnf_transformation,[],[f108]) ).
tff(f372,plain,
div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d) != div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d),
inference(cnf_transformation,[],[f127]) ).
tff(f393,definition,
! [X0: $tType,X2: X0,X1: X0] :
( sQ2_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ2_eqProxy])],[equality_proxy_definition]) ).
tff(f406,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( sQ2_eqProxy(X0,div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1),div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X1)),div_mod(X0,X2,X1)),X1))
| ~ semiring_div(X0) ),
inference(equality_proxy_replacement,[],[f244,f393]) ).
tff(f508,plain,
~ sQ2_eqProxy(int,div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),l),aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e))),d),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),i),iprod(int,ks,e)),d)),d)),
inference(equality_proxy_replacement,[],[f372,f393]) ).
tff(f580,plain,
~ semiring_div(int),
inference(resolution,[],[f406,f508]) ).
tff(f581,plain,
$false,
inference(resolution,[],[f580,f356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM041_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 21:51:25 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 0.19/1.31 % (2688205)Detected formulas, will run a generic FOF schedule.
% 0.19/1.31 % (2688214)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=731764761:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.31 % (2688214)Instruction limit reached!
% 0.19/1.31 % (2688214)------------------------------
% 0.19/1.31 % (2688214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2688214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2688214)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2688214)Termination reason: Instruction limit
% 0.19/1.31 % (2688214)Termination phase: Saturation
% 0.19/1.31 % (2688214)Time elapsed: 0.034 s
% 0.19/1.31 % (2688214)Peak memory usage: 88 MB
% 0.19/1.31 % (2688214)Instructions burned: 120 (million)
% 0.19/1.31 % (2688215)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3091327522:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.31 % (2688213)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=88537339:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.31 % (2688210)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=10337569:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.31 % (2688212)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=13554017:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.31 % (2688211)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=3413206931:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.31 % (2688213)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.31 % (2688213)Refutation not found, incomplete strategy
% 0.19/1.31 % (2688213)------------------------------
% 0.19/1.31 % (2688213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2688213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2688213)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2688213)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.31 % (2688213)Time elapsed: 0.002 s
% 0.19/1.31 % (2688213)Peak memory usage: 88 MB
% 0.19/1.31 % (2688213)Instructions burned: 1 (million)
% 0.19/1.31 % (2688212)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.31 % (2688216)dis-21_1_sil=8000:lcm=predicate:random_seed=2404930005: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)
% 0.19/1.31 % (2688216)First to succeed.
% 0.19/1.31 % (2688216)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2688205"
% 0.19/1.31 % (2688215)Also succeeded, but the first one will report.
% 0.19/1.31 % (2688218)lrs+10_1_sil=8000:sp=occurrence:random_seed=343873977:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.19/1.31 % (2688218)Instruction limit reached!
% 0.19/1.31 % (2688218)------------------------------
% 0.19/1.31 % (2688218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2688218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2688218)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2688218)Termination reason: Instruction limit
% 0.19/1.31 % (2688218)Termination phase: Saturation
% 0.19/1.31 % (2688218)Time elapsed: 0.087 s
% 0.19/1.31 % (2688218)Peak memory usage: 91 MB
% 0.19/1.31 % (2688218)Instructions burned: 286 (million)
% 0.19/1.31 % (2688213)------------------------------
% 0.19/1.31 % (2688213)------------------------------
% 0.19/1.31 % (2688226)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3418506932:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 0.19/1.31 % (2688216)Refutation found. Thanks to Tanya!
% 0.19/1.31 % SZS status Theorem for theBenchmark
% 0.19/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.31 % (2688216)------------------------------
% 0.19/1.31 % (2688216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.31 % (2688216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.31 % (2688216)CaDiCaL version: 2.1.3
% 0.19/1.31 % (2688216)Termination reason: Refutation
% 0.19/1.31 % (2688216)Time elapsed: 0.012 s
% 0.19/1.31 % (2688216)Peak memory usage: 89 MB
% 0.19/1.31 % (2688216)Instructions burned: 20 (million)
% 0.19/1.31 % (2688216)------------------------------
% 0.19/1.31 % (2688216)------------------------------
% 0.19/1.31 % (2688205)Success in time 0.429 s
% 0.19/1.31 % Vampire exiting
%------------------------------------------------------------------------------