%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM034_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 09:40:12 AM UTC 2026
% Result : Theorem 0.50s 0.47s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 11 con; 0-5 aty)
% Number of variables : 30 ( 30 !; 0 ?; 30 :)
% 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,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : fun(X0,fun(X0,X0)) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( X0 > fun(X0,X0) ) ).
tff(func_def_4,type,
succ: int > int ).
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,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_9,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_10,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_11,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_13,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_14,type,
c_PresArith_Oatom_OLe: ( int * list(int) ) > atom ).
tff(func_def_15,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_16,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_17,type,
divisor: atom > int ).
tff(func_def_18,type,
hd_coeff: atom > int ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
a: atom ).
tff(func_def_23,type,
d: int ).
tff(func_def_24,type,
e: list(int) ).
tff(func_def_25,type,
i: int ).
tff(func_def_26,type,
j: int ).
tff(func_def_27,type,
ks: list(int) ).
tff(func_def_28,type,
ks1: list(int) ).
tff(func_def_29,type,
l: int ).
tff(func_def_30,type,
sK0: list(int) ).
tff(func_def_31,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,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_div:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_19,type,
pp: bool > $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),div_mod(X0,X2,X1)),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zmod__simps_I2_J) ).
tff(f12,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),div_mod(X0,X3,X2)),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zmod__simps_I1_J) ).
tff(f107,axiom,
semiring_div(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
tff(f119,conjecture,
div_mod(int,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,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f120,negated_conjecture,
( ( ~ div_mod(int,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,i,d)),div_mod(int,iprod(int,ks,e),d)),d) ),
inference(negated_conjecture,[status(cth)],[f119]) ).
tff(f121,plain,
div_mod(int,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,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(flattening,[],[f120]) ).
tff(f134,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),div_mod(X0,X2,X1)),X1) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X2),X1) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f135,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) )
| ~ semiring_div(X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f226,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(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),X3),div_mod(X0,X2,X1)),X1) ) ),
inference(cnf_transformation,[],[f134]) ).
tff(f227,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ semiring_div(X0)
| ( div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),div_mod(X0,X3,X2)),X1),X2) = div_mod(X0,aa(X0,X0,aa(X0,fun(X0,X0),plus_plus(X0),X3),X1),X2) ) ),
inference(cnf_transformation,[],[f135]) ).
tff(f332,plain,
semiring_div(int),
inference(cnf_transformation,[],[f107]) ).
tff(f344,plain,
div_mod(int,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,i,d)),div_mod(int,iprod(int,ks,e),d)),d),
inference(cnf_transformation,[],[f121]) ).
tff(f749,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X1),X2) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),div_mod(int,X1,X2)),X2) ),
inference(resolution,[],[f226,f332]) ).
tff(f750,plain,
div_mod(int,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,i,d)),iprod(int,ks,e)),d),
inference(backward_demodulation,[],[f344,f749]) ).
tff(f752,plain,
! [X2: int,X0: int,X1: int] : ( div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,X0,X1)),X2),X1) = div_mod(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X0),X2),X1) ),
inference(resolution,[],[f227,f332]) ).
tff(f753,plain,
div_mod(int,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),i),iprod(int,ks,e)),d),
inference(backward_demodulation,[],[f750,f752]) ).
tff(f754,plain,
$false,
inference(trivial_inequality_removal,[],[f753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM034_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.26 % Computer : n007.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 21:48:10 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.32 Running first-order model finding
% 0.25/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.47 % (2886139)Will run a generic schedule for satisfiability detection.
% 0.50/0.47 % (2886144)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1329872871_2999 on theBenchmark for (2999ds/0Mi)
% 0.50/0.47 % Exception at run slice level
% 0.50/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.50/0.47 % (2886145)% WARNING: option uhcvi not known.
% 0.50/0.47 % (2886146)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=588312328:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.50/0.47 % (2886148)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=846975752:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.50/0.47 % (2886149)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=937773306:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.50/0.47 % (2886145)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1627997484:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.50/0.47 % (2886150)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2077726261:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.50/0.47 % (2886147)dis+10_1_sil=32000:sp=arity:random_seed=3791006242:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.50/0.47 % (2886152)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1378150005:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.50/0.47 % Exception at run slice level
% 0.50/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.50/0.47 % (2886160)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4247381484:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.50/0.47 % (2886160) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2886139-2886160"...
% 0.50/0.47 % (2886160)...printing done.
% 0.50/0.47 % (2886160)Refutation found. Thanks to Tanya!
% 0.50/0.47 % SZS status Theorem for theBenchmark
% 0.50/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.50/0.47 % (2886160)------------------------------
% 0.50/0.47 % (2886160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.47 % (2886160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.47 % (2886160)CaDiCaL version: 2.1.3
% 0.50/0.47 % (2886160)Termination reason: Refutation
% 0.50/0.47 % (2886160)Time elapsed: 0.054 s
% 0.50/0.47 % (2886160)Peak memory usage: 13 MB
% 0.50/0.47 % (2886160)Instructions burned: 82 (million)
% 0.50/0.47 % (2886139)Success in time 0.137 s
% 0.50/0.47 % Vampire exiting
%------------------------------------------------------------------------------