%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV629_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 : n018.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 01:19:08 PM UTC 2026
% Result : Theorem 3.49s 1.06s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 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 : 31 ( 29 usr; 1 prp; 0-4 aty)
% Number of functors : 23 ( 23 usr; 3 con; 0-4 aty)
% Number of variables : 9 ( 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
int: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
cnj: complex > complex ).
tff(func_def_1,type,
ii: complex ).
tff(func_def_2,type,
fFT_Mirabelle_root: nat > complex ).
tff(func_def_3,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_5,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_6,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
semiring_1_Nats:
!>[X0: $tType] : fun(X0,bool) ).
tff(func_def_9,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_10,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_11,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_12,type,
fFalse: bool ).
tff(func_def_13,type,
fTrue: bool ).
tff(func_def_14,type,
sK0:
!>[X0: $tType] : ( fun(X0,bool) > nat ) ).
tff(func_def_15,type,
sK1:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_16,type,
sK2: fun(int,bool) > nat ).
tff(func_def_17,type,
sK3: fun(int,bool) > int ).
tff(func_def_18,type,
sK4: fun(int,bool) > int ).
tff(func_def_19,type,
sK5: fun(int,bool) > nat ).
tff(func_def_20,type,
sK6: int > nat ).
tff(func_def_21,type,
sK7: int > nat ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
field:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_23,type,
real_n2089651433ebra_1:
!>[X0: $tType] : $o ).
tff(pred_def_24,type,
iszero:
!>[X0: $tType] : ( X0 > $o ) ).
tff(pred_def_25,type,
nat_tr1645093318rphism:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_26,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_27,type,
vector_space:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X1)) > $o ) ).
tff(pred_def_28,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_29,type,
pp: bool > $o ).
tff(f3,axiom,
! [X0: nat] : ( power_power(complex,fFT_Mirabelle_root(X0),X0) = one_one(complex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_root__unity) ).
tff(f56,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: X0] : ( power_power(X0,X1,one_one(nat)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_power__one__right) ).
tff(f141,axiom,
monoid_mult(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
tff(f157,conjecture,
fFT_Mirabelle_root(one_one(nat)) = one_one(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f158,negated_conjecture,
( ( ~ fFT_Mirabelle_root(one_one(nat)) ) = one_one(complex) ),
inference(negated_conjecture,[status(cth)],[f157]) ).
tff(f161,plain,
one_one(complex) != fFT_Mirabelle_root(one_one(nat)),
inference(flattening,[],[f158]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: X0] : ( power_power(X0,X1,one_one(nat)) = X1 )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f56]) ).
tff(f273,plain,
! [X0: nat] : ( one_one(complex) = power_power(complex,fFT_Mirabelle_root(X0),X0) ),
inference(cnf_transformation,[],[f3]) ).
tff(f329,plain,
! [X0: $tType,X1: X0] :
( ~ monoid_mult(X0)
| ( power_power(X0,X1,one_one(nat)) = X1 ) ),
inference(cnf_transformation,[],[f207]) ).
tff(f427,plain,
monoid_mult(complex),
inference(cnf_transformation,[],[f141]) ).
tff(f442,plain,
one_one(complex) != fFT_Mirabelle_root(one_one(nat)),
inference(cnf_transformation,[],[f161]) ).
tff(f563,plain,
! [X0: complex] : ( power_power(complex,X0,one_one(nat)) = X0 ),
inference(resolution,[],[f329,f427]) ).
tff(f642,plain,
one_one(complex) = fFT_Mirabelle_root(one_one(nat)),
inference(superposition,[],[f273,f563]) ).
tff(f644,plain,
$false,
inference(forward_subsumption_resolution,[],[f642,f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV629_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 12:08:10 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 3.49/1.06 % (3330365)Detected formulas, will run a generic FOF schedule.
% 3.49/1.06 % (3330376)dis-21_1_sil=8000:lcm=predicate:random_seed=1968170323: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)
% 3.49/1.06 % (3330376)Instruction limit reached!
% 3.49/1.06 % (3330376)------------------------------
% 3.49/1.06 % (3330376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330376)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330376)Termination reason: Instruction limit
% 3.49/1.06 % (3330376)Termination phase: Saturation
% 3.49/1.06 % (3330376)Time elapsed: 0.037 s
% 3.49/1.06 % (3330376)Peak memory usage: 89 MB
% 3.49/1.06 % (3330376)Instructions burned: 131 (million)
% 3.49/1.06 % (3330374)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1399952767:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.06 % (3330370)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=2314455023:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.06 % (3330372)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=1464376347:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.06 % (3330373)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2380527705:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.06 % (3330375)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1768599824:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.06 % (3330371)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=4291317991:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.06 % (3330373)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.49/1.06 % (3330373)Refutation not found, incomplete strategy
% 3.49/1.06 % (3330373)------------------------------
% 3.49/1.06 % (3330373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330373)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330373)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.06 % (3330373)Time elapsed: 0.001 s
% 3.49/1.06 % (3330373)Peak memory usage: 88 MB
% 3.49/1.06 % (3330372)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.49/1.06 % (3330375)First to succeed.
% 3.49/1.06 % (3330375)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3330365"
% 3.49/1.06 % (3330374)Instruction limit reached!
% 3.49/1.06 % (3330374)------------------------------
% 3.49/1.06 % (3330374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330374)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330374)Termination reason: Instruction limit
% 3.49/1.06 % (3330374)Termination phase: Saturation
% 3.49/1.06 % (3330374)Time elapsed: 0.063 s
% 3.49/1.06 % (3330374)Peak memory usage: 88 MB
% 3.49/1.06 % (3330374)Instructions burned: 120 (million)
% 3.49/1.06 % (3330384)lrs+10_1_sil=8000:sp=occurrence:random_seed=2866693415:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.49/1.06 % (3330384)Instruction limit reached!
% 3.49/1.06 % (3330384)------------------------------
% 3.49/1.06 % (3330384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330384)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330384)Termination reason: Instruction limit
% 3.49/1.06 % (3330384)Termination phase: Saturation
% 3.49/1.06 % (3330384)Time elapsed: 0.073 s
% 3.49/1.06 % (3330384)Peak memory usage: 90 MB
% 3.49/1.06 % (3330384)Instructions burned: 287 (million)
% 3.49/1.06 % (3330385)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1833859893:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.49/1.06 % (3330385)Refutation not found, incomplete strategy
% 3.49/1.06 % (3330385)------------------------------
% 3.49/1.06 % (3330385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330385)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330385)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.06 % (3330385)Time elapsed: 0.002 s
% 3.49/1.06 % (3330385)Peak memory usage: 88 MB
% 3.49/1.06 % (3330385)Instructions burned: 2 (million)
% 3.49/1.06 % (3330373)------------------------------
% 3.49/1.06 % (3330373)------------------------------
% 3.49/1.06 % (3330375)Refutation found. Thanks to Tanya!
% 3.49/1.06 % SZS status Theorem for theBenchmark
% 3.49/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.06 % (3330375)------------------------------
% 3.49/1.06 % (3330375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.06 % (3330375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.06 % (3330375)CaDiCaL version: 2.1.3
% 3.49/1.06 % (3330375)Termination reason: Refutation
% 3.49/1.06 % (3330375)Time elapsed: 0.011 s
% 3.49/1.06 % (3330375)Peak memory usage: 89 MB
% 3.49/1.06 % (3330375)Instructions burned: 14 (million)
% 3.49/1.06 % (3330375)------------------------------
% 3.49/1.06 % (3330375)------------------------------
% 3.49/1.06 % (3330365)Success in time 0.433 s
% 3.49/1.06 % Vampire exiting
%------------------------------------------------------------------------------