%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV633_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 : n002.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 01:19:09 PM UTC 2026
% Result : Theorem 3.81s 1.33s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 3 |; 0 &)
% ( 0 <=>; 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 : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% 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,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
ii: complex ).
tff(func_def_1,type,
fFT_Mirabelle_root: nat > complex ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
suc: nat > nat ).
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,
i: nat ).
tff(func_def_15,type,
j: nat ).
tff(func_def_16,type,
m: nat ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
uminus:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring:
!>[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,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
boolean_algebra:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f27,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
tff(f84,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
tff(f115,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
tff(f151,conjecture,
power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,bit0(bit1(pls))),j))) = power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),times_times(nat,i,j))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f152,negated_conjecture,
( ( ~ power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,bit0(bit1(pls))),j))) ) = power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),times_times(nat,i,j))) ),
inference(negated_conjecture,[status(cth)],[f151]) ).
tff(f153,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,bit0(bit1(pls))),j))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),times_times(nat,i,j))),
inference(flattening,[],[f152]) ).
tff(f180,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f27]) ).
tff(f191,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,bit0(bit1(pls))),j))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,bit0(bit1(pls))),m)),times_times(nat,number_number_of(nat,bit0(bit1(pls))),times_times(nat,i,j))),
inference(cnf_transformation,[],[f153]) ).
tff(f192,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f84]) ).
tff(f237,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f249,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,X2,times_times(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f180]) ).
tff(f256,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),j))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),m)),times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),times_times(nat,i,j))),
inference(definition_unfolding,[],[f191,f192,f192,f192,f192]) ).
tff(f1019,plain,
( ( power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),j))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),m)),times_times(nat,i,times_times(nat,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))),j))) )
| ~ comm_semiring_1(nat) ),
inference(superposition,[],[f256,f249]) ).
tff(f1027,plain,
~ comm_semiring_1(nat),
inference(trivial_inequality_removal,[],[f1019]) ).
tff(f1047,plain,
$false,
inference(forward_subsumption_resolution,[],[f1027,f237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV633_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n002.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 12:09:25 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 3.81/1.33 % (315491)Detected formulas, will run a generic FOF schedule.
% 3.81/1.33 % (315498)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=920922668:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.81/1.33 % (315498)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.81/1.33 % (315500)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2795769115:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.81/1.33 % (315501)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2469260413:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.81/1.33 % (315497)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=3277445317:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.81/1.33 % (315502)dis-21_1_sil=8000:lcm=predicate:random_seed=3143773734: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)
% 3.81/1.33 % (315496)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=3044353677:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.81/1.33 % (315499)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2982787109:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.81/1.33 % (315499)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.81/1.33 % (315502)Refutation not found, incomplete strategy
% 3.81/1.33 % (315502)------------------------------
% 3.81/1.33 % (315502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.33 % (315502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.33 % (315502)CaDiCaL version: 2.1.3
% 3.81/1.33 % (315502)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.33 % (315502)Time elapsed: 0.008 s
% 3.81/1.33 % (315502)Peak memory usage: 88 MB
% 3.81/1.33 % (315502)Instructions burned: 14 (million)
% 3.81/1.33 % (315500)First to succeed.
% 3.81/1.33 % (315500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-315491"
% 3.81/1.33 % (315501)Also succeeded, but the first one will report.
% 3.81/1.33 % (315499)Instruction limit reached!
% 3.81/1.33 % (315499)------------------------------
% 3.81/1.33 % (315499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.33 % (315499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.33 % (315499)CaDiCaL version: 2.1.3
% 3.81/1.33 % (315499)Termination reason: Instruction limit
% 3.81/1.33 % (315499)Termination phase: Saturation
% 3.81/1.33 % (315499)Time elapsed: 0.059 s
% 3.81/1.33 % (315499)Peak memory usage: 89 MB
% 3.81/1.33 % (315499)Instructions burned: 110 (million)
% 3.81/1.33 % Exception at run slice level
% 3.81/1.33 User error: GNN currently only supports monomorphic FOL.
% 3.81/1.33 % (315510)lrs+10_1_sil=8000:sp=occurrence:random_seed=4209226787:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.81/1.33 % (315510)Also succeeded, but the first one will report.
% 3.81/1.33 % (315502)------------------------------
% 3.81/1.33 % (315502)------------------------------
% 3.81/1.33 % (315500)Refutation found. Thanks to Tanya!
% 3.81/1.33 % SZS status Theorem for theBenchmark
% 3.81/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.33 % (315500)------------------------------
% 3.81/1.33 % (315500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.33 % (315500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.33 % (315500)CaDiCaL version: 2.1.3
% 3.81/1.33 % (315500)Termination reason: Refutation
% 3.81/1.33 % (315500)Time elapsed: 0.018 s
% 3.81/1.33 % (315500)Peak memory usage: 88 MB
% 3.81/1.33 % (315500)Instructions burned: 30 (million)
% 3.81/1.33 % (315500)------------------------------
% 3.81/1.33 % (315500)------------------------------
% 3.81/1.33 % (315491)Success in time 0.452 s
% 3.81/1.33 % Vampire exiting
%------------------------------------------------------------------------------