%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n019.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 01:26:10 PM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 2 =>; 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 : 19 ( 19 usr; 7 con; 0-4 aty)
% Number of variables : 28 ( 28 !; 0 ?; 28 :)
% 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(func_def_17,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
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(f26,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,times_times(X0,X3,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
tff(f28,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I7_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(f154,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(f173,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f26]) ).
tff(f175,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( times_times(X0,X2,X1) = times_times(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f28]) ).
tff(f259,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X3,times_times(X0,X2,X1)) = times_times(X0,times_times(X0,X3,X2),X1) ) ),
inference(cnf_transformation,[],[f173]) ).
tff(f261,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ comm_semiring_1(X0)
| ( times_times(X0,X2,X1) = times_times(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f175]) ).
tff(f320,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f84]) ).
tff(f351,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f387,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,[],[f154]) ).
tff(f421,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,[],[f387,f320,f320,f320,f320]) ).
tff(f452,plain,
! [X0: nat,X1: nat] : ( times_times(nat,X1,X0) = times_times(nat,X0,X1) ),
inference(resolution,[],[f261,f351]) ).
tff(f526,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,times_times(nat,i,j),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(superposition,[],[f421,f452]) ).
tff(f527,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),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,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(nat,times_times(nat,i,j),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f526,f452]) ).
tff(f531,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(nat,times_times(nat,i,j),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(nat,i,times_times(nat,j,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(forward_demodulation,[],[f527,f452]) ).
tff(f684,plain,
! [X2: nat,X0: nat,X1: nat] : ( times_times(nat,times_times(nat,X0,X1),X2) = times_times(nat,X0,times_times(nat,X1,X2)) ),
inference(resolution,[],[f259,f351]) ).
tff(f2293,plain,
power_power(complex,fFT_Mirabelle_root(times_times(nat,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(nat,i,times_times(nat,j,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))) != power_power(complex,fFT_Mirabelle_root(times_times(nat,m,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),times_times(nat,i,times_times(nat,j,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))),
inference(superposition,[],[f531,f684]) ).
tff(f2301,plain,
$false,
inference(trivial_inequality_removal,[],[f2293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV633_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 12:06:51 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.30 % (3958584)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3958593)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=343832934:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3958590)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3958589)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2957943954_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3958590)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2090818437:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3958591)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=977398226:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3958592)dis+10_1_sil=32000:sp=arity:random_seed=3532281580:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (3958594)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=411001072:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3958595)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3541843023:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (3958593) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3958584-3958593"...
% 0.19/0.30 % (3958603)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=884895035:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % (3958593)...printing done.
% 0.19/0.30 % (3958593)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (3958593)------------------------------
% 0.19/0.30 % (3958593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3958593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3958593)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3958593)Termination reason: Refutation
% 0.19/0.30 % (3958593)Time elapsed: 0.031 s
% 0.19/0.30 % (3958593)Peak memory usage: 13 MB
% 0.19/0.30 % (3958593)Instructions burned: 100 (million)
% 0.19/0.30 % (3958584)Success in time 0.06 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------