%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV617_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 : n026.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 01:19:06 PM UTC 2026
% Result : Theorem 3.57s 1.28s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 6 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 23 ( 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
fFT_Mirabelle_root: nat > complex ).
tff(func_def_1,type,
inverse_divide:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_5,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
k: nat ).
tff(func_def_11,type,
n: nat ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
field:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
division_ring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linordered_field:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
field_inverse_zero:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
divisi14063676e_zero:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
linord1117847801e_zero:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_23,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_24,type,
pp: bool > $o ).
tff(f4,axiom,
! [X0: nat] : ( power_power(complex,fFT_Mirabelle_root(X0),X0) = one_one(complex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_root__unity) ).
tff(f6,axiom,
! [X0: $tType] :
( monoid_mult(X0)
=> ! [X1: nat] : ( power_power(X0,one_one(X0),X1) = one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_power__one) ).
tff(f7,axiom,
! [X0: $tType] :
( division_ring(X0)
=> ! [X1: X0] : ( inverse_divide(X0,zero_zero(X0),X1) = zero_zero(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_divide__zero__left) ).
tff(f10,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0] : ( minus_minus(X0,X1,X1) = zero_zero(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_diff__self) ).
tff(f115,axiom,
division_ring(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring) ).
tff(f117,axiom,
monoid_mult(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
tff(f119,axiom,
group_add(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ogroup__add) ).
tff(f127,conjecture,
inverse_divide(complex,minus_minus(complex,power_power(complex,power_power(complex,fFT_Mirabelle_root(n),n),k),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))) = zero_zero(complex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
( ( ~ inverse_divide(complex,minus_minus(complex,power_power(complex,power_power(complex,fFT_Mirabelle_root(n),n),k),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))) ) = zero_zero(complex) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f129,plain,
inverse_divide(complex,minus_minus(complex,power_power(complex,power_power(complex,fFT_Mirabelle_root(n),n),k),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))) != zero_zero(complex),
inference(flattening,[],[f128]) ).
tff(f143,plain,
! [X0: $tType] :
( ! [X1: nat] : ( power_power(X0,one_one(X0),X1) = one_one(X0) )
| ~ monoid_mult(X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f144,plain,
! [X0: $tType] :
( ! [X1: X0] : ( inverse_divide(X0,zero_zero(X0),X1) = zero_zero(X0) )
| ~ division_ring(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f148,plain,
! [X0: $tType] :
( ! [X1: X0] : ( minus_minus(X0,X1,X1) = zero_zero(X0) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f251,plain,
! [X0: nat] : ( one_one(complex) = power_power(complex,fFT_Mirabelle_root(X0),X0) ),
inference(cnf_transformation,[],[f4]) ).
tff(f254,plain,
! [X0: $tType,X1: nat] :
( ~ monoid_mult(X0)
| ( one_one(X0) = power_power(X0,one_one(X0),X1) ) ),
inference(cnf_transformation,[],[f143]) ).
tff(f255,plain,
! [X0: $tType,X1: X0] :
( ~ division_ring(X0)
| ( zero_zero(X0) = inverse_divide(X0,zero_zero(X0),X1) ) ),
inference(cnf_transformation,[],[f144]) ).
tff(f260,plain,
! [X0: $tType,X1: X0] :
( ~ group_add(X0)
| ( zero_zero(X0) = minus_minus(X0,X1,X1) ) ),
inference(cnf_transformation,[],[f148]) ).
tff(f397,plain,
division_ring(complex),
inference(cnf_transformation,[],[f115]) ).
tff(f399,plain,
monoid_mult(complex),
inference(cnf_transformation,[],[f117]) ).
tff(f401,plain,
group_add(complex),
inference(cnf_transformation,[],[f119]) ).
tff(f409,plain,
inverse_divide(complex,minus_minus(complex,power_power(complex,power_power(complex,fFT_Mirabelle_root(n),n),k),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))) != zero_zero(complex),
inference(cnf_transformation,[],[f129]) ).
tff(f449,plain,
zero_zero(complex) != inverse_divide(complex,minus_minus(complex,power_power(complex,one_one(complex),k),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))),
inference(superposition,[],[f409,f251]) ).
tff(f450,plain,
! [X0: complex] : ( zero_zero(complex) = minus_minus(complex,X0,X0) ),
inference(resolution,[],[f260,f401]) ).
tff(f463,plain,
! [X0: nat] : ( one_one(complex) = power_power(complex,one_one(complex),X0) ),
inference(resolution,[],[f254,f399]) ).
tff(f465,plain,
zero_zero(complex) != inverse_divide(complex,minus_minus(complex,one_one(complex),one_one(complex)),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))),
inference(superposition,[],[f449,f463]) ).
tff(f466,plain,
zero_zero(complex) != inverse_divide(complex,zero_zero(complex),minus_minus(complex,power_power(complex,fFT_Mirabelle_root(n),k),one_one(complex))),
inference(forward_demodulation,[],[f465,f450]) ).
tff(f467,plain,
! [X0: complex] : ( zero_zero(complex) = inverse_divide(complex,zero_zero(complex),X0) ),
inference(resolution,[],[f255,f397]) ).
tff(f468,plain,
zero_zero(complex) != zero_zero(complex),
inference(superposition,[],[f466,f467]) ).
tff(f469,plain,
$false,
inference(trivial_inequality_removal,[],[f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV617_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 12:06:26 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.57/1.28 % (3812146)Detected formulas, will run a generic FOF schedule.
% 3.57/1.28 % (3812154)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3930203477:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.28 % (3812154)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.57/1.28 % (3812154)Refutation not found, incomplete strategy
% 3.57/1.28 % (3812154)------------------------------
% 3.57/1.28 % (3812154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.28 % (3812154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.28 % (3812154)CaDiCaL version: 2.1.3
% 3.57/1.28 % (3812154)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.28 % (3812154)Time elapsed: 0.002 s
% 3.57/1.28 % (3812154)Peak memory usage: 88 MB
% 3.57/1.28 % (3812154)Instructions burned: 2 (million)
% 3.57/1.28 % (3812156)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=994922074:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.28 % (3812151)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=1111950025:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.28 % (3812155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2132907481:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.28 % (3812157)dis-21_1_sil=8000:lcm=predicate:random_seed=1363628786: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)
% 3.57/1.28 % (3812152)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=2150006514:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.28 % (3812153)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=1471513108:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.28 % (3812153)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.57/1.28 % (3812156)First to succeed.
% 3.57/1.28 % (3812156)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3812146"
% 3.57/1.28 % (3812155)Instruction limit reached!
% 3.57/1.28 % (3812155)------------------------------
% 3.57/1.28 % (3812155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.28 % (3812155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.28 % (3812155)CaDiCaL version: 2.1.3
% 3.57/1.28 % (3812155)Termination reason: Instruction limit
% 3.57/1.28 % (3812155)Termination phase: Saturation
% 3.57/1.28 % (3812155)Time elapsed: 0.064 s
% 3.57/1.28 % (3812155)Peak memory usage: 87 MB
% 3.57/1.28 % (3812155)Instructions burned: 119 (million)
% 3.57/1.28 % (3812157)Instruction limit reached!
% 3.57/1.28 % (3812157)------------------------------
% 3.57/1.28 % (3812157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.28 % (3812157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.28 % (3812157)CaDiCaL version: 2.1.3
% 3.57/1.28 % (3812157)Termination reason: Instruction limit
% 3.57/1.28 % (3812157)Termination phase: Saturation
% 3.57/1.28 % (3812157)Time elapsed: 0.072 s
% 3.57/1.28 % (3812157)Peak memory usage: 89 MB
% 3.57/1.28 % (3812157)Instructions burned: 130 (million)
% 3.57/1.28 % (3812154)------------------------------
% 3.57/1.28 % (3812154)------------------------------
% 3.57/1.28 % (3812167)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1264707589:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.57/1.28 % (3812167)Also succeeded, but the first one will report.
% 3.57/1.28 % (3812165)lrs+10_1_sil=8000:sp=occurrence:random_seed=3855536075:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.57/1.28 % (3812166)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4233420826:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.57/1.28 % (3812156)Refutation found. Thanks to Tanya!
% 3.57/1.28 % SZS status Theorem for theBenchmark
% 3.57/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.28 % (3812156)------------------------------
% 3.57/1.28 % (3812156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.28 % (3812156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.28 % (3812156)CaDiCaL version: 2.1.3
% 3.57/1.28 % (3812156)Termination reason: Refutation
% 3.57/1.28 % (3812156)Time elapsed: 0.008 s
% 3.57/1.28 % (3812156)Peak memory usage: 89 MB
% 3.57/1.28 % (3812156)Instructions burned: 12 (million)
% 3.57/1.28 % (3812156)------------------------------
% 3.57/1.28 % (3812156)------------------------------
% 3.57/1.28 % (3812146)Success in time 0.419 s
% 3.57/1.28 % Vampire exiting
%------------------------------------------------------------------------------