%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM952_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 : 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 12:17:41 PM UTC 2026
% Result : Theorem 3.46s 1.46s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
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,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
min: 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,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
legendre: ( int * int ) > int ).
tff(func_def_11,type,
fFalse: bool ).
tff(func_def_12,type,
fTrue: bool ).
tff(func_def_13,type,
m: int ).
tff(func_def_14,type,
s: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zprime: int > $o ).
tff(pred_def_10,type,
quadRes: ( int * int ) > $o ).
tff(pred_def_11,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sP0: int > $o ).
tff(pred_def_14,type,
sP1: int > $o ).
tff(pred_def_15,type,
sP2: int > $o ).
tff(pred_def_16,type,
sP3: int > $o ).
tff(pred_def_17,type,
sP4: int > $o ).
tff(pred_def_18,type,
sP5: int > $o ).
tff(f1,axiom,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(f2,axiom,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
tff(f80,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Bit0__def) ).
tff(f89,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Bit1__def) ).
tff(f113,conjecture,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(flattening,[],[f114]) ).
tff(f127,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
inference(cnf_transformation,[],[f115]) ).
tff(f128,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f89]) ).
tff(f132,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f80]) ).
tff(f170,plain,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min))),
inference(cnf_transformation,[],[f2]) ).
tff(f171,plain,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f172,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int))),
inference(definition_unfolding,[],[f127,f132,f132,f128,f132,f128]) ).
tff(f199,plain,
dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min))),
inference(definition_unfolding,[],[f170,f132,f132,f128,f132,f128]) ).
tff(f200,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),one_one(int)) = minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min)),
inference(definition_unfolding,[],[f171,f132,f128,f132,f128]) ).
tff(f215,plain,
~ dvd_dvd(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)),minus_minus(int,power_power(int,s,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(int,min))),
inference(forward_demodulation,[],[f172,f200]) ).
tff(f216,plain,
$false,
inference(forward_subsumption_resolution,[],[f215,f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM952_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:47:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.46/1.46 % (3440833)Detected formulas, will run a generic FOF schedule.
% 3.46/1.46 % (3440844)dis-21_1_sil=8000:lcm=predicate:random_seed=946809363: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)
% 3.46/1.46 % (3440844)Instruction limit reached!
% 3.46/1.46 % (3440844)------------------------------
% 3.46/1.46 % (3440844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (3440844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (3440844)CaDiCaL version: 2.1.3
% 3.46/1.46 % (3440844)Termination reason: Instruction limit
% 3.46/1.46 % (3440844)Termination phase: Saturation
% 3.46/1.46 % (3440844)Time elapsed: 0.033 s
% 3.46/1.46 % (3440844)Peak memory usage: 89 MB
% 3.46/1.46 % (3440844)Instructions burned: 132 (million)
% 3.46/1.46 % (3440841)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=640972741:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.46 % (3440841)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.46/1.46 % (3440842)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3970421604:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.46 % (3440838)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=3775298676:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.46 % (3440839)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=3341223207:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.46 % (3440840)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=236649372:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.46 % (3440841)First to succeed.
% 3.46/1.46 % (3440841)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3440833"
% 3.46/1.46 % (3440840)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.46/1.46 % (3440843)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1069342451:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.46 % (3440843)Also succeeded, but the first one will report.
% 3.46/1.46 % (3440842)Also succeeded, but the first one will report.
% 3.46/1.46 % (3440847)lrs+10_1_sil=8000:sp=occurrence:random_seed=2727870178:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.46/1.46 % (3440847)Also succeeded, but the first one will report.
% 3.46/1.46 % (3440841)Refutation found. Thanks to Tanya!
% 3.46/1.46 % SZS status Theorem for theBenchmark
% 3.46/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.46 % (3440841)------------------------------
% 3.46/1.46 % (3440841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (3440841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (3440841)CaDiCaL version: 2.1.3
% 3.46/1.46 % (3440841)Termination reason: Refutation
% 3.46/1.46 % (3440841)Time elapsed: 0.005 s
% 3.46/1.46 % (3440841)Peak memory usage: 88 MB
% 3.46/1.46 % (3440841)Instructions burned: 6 (million)
% 3.46/1.46 % (3440841)------------------------------
% 3.46/1.46 % (3440841)------------------------------
% 3.46/1.46 % (3440833)Success in time 0.409 s
% 3.46/1.46 % Vampire exiting
%------------------------------------------------------------------------------