%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN004_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 : n006.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 12:26:34 PM UTC 2026
% Result : Theorem 0.95s 1.03s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 1 def)
% Number of atoms : 22 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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 : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 6 ( 3 !; 3 ?; 6 :)
% 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,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m: int ).
tff(func_def_13,type,
m1: int ).
tff(func_def_14,type,
n: nat ).
tff(func_def_15,type,
t: int ).
tff(func_def_16,type,
v: int ).
tff(func_def_17,type,
w: int ).
tff(func_def_18,type,
x: int ).
tff(func_def_19,type,
y: int ).
tff(func_def_20,type,
sK0: int ).
tff(func_def_21,type,
sK1: int ).
tff(func_def_22,type,
sK2: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
zprime: int > $o ).
tff(pred_def_14,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_15,type,
dvd_dvd:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_17,type,
pp: bool > $o ).
tff(pred_def_18,type,
sP3: int > $o ).
tff(pred_def_19,type,
sP4: int > $o ).
tff(pred_def_20,type,
sP5: int > $o ).
tff(pred_def_21,type,
sP6: int > $o ).
tff(pred_def_22,type,
sP7: int > $o ).
tff(pred_def_23,type,
sP8: int > $o ).
tff(pred_def_24,type,
sP9: int > $o ).
tff(f2,axiom,
plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_xy) ).
tff(f3,axiom,
~ ! [X0: int,X1: int] : ( plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_A_I1_A_L_Aint_An_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f4,axiom,
~ ! [X0: int] : ( plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) != times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096_B_Bthesis_O_A_I_B_Bm1_O_Av_A_094_A2_A_L_Aw_A_094_A2_A_061_A_I1_A_L_Aint_An_J_A_K_Am1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f118,conjecture,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) = times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f119,negated_conjecture,
( ( ~ times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ) = times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
tff(f120,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) != times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(flattening,[],[f119]) ).
tff(f122,plain,
? [X0: int,X1: int] : ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(ennf_transformation,[],[f3]) ).
tff(f123,plain,
? [X0: int] : ( plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f130,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f122]) ).
tff(f131,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f123]) ).
tff(f132,plain,
times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) != times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))),
inference(cnf_transformation,[],[f120]) ).
tff(f170,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f130]) ).
tff(f172,plain,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2),
inference(cnf_transformation,[],[f131]) ).
tff(f173,plain,
plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f2]) ).
tff(f174,definition,
~ sP3(times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))))),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
tff(f175,plain,
sP3(times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))))),
inference(inequality_splitting,[],[f132,f174]) ).
tff(f191,plain,
~ sP3(times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2))),
inference(forward_demodulation,[],[f174,f172]) ).
tff(f192,plain,
sP3(times_times(int,plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,number_number_of(nat,bit0(bit1(pls))))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2))),
inference(forward_demodulation,[],[f175,f172]) ).
tff(f193,plain,
~ sP3(times_times(int,plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2))),
inference(forward_demodulation,[],[f191,f170]) ).
tff(f194,plain,
sP3(times_times(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2))),
inference(forward_demodulation,[],[f192,f173]) ).
tff(f195,plain,
sP3(times_times(int,plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),sK2))),
inference(forward_demodulation,[],[f194,f170]) ).
tff(f196,plain,
$false,
inference(forward_subsumption_resolution,[],[f195,f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN004_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.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 21:49:26 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
% 0.95/1.03 % (3352438)Detected formulas, will run a generic FOF schedule.
% 0.95/1.03 % (3352448)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1962962525:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.95/1.03 % (3352444)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=1291682931:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.95/1.03 % (3352447)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1707627960:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.95/1.03 % (3352446)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3336411623:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.95/1.03 % (3352445)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=2531212030:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.95/1.03 % (3352443)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=595819379:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.95/1.03 % (3352449)dis-21_1_sil=8000:lcm=predicate:random_seed=824880250: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)
% 0.95/1.03 % (3352446)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.95/1.03 % (3352446)First to succeed.
% 0.95/1.03 % (3352445)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.95/1.03 % (3352446)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3352438"
% 0.95/1.03 % (3352447)Also succeeded, but the first one will report.
% 0.95/1.03 % (3352448)Also succeeded, but the first one will report.
% 0.95/1.03 % (3352449)Instruction limit reached!
% 0.95/1.03 % (3352449)------------------------------
% 0.95/1.03 % (3352449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.95/1.03 % (3352449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/1.03 % (3352449)CaDiCaL version: 2.1.3
% 0.95/1.03 % (3352449)Termination reason: Instruction limit
% 0.95/1.03 % (3352449)Termination phase: Saturation
% 0.95/1.03 % (3352449)Time elapsed: 0.071 s
% 0.95/1.03 % (3352449)Peak memory usage: 90 MB
% 0.95/1.03 % (3352449)Instructions burned: 130 (million)
% 0.95/1.03 % (3352457)lrs+10_1_sil=8000:sp=occurrence:random_seed=3487596225:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.95/1.03 % (3352457)Also succeeded, but the first one will report.
% 0.95/1.03 % (3352446)Refutation found. Thanks to Tanya!
% 0.95/1.03 % SZS status Theorem for theBenchmark
% 0.95/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.30/1.23 % (3352446)------------------------------
% 3.30/1.23 % (3352446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.23 % (3352446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.23 % (3352446)CaDiCaL version: 2.1.3
% 3.30/1.23 % (3352446)Termination reason: Refutation
% 3.30/1.23 % (3352446)Time elapsed: 0.004 s
% 3.30/1.23 % (3352446)Peak memory usage: 88 MB
% 3.30/1.23 % (3352446)Instructions burned: 6 (million)
% 3.30/1.23 % (3352446)------------------------------
% 3.30/1.23 % (3352446)------------------------------
% 3.30/1.23 % (3352438)Success in time 0.412 s
% 3.30/1.23 % Vampire exiting
%------------------------------------------------------------------------------