%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:17:29 PM UTC 2026
% Result : Theorem 0.29s 1.50s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_3,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
times_times_int: ( int * int ) > int ).
tff(func_def_5,type,
times_times_nat: ( nat * nat ) > nat ).
tff(func_def_6,type,
zero_zero_int: int ).
tff(func_def_7,type,
zero_zero_nat: nat ).
tff(func_def_8,type,
bit0: int > int ).
tff(func_def_9,type,
bit1: int > int ).
tff(func_def_10,type,
pls: int ).
tff(func_def_11,type,
number_number_of_int: int > int ).
tff(func_def_12,type,
number_number_of_nat: int > nat ).
tff(func_def_13,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_14,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_15,type,
m: int ).
tff(func_def_16,type,
s: int ).
tff(func_def_17,type,
t: int ).
tff(func_def_18,type,
sK0: int ).
tff(pred_def_1,type,
zprime: int > $o ).
tff(pred_def_2,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_3,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(pred_def_4,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(pred_def_5,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff(pred_def_6,type,
twoSqu1431725154sum2sq: int > $o ).
tff(f3,axiom,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(f4,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(f25,axiom,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(f26,axiom,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(f67,axiom,
! [X0: int] : ( times_times_int(pls,X0) = pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(f105,axiom,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
tff(f106,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(f107,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f108,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(flattening,[],[f108]) ).
tff(f169,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(cnf_transformation,[],[f109]) ).
tff(f204,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
tff(f208,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f106]) ).
tff(f263,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnf_transformation,[],[f4]) ).
tff(f274,plain,
! [X0: int] : ( pls = times_times_int(pls,X0) ),
inference(cnf_transformation,[],[f67]) ).
tff(f281,plain,
! [X0: int,X1: int] : ( times_times_int(X0,X1) = times_times_int(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f292,plain,
! [X0: int] : ( number_number_of_int(X0) = X0 ),
inference(cnf_transformation,[],[f25]) ).
tff(f295,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f3]) ).
tff(f317,plain,
zero_zero_int = pls,
inference(superposition,[],[f292,f208]) ).
tff(f322,plain,
! [X0: int] : ( zero_zero_int = times_times_int(zero_zero_int,X0) ),
inference(forward_demodulation,[],[f274,f317]) ).
tff(f341,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(superposition,[],[f169,f204]) ).
tff(f343,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))),zero_zero_int),
inference(forward_demodulation,[],[f341,f317]) ).
tff(f1925,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),
inference(forward_demodulation,[],[f263,f204]) ).
tff(f1926,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int),t),
inference(forward_demodulation,[],[f1925,f317]) ).
tff(f1927,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))) = times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int)),
inference(forward_demodulation,[],[f1926,f281]) ).
tff(f1928,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m))),
inference(forward_demodulation,[],[f1927,f204]) ).
tff(f1929,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(zero_zero_int))))))),
inference(forward_demodulation,[],[f1928,f281]) ).
tff(f1930,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int)))))),
inference(forward_demodulation,[],[f1929,f292]) ).
tff(f1998,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))),
inference(forward_demodulation,[],[f295,f281]) ).
tff(f1999,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),zero_zero_int),
inference(forward_demodulation,[],[f1998,f322]) ).
tff(f2000,plain,
ord_less_int(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),zero_zero_int),
inference(forward_demodulation,[],[f1999,f281]) ).
tff(f2001,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))),zero_zero_int),
inference(forward_demodulation,[],[f2000,f204]) ).
tff(f2002,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))),zero_zero_int),
inference(forward_demodulation,[],[f2001,f281]) ).
tff(f2003,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),zero_zero_int),
inference(forward_demodulation,[],[f2002,f292]) ).
tff(f2004,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(zero_zero_int)))))),zero_zero_int),
inference(forward_demodulation,[],[f2003,f317]) ).
tff(f2005,plain,
ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(zero_zero_int))))),zero_zero_int),
inference(forward_demodulation,[],[f2004,f1930]) ).
tff(f2006,plain,
$false,
inference(forward_subsumption_resolution,[],[f2005,f343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM924_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 % Computer : n019.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sun Sep 27 21:40:49 UTC 2026
% 0.27/0.48 % CPUTime :
% 0.27/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.52 Running first-order theorem proving
% 0.27/0.52 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.29/1.50 % (3435151)Detected formulas, will run a generic FOF schedule.
% 0.29/1.50 % (3435160)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2263266352:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.29/1.50 % (3435160)First to succeed.
% 0.29/1.50 % (3435160)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3435151"
% 0.29/1.50 % (3435156)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=106082613:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.29/1.50 % (3435159)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2281131947:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.29/1.50 % (3435158)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=2945395950:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.29/1.50 % (3435161)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3349965740:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.29/1.50 % (3435157)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=2627587564:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.29/1.50 % (3435159)Refutation not found, incomplete strategy
% 0.29/1.50 % (3435159)------------------------------
% 0.29/1.50 % (3435159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.50 % (3435159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.50 % (3435159)CaDiCaL version: 2.1.3
% 0.29/1.50 % (3435159)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.50 % (3435159)Time elapsed: 0.008 s
% 0.29/1.50 % (3435159)Peak memory usage: 88 MB
% 0.29/1.50 % (3435159)Instructions burned: 10 (million)
% 0.29/1.50 % (3435162)dis-21_1_sil=8000:lcm=predicate:random_seed=3643999371: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)
% 0.29/1.50 % (3435161)Also succeeded, but the first one will report.
% 0.29/1.50 % (3435162)Instruction limit reached!
% 0.29/1.50 % (3435162)------------------------------
% 0.29/1.50 % (3435162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.50 % (3435162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.50 % (3435162)CaDiCaL version: 2.1.3
% 0.29/1.50 % (3435162)Termination reason: Instruction limit
% 0.29/1.50 % (3435162)Termination phase: Saturation
% 0.29/1.50 % (3435162)Time elapsed: 0.082 s
% 0.29/1.50 % (3435162)Peak memory usage: 90 MB
% 0.29/1.50 % (3435162)Instructions burned: 130 (million)
% 0.29/1.50 % (3435160)Refutation found. Thanks to Tanya!
% 0.29/1.50 % SZS status Theorem for theBenchmark
% 0.29/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/1.50 % (3435160)------------------------------
% 0.29/1.50 % (3435160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.50 % (3435160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.50 % (3435160)CaDiCaL version: 2.1.3
% 0.29/1.50 % (3435160)Termination reason: Refutation
% 0.29/1.50 % (3435160)Time elapsed: 0.022 s
% 0.29/1.50 % (3435160)Peak memory usage: 89 MB
% 0.29/1.50 % (3435160)Instructions burned: 66 (million)
% 0.29/1.50 % (3435160)------------------------------
% 0.29/1.50 % (3435160)------------------------------
% 0.29/1.50 % (3435151)Success in time 0.316 s
% 0.29/1.50 % Vampire exiting
%------------------------------------------------------------------------------