%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:17:28 PM UTC 2026
% Result : Theorem 3.88s 1.53s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 37 unt; 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 predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(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/sandbox/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) ).
fof(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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(f25,axiom,
! [X0] : number_number_of_int(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
fof(f26,axiom,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
fof(f67,axiom,
! [X0] : times_times_int(pls,X0) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
fof(f105,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
fof(f106,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
fof(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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(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]) ).
fof(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]) ).
fof(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]) ).
fof(f191,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f106]) ).
fof(f241,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f105]) ).
fof(f247,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]) ).
fof(f279,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(cnf_transformation,[],[f25]) ).
fof(f285,plain,
! [X0] : pls = times_times_int(pls,X0),
inference(cnf_transformation,[],[f67]) ).
fof(f292,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(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]) ).
fof(f317,plain,
zero_zero_int = pls,
inference(superposition,[],[f279,f191]) ).
fof(f322,plain,
! [X0] : zero_zero_int = times_times_int(zero_zero_int,X0),
inference(forward_demodulation,[],[f285,f317]) ).
fof(f361,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,f241]) ).
fof(f363,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,[],[f361,f317]) ).
fof(f1941,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,[],[f247,f241]) ).
fof(f1942,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,[],[f1941,f317]) ).
fof(f1943,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,[],[f1942,f292]) ).
fof(f1944,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,[],[f1943,f241]) ).
fof(f1945,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,[],[f1944,f292]) ).
fof(f1946,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,[],[f1945,f279]) ).
fof(f1978,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,f292]) ).
fof(f1979,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,[],[f1978,f322]) ).
fof(f1980,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,[],[f1979,f292]) ).
fof(f1981,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,[],[f1980,f241]) ).
fof(f1982,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,[],[f1981,f292]) ).
fof(f1983,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,[],[f1982,f279]) ).
fof(f1984,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,[],[f1983,f317]) ).
fof(f1985,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,[],[f1984,f1946]) ).
fof(f1986,plain,
$false,
inference(forward_subsumption_resolution,[],[f1985,f363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n001.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:46:46 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.88/1.53 % (3986458)Detected formulas, will run a generic FOF schedule.
% 3.88/1.53 % (3986566)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=1789506474:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.88/1.53 % (3986569)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2947554393:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.88/1.53 % (3986565)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=60103594:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.88/1.53 % (3986564)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=2632040541:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.88/1.53 % (3986568)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1015433694:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.88/1.53 % (3986567)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=23677899:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.88/1.53 % (3986567)Refutation not found, incomplete strategy
% 3.88/1.53 % (3986567)------------------------------
% 3.88/1.53 % (3986567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.53 % (3986567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.53 % (3986567)CaDiCaL version: 2.1.3
% 3.88/1.53 % (3986567)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.53 % (3986567)Time elapsed: 0.008 s
% 3.88/1.53 % (3986567)Peak memory usage: 89 MB
% 3.88/1.53 % (3986567)Instructions burned: 10 (million)
% 3.88/1.53 % (3986570)dis-21_1_sil=8000:lcm=predicate:random_seed=3090769239: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)
% 3.88/1.53 % (3986568)First to succeed.
% 3.88/1.53 % (3986568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3986458"
% 3.88/1.53 % (3986569)Also succeeded, but the first one will report.
% 3.88/1.53 % (3986570)Instruction limit reached!
% 3.88/1.53 % (3986570)------------------------------
% 3.88/1.53 % (3986570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.53 % (3986570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.53 % (3986570)CaDiCaL version: 2.1.3
% 3.88/1.53 % (3986570)Termination reason: Instruction limit
% 3.88/1.53 % (3986570)Termination phase: Saturation
% 3.88/1.53 % (3986570)Time elapsed: 0.083 s
% 3.88/1.53 % (3986570)Peak memory usage: 89 MB
% 3.88/1.53 % (3986570)Instructions burned: 129 (million)
% 3.88/1.53 % (3986567)------------------------------
% 3.88/1.53 % (3986567)------------------------------
% 3.88/1.53 % (3986588)lrs+10_1_sil=8000:sp=occurrence:random_seed=720387833:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.88/1.53 % (3986568)Refutation found. Thanks to Tanya!
% 3.88/1.53 % SZS status Theorem for theBenchmark
% 3.88/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.53 % (3986568)------------------------------
% 3.88/1.53 % (3986568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.53 % (3986568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.53 % (3986568)CaDiCaL version: 2.1.3
% 3.88/1.53 % (3986568)Termination reason: Refutation
% 3.88/1.53 % (3986568)Time elapsed: 0.041 s
% 3.88/1.53 % (3986568)Peak memory usage: 88 MB
% 3.88/1.53 % (3986568)Instructions burned: 65 (million)
% 3.88/1.53 % (3986568)------------------------------
% 3.88/1.53 % (3986568)------------------------------
% 3.88/1.53 % (3986458)Success in time 0.458 s
% 3.88/1.53 % Vampire exiting
%------------------------------------------------------------------------------