%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925_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 : n003.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 12:17:32 PM UTC 2026
% Result : Theorem 0.18s 1.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 18 |; 9 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?; 29 :)
% 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,
zero_zero_int: int ).
tff(func_def_5,type,
zero_zero_nat: nat ).
tff(func_def_6,type,
bit0: int > int ).
tff(func_def_7,type,
bit1: int > int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of_int: int > int ).
tff(func_def_10,type,
number_number_of_nat: int > nat ).
tff(func_def_11,type,
semiri1621563631at_int: nat > int ).
tff(func_def_12,type,
semiri984289939at_nat: nat > 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,
n: nat ).
tff(func_def_16,type,
t: int ).
tff(pred_def_1,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_2,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(f53,axiom,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
tff(f66,axiom,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
<=> ( ord_less_int(X0,X1)
| ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
tff(f67,axiom,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
tff(f79,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pls__def) ).
tff(f93,axiom,
! [X0: int,X1: int] :
( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
<=> ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
tff(f107,conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f108,negated_conjecture,
( ( ~ power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) ) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f108]) ).
tff(f141,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& ( X0 != X1 ) ) )
& ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(nnf_transformation,[],[f66]) ).
tff(f142,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& ( X0 != X1 ) ) )
& ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(flattening,[],[f141]) ).
tff(f149,plain,
! [X0: int,X1: int] :
( ( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = number_number_of_nat(X1) ) )
& ( ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ) ),
inference(nnf_transformation,[],[f93]) ).
tff(f150,plain,
! [X0: int,X1: int] :
( ( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = number_number_of_nat(X1) ) )
& ( ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ) ),
inference(flattening,[],[f149]) ).
tff(f227,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f251,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f142]) ).
tff(f253,plain,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
inference(cnf_transformation,[],[f67]) ).
tff(f271,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
tff(f286,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ),
inference(cnf_transformation,[],[f150]) ).
tff(f306,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f109]) ).
tff(f319,plain,
! [X1: int] : ord_less_int(X1,plus_plus_int(X1,one_one_int)),
inference(equality_resolution,[],[f251]) ).
tff(f333,plain,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),pls),
inference(forward_demodulation,[],[f253,f271]) ).
tff(f360,plain,
! [X0: int] : ord_less_int(X0,plus_plus_int(one_one_int,X0)),
inference(superposition,[],[f319,f227]) ).
tff(f614,plain,
! [X0: int,X1: int] :
( ( pls = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ),
inference(forward_demodulation,[],[f286,f271]) ).
tff(f615,plain,
! [X0: int,X1: int] :
( ( pls != power_power_int(X0,number_number_of_nat(X1)) )
| ( pls = X0 ) ),
inference(forward_demodulation,[],[f614,f271]) ).
tff(f625,plain,
( ( zero_zero_int != pls )
| ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls ) ),
inference(superposition,[],[f615,f306]) ).
tff(f629,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(forward_subsumption_resolution,[],[f625,f271]) ).
tff(f636,plain,
ord_less_int(semiri1621563631at_int(n),pls),
inference(superposition,[],[f360,f629]) ).
tff(f637,plain,
$false,
inference(forward_subsumption_resolution,[],[f636,f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n003.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 21:43:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.18/1.40 % (944197)Detected formulas, will run a generic FOF schedule.
% 0.18/1.40 % (944264)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=155246091:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.40 % (944268)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2576001126:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.40 % (944272)dis-21_1_sil=8000:lcm=predicate:random_seed=419289455: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)
% 0.18/1.40 % (944269)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4182293251:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.40 % (944271)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=506960620:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.40 % (944267)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=680260363:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.40 % (944271)First to succeed.
% 0.18/1.40 % (944271)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-944197"
% 0.18/1.40 % (944265)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=610180557:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.40 % (944269)Also succeeded, but the first one will report.
% 0.18/1.40 % (944268)Instruction limit reached!
% 0.18/1.40 % (944268)------------------------------
% 0.18/1.40 % (944268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.40 % (944268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.40 % (944268)CaDiCaL version: 2.1.3
% 0.18/1.40 % (944268)Termination reason: Instruction limit
% 0.18/1.40 % (944268)Termination phase: Saturation
% 0.18/1.40 % (944268)Time elapsed: 0.059 s
% 0.18/1.40 % (944268)Peak memory usage: 89 MB
% 0.18/1.40 % (944268)Instructions burned: 110 (million)
% 0.18/1.40 % (944272)Instruction limit reached!
% 0.18/1.40 % (944272)------------------------------
% 0.18/1.40 % (944272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.40 % (944272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.40 % (944272)CaDiCaL version: 2.1.3
% 0.18/1.40 % (944272)Termination reason: Instruction limit
% 0.18/1.40 % (944272)Termination phase: Saturation
% 0.18/1.40 % (944272)Time elapsed: 0.075 s
% 0.18/1.40 % (944272)Peak memory usage: 89 MB
% 0.18/1.40 % (944272)Instructions burned: 131 (million)
% 0.18/1.40 % (944300)lrs+10_1_sil=8000:sp=occurrence:random_seed=974408043:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.40 % (944300)Also succeeded, but the first one will report.
% 0.18/1.40 % (944301)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1742910974:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.18/1.40 % (944271)Refutation found. Thanks to Tanya!
% 0.18/1.40 % SZS status Theorem for theBenchmark
% 0.18/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.40 % (944271)------------------------------
% 0.18/1.40 % (944271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.40 % (944271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.40 % (944271)CaDiCaL version: 2.1.3
% 0.18/1.40 % (944271)Termination reason: Refutation
% 0.18/1.40 % (944271)Time elapsed: 0.013 s
% 0.18/1.40 % (944271)Peak memory usage: 89 MB
% 0.18/1.40 % (944271)Instructions burned: 18 (million)
% 0.18/1.40 % (944271)------------------------------
% 0.18/1.40 % (944271)------------------------------
% 0.18/1.40 % (944197)Success in time 0.439 s
% 0.18/1.40 % Vampire exiting
%------------------------------------------------------------------------------