%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925+2 : 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 : n008.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 3.57s 1.49s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 22 unt; 0 def)
% Number of atoms : 43 ( 35 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 9 |; 5 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f104,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f109,axiom,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f134,axiom,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f276,axiom,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__add__one) ).
fof(f291,axiom,
! [X0,X1] :
( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int
<=> ( X0 = zero_zero_int
& X1 != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).
fof(f294,axiom,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).
fof(f351,axiom,
! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f708,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f709,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f708]) ).
fof(f710,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f709]) ).
fof(f1024,plain,
! [X0,X1] :
( ( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int
| zero_zero_int != X0
| zero_zero_nat = X1 )
& ( ( X0 = zero_zero_int
& X1 != zero_zero_nat )
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ),
inference(nnf_transformation,[],[f291]) ).
fof(f1025,plain,
! [X0,X1] :
( ( hAPP_nat_int(power_power_int(X0),X1) = zero_zero_int
| zero_zero_int != X0
| zero_zero_nat = X1 )
& ( ( X0 = zero_zero_int
& X1 != zero_zero_nat )
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ),
inference(flattening,[],[f1024]) ).
fof(f1132,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f710]) ).
fof(f1174,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f104]) ).
fof(f1193,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(X0),one_one_int))),
inference(cnf_transformation,[],[f276]) ).
fof(f1203,plain,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
inference(cnf_transformation,[],[f134]) ).
fof(f1221,plain,
! [X0,X1] : hAPP_int_int(plus_plus_int(X0),X1) = hAPP_int_int(plus_plus_int(X1),X0),
inference(cnf_transformation,[],[f351]) ).
fof(f1267,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f294]) ).
fof(f1320,plain,
! [X0,X1] :
( zero_zero_int = X0
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ),
inference(cnf_transformation,[],[f1025]) ).
fof(f1388,plain,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
inference(cnf_transformation,[],[f109]) ).
fof(f1729,plain,
pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(definition_unfolding,[],[f1132,f1174,f1388,f1203]) ).
fof(f1802,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f1267,f1174]) ).
fof(f1829,plain,
! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X0),X1)
| pls = X0 ),
inference(definition_unfolding,[],[f1320,f1174,f1174]) ).
fof(f2082,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),hAPP_int_int(plus_plus_int(one_one_int),X0))),
inference(superposition,[],[f1193,f1221]) ).
fof(f2134,plain,
( pls != pls
| hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls ),
inference(superposition,[],[f1829,f1729]) ).
fof(f2139,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(trivial_inequality_removal,[],[f2134]) ).
fof(f2155,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),pls)),
inference(superposition,[],[f2082,f2139]) ).
fof(f2159,plain,
$false,
inference(forward_subsumption_resolution,[],[f2155,f1802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 21:42:40 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.57/1.48 % (1629771)Detected formulas, will run a generic FOF schedule.
% 3.57/1.48 % (1629778)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=2811379261:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.48 % (1629780)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4103672195:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.48 % (1629777)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=4131576917:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.48 % (1629782)dis-21_1_sil=8000:lcm=predicate:random_seed=1780386453: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)
% 3.57/1.48 % (1629779)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=999428560:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.48 % (1629776)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=1561866226:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.49 % (1629781)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=350106153:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.49 % (1629780)First to succeed.
% 3.57/1.49 % (1629779)Also succeeded, but the first one will report.
% 3.57/1.49 % (1629780)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1629771"
% 3.57/1.49 % (1629781)Also succeeded, but the first one will report.
% 3.57/1.49 % (1629782)Instruction limit reached!
% 3.57/1.49 % (1629782)------------------------------
% 3.57/1.49 % (1629782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.49 % (1629782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.49 % (1629782)CaDiCaL version: 2.1.3
% 3.57/1.49 % (1629782)Termination reason: Instruction limit
% 3.57/1.49 % (1629782)Termination phase: Saturation
% 3.57/1.49 % (1629782)Time elapsed: 0.071 s
% 3.57/1.49 % (1629782)Peak memory usage: 90 MB
% 3.57/1.49 % (1629782)Instructions burned: 130 (million)
% 3.57/1.49 % (1629790)lrs+10_1_sil=8000:sp=occurrence:random_seed=935031231:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.57/1.49 % (1629790)Also succeeded, but the first one will report.
% 3.57/1.49 % (1629780)Refutation found. Thanks to Tanya!
% 3.57/1.49 % SZS status Theorem for theBenchmark
% 3.57/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.49 % (1629780)------------------------------
% 3.57/1.49 % (1629780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.49 % (1629780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.49 % (1629780)CaDiCaL version: 2.1.3
% 3.57/1.49 % (1629780)Termination reason: Refutation
% 3.57/1.49 % (1629780)Time elapsed: 0.022 s
% 3.57/1.49 % (1629780)Peak memory usage: 89 MB
% 3.57/1.49 % (1629780)Instructions burned: 41 (million)
% 3.57/1.49 % (1629780)------------------------------
% 3.57/1.49 % (1629780)------------------------------
% 3.57/1.49 % (1629771)Success in time 0.453 s
% 3.57/1.49 % Vampire exiting
%------------------------------------------------------------------------------