%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM925+6 : 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 12:17:34 PM UTC 2026
% Result : Theorem 2.24s 1.30s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 21 unt; 0 def)
% Number of atoms : 56 ( 21 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 45 ( 21 ~; 14 |; 7 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f75,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
fof(f119,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f206,axiom,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_less__0__number__of) ).
fof(f350,axiom,
! [X0] :
( zero_zero(nat) = number_number_of(nat,X0)
<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_eq__0__number__of) ).
fof(f375,axiom,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_power2__ge__self) ).
fof(f395,axiom,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
<=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_nat__less__le) ).
fof(f660,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f661,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f660]) ).
fof(f662,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(flattening,[],[f661]) ).
fof(f777,plain,
! [X0] :
( ( zero_zero(nat) = number_number_of(nat,X0)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| zero_zero(nat) != number_number_of(nat,X0) ) ),
inference(nnf_transformation,[],[f350]) ).
fof(f778,plain,
! [X0] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) )
& ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0))) ) ),
inference(nnf_transformation,[],[f206]) ).
fof(f853,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| X0 = X1 )
& ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
& X0 != X1 )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(nnf_transformation,[],[f395]) ).
fof(f854,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| X0 = X1 )
& ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
& X0 != X1 )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(flattening,[],[f853]) ).
fof(f863,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(cnf_transformation,[],[f662]) ).
fof(f879,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(cnf_transformation,[],[f375]) ).
fof(f929,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(cnf_transformation,[],[f75]) ).
fof(f965,plain,
! [X0] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),pls))
| zero_zero(nat) = number_number_of(nat,X0) ),
inference(cnf_transformation,[],[f777]) ).
fof(f968,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),number_number_of(nat,X0)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),X0)) ),
inference(cnf_transformation,[],[f778]) ).
fof(f975,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f119]) ).
fof(f1002,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf_transformation,[],[f46]) ).
fof(f1187,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f854]) ).
fof(f1235,plain,
! [X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
inference(equality_resolution,[],[f1187]) ).
fof(f1265,plain,
! [X0] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))),
inference(forward_demodulation,[],[f879,f929]) ).
fof(f1269,plain,
zero_zero(int) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),
inference(forward_demodulation,[],[f863,f929]) ).
fof(f1286,plain,
pls = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),
inference(forward_demodulation,[],[f1269,f975]) ).
fof(f1974,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(superposition,[],[f1002,f975]) ).
fof(f2550,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),pls)),
inference(superposition,[],[f1265,f1286]) ).
fof(f2568,plain,
zero_zero(nat) = number_number_of(nat,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
inference(resolution,[],[f2550,f965]) ).
fof(f2805,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),zero_zero(nat)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(superposition,[],[f968,f2568]) ).
fof(f2807,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(forward_subsumption_resolution,[],[f2805,f1235]) ).
fof(f2809,plain,
$false,
inference(forward_subsumption_resolution,[],[f2807,f1974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 21:43:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.24/1.30 % (3437222)Detected formulas, will run a generic FOF schedule.
% 2.24/1.30 % (3437231)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4061512682:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.24/1.30 % (3437231)Instruction limit reached!
% 2.24/1.30 % (3437231)------------------------------
% 2.24/1.30 % (3437231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.30 % (3437231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.30 % (3437231)CaDiCaL version: 2.1.3
% 2.24/1.30 % (3437231)Termination reason: Instruction limit
% 2.24/1.30 % (3437231)Termination phase: Saturation
% 2.24/1.30 % (3437231)Time elapsed: 0.036 s
% 2.24/1.30 % (3437231)Peak memory usage: 89 MB
% 2.24/1.30 % (3437231)Instructions burned: 121 (million)
% 2.24/1.30 % (3437230)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2277352567:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.24/1.30 % (3437229)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=1028110348:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.24/1.30 % (3437228)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=1483683462:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.24/1.30 % (3437227)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=2867767388:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.24/1.30 % (3437232)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=118915433:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.24/1.30 % (3437233)dis-21_1_sil=8000:lcm=predicate:random_seed=3938613889: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)
% 2.24/1.30 % (3437230)Refutation not found, incomplete strategy
% 2.24/1.30 % (3437230)------------------------------
% 2.24/1.30 % (3437230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.30 % (3437230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.30 % (3437230)CaDiCaL version: 2.1.3
% 2.24/1.30 % (3437230)Termination reason: Refutation not found, incomplete strategy
% 2.24/1.30 % (3437230)Time elapsed: 0.028 s
% 2.24/1.30 % (3437230)Peak memory usage: 89 MB
% 2.24/1.30 % (3437230)Instructions burned: 57 (million)
% 2.24/1.30 % (3437233)Instruction limit reached!
% 2.24/1.30 % (3437233)------------------------------
% 2.24/1.30 % (3437233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.30 % (3437233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.30 % (3437233)CaDiCaL version: 2.1.3
% 2.24/1.30 % (3437233)Termination reason: Instruction limit
% 2.24/1.30 % (3437233)Termination phase: Saturation
% 2.24/1.30 % (3437233)Time elapsed: 0.057 s
% 2.24/1.30 % (3437233)Peak memory usage: 89 MB
% 2.24/1.30 % (3437233)Instructions burned: 130 (million)
% 2.24/1.30 % (3437232)Instruction limit reached!
% 2.24/1.30 % (3437232)------------------------------
% 2.24/1.30 % (3437232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.30 % (3437232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.30 % (3437232)CaDiCaL version: 2.1.3
% 2.24/1.30 % (3437232)Termination reason: Instruction limit
% 2.24/1.30 % (3437232)Termination phase: Saturation
% 2.24/1.30 % (3437232)Time elapsed: 0.071 s
% 2.24/1.30 % (3437232)Peak memory usage: 90 MB
% 2.24/1.30 % (3437232)Instructions burned: 139 (million)
% 2.24/1.30 % (3437235)lrs+10_1_sil=8000:sp=occurrence:random_seed=252597229:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.24/1.30 % (3437235)First to succeed.
% 2.24/1.30 % (3437235)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3437222"
% 2.24/1.30 % (3437242)lrs+10_1_sil=32000:urr=on:br=off:random_seed=702989817:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.24/1.30 % (3437244)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2864927857:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.24/1.30 % (3437235)Refutation found. Thanks to Tanya!
% 2.24/1.30 % SZS status Theorem for theBenchmark
% 2.24/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 2.24/1.39 % (3437235)------------------------------
% 2.24/1.39 % (3437235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/1.39 % (3437235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/1.39 % (3437235)CaDiCaL version: 2.1.3
% 2.24/1.39 % (3437235)Termination reason: Refutation
% 2.24/1.39 % (3437235)Time elapsed: 0.036 s
% 2.24/1.39 % (3437235)Peak memory usage: 90 MB
% 2.24/1.39 % (3437235)Instructions burned: 115 (million)
% 2.24/1.39 % (3437235)------------------------------
% 2.24/1.39 % (3437235)------------------------------
% 2.24/1.39 % (3437222)Success in time 0.462 s
% 2.24/1.39 % Vampire exiting
%------------------------------------------------------------------------------