%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:26:10 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 41 unt; 0 def)
% Number of atoms : 131 ( 62 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 132 ( 60 ~; 52 |; 14 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
fof(f80,axiom,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(f93,axiom,
! [X0,X1] :
( 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_60_zless__add1__eq) ).
fof(f94,axiom,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
fof(f106,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(f109,axiom,
! [X0] : plus_plus(int,pls,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__Pls) ).
fof(f111,axiom,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
fof(f117,axiom,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
fof(f119,axiom,
! [X0] :
( ( power(X0)
& mult_zero(X0)
& no_zero_divisors(X0)
& zero_neq_one(X0) )
=> ! [X1,X2] :
( power_power(X0,X1,number_number_of(nat,X2)) = zero_zero(X0)
<=> ( ti(X0,X1) = zero_zero(X0)
& number_number_of(nat,X2) != zero_zero(nat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_power__eq__0__iff__number__of) ).
fof(f125,axiom,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
fof(f133,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
fof(f136,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
fof(f139,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
fof(f141,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(f142,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
fof(f153,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f154,negated_conjecture,
~ ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f153]) ).
fof(f155,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f154]) ).
fof(f219,plain,
! [X0] :
( ! [X1] : plus_plus(X0,number_number_of(X0,pls),X1) = ti(X0,X1)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f117]) ).
fof(f221,plain,
! [X0] :
( ! [X1,X2] :
( power_power(X0,X1,number_number_of(nat,X2)) = zero_zero(X0)
<=> ( ti(X0,X1) = zero_zero(X0)
& number_number_of(nat,X2) != zero_zero(nat) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f222,plain,
! [X0] :
( ! [X1,X2] :
( power_power(X0,X1,number_number_of(nat,X2)) = zero_zero(X0)
<=> ( ti(X0,X1) = zero_zero(X0)
& number_number_of(nat,X2) != zero_zero(nat) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(flattening,[],[f221]) ).
fof(f259,plain,
! [X0,X1] :
( ( 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,[],[f93]) ).
fof(f260,plain,
! [X0,X1] :
( ( 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,[],[f259]) ).
fof(f267,plain,
! [X0] :
( ! [X1,X2] :
( ( power_power(X0,X1,number_number_of(nat,X2)) = zero_zero(X0)
| zero_zero(X0) != ti(X0,X1)
| zero_zero(nat) = number_number_of(nat,X2) )
& ( ( ti(X0,X1) = zero_zero(X0)
& number_number_of(nat,X2) != zero_zero(nat) )
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2)) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(nnf_transformation,[],[f222]) ).
fof(f268,plain,
! [X0] :
( ! [X1,X2] :
( ( power_power(X0,X1,number_number_of(nat,X2)) = zero_zero(X0)
| zero_zero(X0) != ti(X0,X1)
| zero_zero(nat) = number_number_of(nat,X2) )
& ( ( ti(X0,X1) = zero_zero(X0)
& number_number_of(nat,X2) != zero_zero(nat) )
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2)) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(flattening,[],[f267]) ).
fof(f333,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f52]) ).
fof(f373,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f80]) ).
fof(f397,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| X0 != X1 ),
inference(cnf_transformation,[],[f260]) ).
fof(f399,plain,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f94]) ).
fof(f417,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f106]) ).
fof(f420,plain,
! [X0] : plus_plus(int,pls,X0) = X0,
inference(cnf_transformation,[],[f109]) ).
fof(f422,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(cnf_transformation,[],[f111]) ).
fof(f428,plain,
! [X0,X1] :
( ~ number_ring(X0)
| ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1) ),
inference(cnf_transformation,[],[f219]) ).
fof(f431,plain,
! [X2,X0,X1] :
( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2))
| zero_zero(X0) = ti(X0,X1)
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f438,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(cnf_transformation,[],[f125]) ).
fof(f449,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f133]) ).
fof(f452,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f136]) ).
fof(f455,plain,
mult_zero(int),
inference(cnf_transformation,[],[f139]) ).
fof(f457,plain,
number_ring(int),
inference(cnf_transformation,[],[f141]) ).
fof(f458,plain,
power(int),
inference(cnf_transformation,[],[f142]) ).
fof(f469,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f155]) ).
fof(f540,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
inference(definition_unfolding,[],[f469,f422,f438]) ).
fof(f546,plain,
! [X1] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f397]) ).
fof(f551,plain,
pls = number_number_of(int,pls),
inference(forward_demodulation,[],[f333,f417]) ).
fof(f560,plain,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls),
inference(forward_demodulation,[],[f399,f417]) ).
fof(f579,plain,
! [X0] : ord_less(int,X0,plus_plus(int,one_one(int),X0)),
inference(superposition,[],[f546,f373]) ).
fof(f864,plain,
! [X0] : ti(int,X0) = plus_plus(int,number_number_of(int,pls),X0),
inference(resolution,[],[f428,f457]) ).
fof(f865,plain,
! [X0] : ti(int,X0) = plus_plus(int,pls,X0),
inference(forward_demodulation,[],[f864,f551]) ).
fof(f866,plain,
! [X0] : ti(int,X0) = X0,
inference(forward_demodulation,[],[f865,f420]) ).
fof(f2815,plain,
( zero_zero(int) != zero_zero(int)
| zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ power(int)
| ~ mult_zero(int)
| ~ no_zero_divisors(int)
| ~ zero_neq_one(int) ),
inference(superposition,[],[f431,f540]) ).
fof(f2819,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ power(int)
| ~ mult_zero(int)
| ~ no_zero_divisors(int)
| ~ zero_neq_one(int) ),
inference(trivial_inequality_removal,[],[f2815]) ).
fof(f2823,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ mult_zero(int)
| ~ no_zero_divisors(int)
| ~ zero_neq_one(int) ),
inference(forward_subsumption_resolution,[],[f2819,f458]) ).
fof(f2827,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ no_zero_divisors(int)
| ~ zero_neq_one(int) ),
inference(forward_subsumption_resolution,[],[f2823,f455]) ).
fof(f2831,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ zero_neq_one(int) ),
inference(forward_subsumption_resolution,[],[f2827,f449]) ).
fof(f2835,plain,
zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(forward_subsumption_resolution,[],[f2831,f452]) ).
fof(f2839,plain,
zero_zero(int) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
inference(forward_demodulation,[],[f2835,f866]) ).
fof(f2843,plain,
pls = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
inference(forward_demodulation,[],[f2839,f417]) ).
fof(f2849,plain,
ord_less(int,semiring_1_of_nat(int,n),pls),
inference(superposition,[],[f579,f2843]) ).
fof(f2888,plain,
$false,
inference(forward_subsumption_resolution,[],[f2849,f560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:43:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.48 % (1630953)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (1630961)dis+10_1_sil=32000:sp=arity:random_seed=867205460:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (1630959)% WARNING: option uhcvi not known.
% 0.15/0.48 % (1630958)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1721386652_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (1630959)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4003913245:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (1630960)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1466620416:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (1630962)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2691207796:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (1630964)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4239924220:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % (1630963)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=484776212:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (1630961) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1630953-1630961"...
% 0.15/0.48 % (1630961)...printing done.
% 0.15/0.48 % (1630961)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (1630961)------------------------------
% 0.15/0.48 % (1630961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (1630961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (1630961)CaDiCaL version: 2.1.3
% 0.15/0.48 % (1630961)Termination reason: Refutation
% 0.15/0.48 % (1630961)Time elapsed: 0.034 s
% 0.15/0.48 % (1630961)Peak memory usage: 13 MB
% 0.15/0.48 % (1630961)Instructions burned: 103 (million)
% 0.15/0.48 % (1630953)Success in time 0.064 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------