%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:26:08 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 21 unt; 0 def)
% Number of atoms : 59 ( 41 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 23 ~; 17 |; 9 &)
% ( 2 <=>; 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
fof(f66,axiom,
! [X0,X1] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
<=> ( ord_less_int(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
fof(f67,axiom,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
fof(f79,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
fof(f84,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
fof(f93,axiom,
! [X0,X1] :
( 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/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
fof(f100,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
fof(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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(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]) ).
fof(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]) ).
fof(f141,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,[],[f66]) ).
fof(f142,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,[],[f141]) ).
fof(f149,plain,
! [X0,X1] :
( ( 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]) ).
fof(f150,plain,
! [X0,X1] :
( ( 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]) ).
fof(f227,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f251,plain,
! [X0,X1] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| X0 != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f253,plain,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
inference(cnf_transformation,[],[f67]) ).
fof(f271,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
fof(f276,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f84]) ).
fof(f286,plain,
! [X0,X1] :
( zero_zero_int = X0
| zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f296,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f100]) ).
fof(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]) ).
fof(f369,plain,
! [X0] : ~ ord_less_int(semiri1621563631at_int(X0),pls),
inference(definition_unfolding,[],[f253,f271]) ).
fof(f395,plain,
! [X0,X1] :
( pls != power_power_int(X0,number_number_of_nat(X1))
| pls = X0 ),
inference(definition_unfolding,[],[f286,f271,f271]) ).
fof(f406,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_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,[],[f306,f271,f276,f296]) ).
fof(f419,plain,
! [X1] : ord_less_int(X1,plus_plus_int(X1,one_one_int)),
inference(equality_resolution,[],[f251]) ).
fof(f444,plain,
! [X0] : ord_less_int(X0,plus_plus_int(one_one_int,X0)),
inference(superposition,[],[f419,f227]) ).
fof(f609,plain,
( pls != pls
| plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls ),
inference(superposition,[],[f395,f406]) ).
fof(f613,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(trivial_inequality_removal,[],[f609]) ).
fof(f619,plain,
ord_less_int(semiri1621563631at_int(n),pls),
inference(superposition,[],[f444,f613]) ).
fof(f620,plain,
$false,
inference(forward_subsumption_resolution,[],[f619,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 21:44:12 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (3235282)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3235287)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1968831212_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3235288)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3235289)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=462742530:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3235288)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1771159832:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3235290)dis+10_1_sil=32000:sp=arity:random_seed=1200771880:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3235291)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2174468604:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3235292)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3717066473:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3235293)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2647508103:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (3235290) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3235282-3235290"...
% 0.16/0.48 % (3235290)...printing done.
% 0.16/0.48 % (3235288) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3235282-3235288"...
% 0.16/0.48 % (3235290)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3235290)------------------------------
% 0.16/0.48 % (3235290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3235290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (3235290)CaDiCaL version: 2.1.3
% 0.16/0.49 % (3235290)Termination reason: Refutation
% 0.16/0.49 % (3235290)Time elapsed: 0.009 s
% 0.16/0.49 % (3235290)Peak memory usage: 12 MB
% 0.16/0.49 % (3235290)Instructions burned: 15 (million)
% 0.16/0.49 % (3235282)Success in time 0.052 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------