%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 14:31:42 EDT 2022
% Result : Theorem 0.51s 0.72s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 17 unt; 0 nHn; 19 RR)
% Number of literals : 21 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(zero_zero_int,pls),
file('NUM925+2.p',unknown),
[] ).
cnf(20,axiom,
equal(number_number_of_int(u),u),
file('NUM925+2.p',unknown),
[] ).
cnf(38,axiom,
equal(number_number_of_int(bit1(pls)),one_one_int),
file('NUM925+2.p',unknown),
[] ).
cnf(49,axiom,
equal(bit1(pls),succ(pls)),
file('NUM925+2.p',unknown),
[] ).
cnf(117,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('NUM925+2.p',unknown),
[] ).
cnf(235,axiom,
equal(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(u)),number_number_of_int(succ(u))),
file('NUM925+2.p',unknown),
[] ).
cnf(259,axiom,
( ~ equal(hAPP_nat_int(power_power_int(u),v),zero_zero_int)
| equal(u,zero_zero_int) ),
file('NUM925+2.p',unknown),
[] ).
cnf(282,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('NUM925+2.p',unknown),
[] ).
cnf(419,axiom,
equal(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('NUM925+2.p',unknown),
[] ).
cnf(978,plain,
equal(succ(pls),one_one_int),
inference(rew,[status(thm),theory(equality)],[20,38,49]),
[iquote('0:Rew:20.0,38.0,49.0,38.0')] ).
cnf(979,plain,
equal(bit1(pls),one_one_int),
inference(rew,[status(thm),theory(equality)],[978,49]),
[iquote('0:Rew:978.0,49.0')] ).
cnf(1013,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(rew,[status(thm),theory(equality)],[3,117]),
[iquote('0:Rew:3.0,117.0')] ).
cnf(1019,plain,
equal(hAPP_int_int(plus_plus_int(one_one_int),u),succ(u)),
inference(rew,[status(thm),theory(equality)],[20,235]),
[iquote('0:Rew:20.0,235.0,20.0,235.0')] ).
cnf(1050,plain,
( ~ equal(hAPP_nat_int(power_power_int(u),v),pls)
| equal(u,pls) ),
inference(rew,[status(thm),theory(equality)],[3,259]),
[iquote('0:Rew:3.0,259.1,3.0,259.0')] ).
cnf(1067,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),succ(hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rew,[status(thm),theory(equality)],[3,282,1019]),
[iquote('0:Rew:3.0,282.0,1019.0,282.0')] ).
cnf(1122,plain,
equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),pls),
inference(rew,[status(thm),theory(equality)],[1019,419,979,3]),
[iquote('0:Rew:1019.0,419.0,979.0,419.0,3.0,419.0')] ).
cnf(1283,plain,
equal(succ(hAPP_nat_int(semiri1621563631at_int,n)),pls),
inference(res,[status(thm),theory(equality)],[1122,1050]),
[iquote('0:Res:1122.0,1050.0')] ).
cnf(1339,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(rew,[status(thm),theory(equality)],[1283,1067]),
[iquote('0:Rew:1283.0,1067.0')] ).
cnf(1341,plain,
$false,
inference(mrr,[status(thm)],[1339,1013]),
[iquote('0:MRR:1339.0,1013.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 19:16:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.51/0.72
% 0.51/0.72 SPASS V 3.9
% 0.51/0.72 SPASS beiseite: Proof found.
% 0.51/0.72 % SZS status Theorem
% 0.51/0.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.72 SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 576 clauses.
% 0.51/0.72 SPASS allocated 101171 KBytes.
% 0.51/0.72 SPASS spent 0:00:00.36 on the problem.
% 0.51/0.72 0:00:00.05 for the input.
% 0.51/0.72 0:00:00.14 for the FLOTTER CNF translation.
% 0.51/0.72 0:00:00.00 for inferences.
% 0.51/0.72 0:00:00.00 for the backtracking.
% 0.51/0.72 0:00:00.12 for the reduction.
% 0.51/0.72
% 0.51/0.72
% 0.51/0.72 Here is a proof with depth 1, length 19 :
% 0.51/0.72 % SZS output start Refutation
% See solution above
% 0.51/0.72 Formulae used in the proof : fact_98_Pls__def fact_176_number__of__is__id fact_145_semiring__numeral__1__eq__1 fact_567_succ__Pls fact_79_bin__less__0__simps_I1_J fact_583_number__of__succ fact_285_power__eq__0__iff fact_0_n1pos conj_0
% 0.51/0.72
%------------------------------------------------------------------------------