%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:31:41 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 15 ( 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 : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(zero_zero_int,pls),
file('NUM925+1.p',unknown),
[] ).
cnf(11,axiom,
~ ord_less_int(pls,zero_zero_int),
file('NUM925+1.p',unknown),
[] ).
cnf(30,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('NUM925+1.p',unknown),
[] ).
cnf(48,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
file('NUM925+1.p',unknown),
[] ).
cnf(124,axiom,
equal(power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('NUM925+1.p',unknown),
[] ).
cnf(133,axiom,
( ~ equal(power_power_int(u,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int)
| equal(u,zero_zero_int) ),
file('NUM925+1.p',unknown),
[] ).
cnf(158,plain,
~ ord_less_int(pls,pls),
inference(rew,[status(thm),theory(equality)],[4,11]),
[iquote('0:Rew:4.0,11.0')] ).
cnf(166,plain,
ord_less_int(pls,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(rew,[status(thm),theory(equality)],[4,30]),
[iquote('0:Rew:4.0,30.0')] ).
cnf(198,plain,
equal(power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),plus_plus_nat(one_one_nat,one_one_nat)),pls),
inference(rew,[status(thm),theory(equality)],[48,124,4]),
[iquote('0:Rew:48.0,124.0,4.0,124.0')] ).
cnf(201,plain,
( ~ equal(power_power_int(u,plus_plus_nat(one_one_nat,one_one_nat)),pls)
| equal(u,pls) ),
inference(rew,[status(thm),theory(equality)],[4,133,48]),
[iquote('0:Rew:4.0,133.1,48.0,133.0,4.0,133.0')] ).
cnf(211,plain,
equal(plus_plus_int(one_one_int,semiri1621563631at_int(n)),pls),
inference(res,[status(thm),theory(equality)],[198,201]),
[iquote('0:Res:198.0,201.0')] ).
cnf(228,plain,
ord_less_int(pls,pls),
inference(rew,[status(thm),theory(equality)],[211,166]),
[iquote('0:Rew:211.0,166.0')] ).
cnf(230,plain,
$false,
inference(mrr,[status(thm)],[228,158]),
[iquote('0:MRR:228.0,158.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+1 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.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 : Tue Jul 5 06:45:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 111 clauses.
% 0.19/0.47 SPASS allocated 85470 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.01 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 1, length 13 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : fact_78_Pls__def fact_62_bin__less__0__simps_I1_J fact_0_n1pos fact_33_nat__1__add__1 conj_0 fact_7_zero__eq__power2
% 0.19/0.47
%------------------------------------------------------------------------------