TSTP Solution File: NUM925+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:31:44 EDT 2022
% Result : Theorem 105.54s 105.77s
% Output : Refutation 105.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 12 unt; 0 nHn; 16 RR)
% Number of literals : 20 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(46,axiom,
equal(zero_zero_int,pls),
file('NUM925+4.p',unknown),
[] ).
cnf(269,axiom,
equal(hAPP_nat_nat(suc,zero_zero_nat),one_one_nat),
file('NUM925+4.p',unknown),
[] ).
cnf(469,axiom,
~ equal(hAPP_nat_nat(suc,u),zero_zero_nat),
file('NUM925+4.p',unknown),
[] ).
cnf(1006,axiom,
( ~ equal(hAPP_nat_int(semiri1621563631at_int,u),zero_zero_int)
| equal(u,zero_zero_nat) ),
file('NUM925+4.p',unknown),
[] ).
cnf(1548,axiom,
( ~ equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,u),v),zero_zero_nat)
| equal(u,zero_zero_nat) ),
file('NUM925+4.p',unknown),
[] ).
cnf(2043,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,u)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,u))),
file('NUM925+4.p',unknown),
[] ).
cnf(2047,axiom,
equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
file('NUM925+4.p',unknown),
[] ).
cnf(2632,axiom,
equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,u)),v),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,u),v))),
file('NUM925+4.p',unknown),
[] ).
cnf(4081,axiom,
equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int),
file('NUM925+4.p',unknown),
[] ).
cnf(7785,plain,
( ~ equal(hAPP_nat_int(semiri1621563631at_int,u),pls)
| equal(u,zero_zero_nat) ),
inference(rew,[status(thm),theory(equality)],[46,1006]),
[iquote('0:Rew:46.0,1006.0')] ).
cnf(8033,plain,
equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_nat_nat(suc,one_one_nat)),
inference(rew,[status(thm),theory(equality)],[269,2047]),
[iquote('0:Rew:269.0,2047.0')] ).
cnf(8806,plain,
equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),pls),
inference(rew,[status(thm),theory(equality)],[2632,4081,2043,8033,46]),
[iquote('0:Rew:2632.0,4081.0,2043.0,4081.0,8033.0,4081.0,46.0,4081.0')] ).
cnf(10635,plain,
equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)),zero_zero_nat),
inference(res,[status(thm),theory(equality)],[8806,7785]),
[iquote('0:Res:8806.0,7785.0')] ).
cnf(25987,plain,
( ~ equal(zero_zero_nat,zero_zero_nat)
| equal(hAPP_nat_nat(suc,n),zero_zero_nat) ),
inference(spl,[status(thm),theory(equality)],[10635,1548]),
[iquote('0:SpL:10635.0,1548.0')] ).
cnf(25990,plain,
equal(hAPP_nat_nat(suc,n),zero_zero_nat),
inference(obv,[status(thm),theory(equality)],[25987]),
[iquote('0:Obv:25987.0')] ).
cnf(25991,plain,
$false,
inference(mrr,[status(thm)],[25990,469]),
[iquote('0:MRR:25990.0,469.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jul 7 13:13:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 105.54/105.77
% 105.54/105.77 SPASS V 3.9
% 105.54/105.77 SPASS beiseite: Proof found.
% 105.54/105.77 % SZS status Theorem
% 105.54/105.77 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 105.54/105.77 SPASS derived 11944 clauses, backtracked 1637 clauses, performed 10 splits and kept 10767 clauses.
% 105.54/105.77 SPASS allocated 169221 KBytes.
% 105.54/105.77 SPASS spent 0:1:41.53 on the problem.
% 105.54/105.77 0:00:00.15 for the input.
% 105.54/105.77 0:0:20.93 for the FLOTTER CNF translation.
% 105.54/105.77 0:00:01.28 for inferences.
% 105.54/105.77 0:00:00.87 for the backtracking.
% 105.54/105.77 0:1:11.41 for the reduction.
% 105.54/105.77
% 105.54/105.77
% 105.54/105.77 Here is a proof with depth 2, length 16 :
% 105.54/105.77 % SZS output start Refutation
% See solution above
% 105.54/105.77 Formulae used in the proof : fact_151_Pls__def fact_3047_One__nat__def fact_2997_Suc__neq__Zero fact_71_int__eq__0__conv fact_1005_nat__power__eq__0__iff fact_3105_int__Suc fact_3135_semiring__norm_I115_J fact_390_Nat__Transfer_Otransfer__int__nat__functions_I4_J conj_0
% 105.54/105.77
%------------------------------------------------------------------------------