TSTP Solution File: NUM924+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM924+4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:31:39 EDT 2022
% Result : Theorem 49.79s 49.97s
% Output : Refutation 49.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 21 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(32,axiom,
equal(zero_zero_int,pls),
file('NUM924+4.p',unknown),
[] ).
cnf(260,axiom,
equal(hAPP_nat_nat(suc,zero_zero_nat),one_one_nat),
file('NUM924+4.p',unknown),
[] ).
cnf(599,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,zero_zero_int),u),zero_zero_int),
file('NUM924+4.p',unknown),
[] ).
cnf(1464,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,u),v),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,v),u)),
file('NUM924+4.p',unknown),
[] ).
cnf(1471,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,u),v),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,v),u)),
file('NUM924+4.p',unknown),
[] ).
cnf(1957,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('NUM924+4.p',unknown),
[] ).
cnf(3176,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,u),u),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,u),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),
file('NUM924+4.p',unknown),
[] ).
cnf(4662,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),zero_zero_int)),
file('NUM924+4.p',unknown),
[] ).
cnf(6286,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int))),
file('NUM924+4.p',unknown),
[] ).
cnf(6948,axiom,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)),
file('NUM924+4.p',unknown),
[] ).
cnf(7263,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
file('NUM924+4.p',unknown),
[] ).
cnf(7606,plain,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),u),pls),
inference(rew,[status(thm),theory(equality)],[32,599]),
[iquote('0:Rew:32.0,599.0')] ).
cnf(7956,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)],[260,1957]),
[iquote('0:Rew:260.0,1957.0')] ).
cnf(8447,plain,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,u),u),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,u),hAPP_nat_nat(suc,one_one_nat))),
inference(rew,[status(thm),theory(equality)],[7956,3176]),
[iquote('0:Rew:7956.0,3176.0')] ).
cnf(9028,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s))),pls)),
inference(rew,[status(thm),theory(equality)],[1471,4662,8447,7956,32]),
[iquote('0:Rew:1471.0,4662.0,8447.0,4662.0,7956.0,4662.0,32.0,4662.0')] ).
cnf(9771,plain,
equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,t),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,m),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))),hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int))),
inference(rew,[status(thm),theory(equality)],[1464,6286,1471]),
[iquote('0:Rew:1464.0,6286.0,1471.0,6286.0,1464.0,6286.0')] ).
cnf(10213,plain,
equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,s),s)),hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int))),
inference(rew,[status(thm),theory(equality)],[9771,6948,1464,1471,8447,7956]),
[iquote('0:Rew:9771.0,6948.0,1464.0,6948.0,1471.0,6948.0,1464.0,6948.0,1471.0,6948.0,8447.0,6948.0,7956.0,6948.0')] ).
cnf(10215,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int))),pls)),
inference(rew,[status(thm),theory(equality)],[10213,9028]),
[iquote('0:Rew:10213.0,9028.0')] ).
cnf(10437,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_P1175774780nt_int(twoSqu1907779896sum2sq,hAPP_i1524277240nt_int(hAPP_i1584592887nt_int(product_Pair_int_int,s),one_one_int))),pls)),
inference(rew,[status(thm),theory(equality)],[9771,7263,1464,7606,1471,32]),
[iquote('0:Rew:9771.0,7263.0,1464.0,7263.0,7606.0,7263.0,1464.0,7263.0,1471.0,7263.0,1464.0,7263.0,32.0,7263.0')] ).
cnf(10438,plain,
$false,
inference(mrr,[status(thm)],[10437,10215]),
[iquote('0:MRR:10437.0,10215.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM924+4 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jul 5 14:36:02 EDT 2022
% 0.11/0.33 % CPUTime :
% 49.79/49.97
% 49.79/49.97 SPASS V 3.9
% 49.79/49.97 SPASS beiseite: Proof found.
% 49.79/49.97 % SZS status Theorem
% 49.79/49.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.79/49.97 SPASS derived 159 clauses, backtracked 0 clauses, performed 0 splits and kept 5672 clauses.
% 49.79/49.97 SPASS allocated 173905 KBytes.
% 49.79/49.97 SPASS spent 0:0:47.42 on the problem.
% 49.79/49.97 0:00:00.16 for the input.
% 49.79/49.97 0:0:21.46 for the FLOTTER CNF translation.
% 49.79/49.97 0:00:00.00 for inferences.
% 49.79/49.97 0:00:00.00 for the backtracking.
% 49.79/49.97 0:0:20.97 for the reduction.
% 49.79/49.97
% 49.79/49.97
% 49.79/49.97 Here is a proof with depth 0, length 20 :
% 49.79/49.97 % SZS output start Refutation
% See solution above
% 49.79/49.97 Formulae used in the proof : fact_256_Pls__def fact_3057_One__nat__def fact_846_mult__zero__left fact_513_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J fact_520_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_3196_semiring__norm_I115_J fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J conj_0 fact_1836__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096 fact_3_t fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096
% 49.79/49.97
%------------------------------------------------------------------------------