TSTP Solution File: NUM924+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM924+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:31:38 EDT 2022
% Result : Theorem 1.07s 1.33s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 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 : 24 ( 24 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
equal(zero_zero_int,pls),
file('NUM924+3.p',unknown),
[] ).
cnf(36,axiom,
equal(number_number_of_int(pls),zero_zero_int),
file('NUM924+3.p',unknown),
[] ).
cnf(68,axiom,
equal(number_number_of_int(bit1(pls)),one_one_int),
file('NUM924+3.p',unknown),
[] ).
cnf(126,axiom,
equal(hAPP_int_int(times_times_int(zero_zero_int),u),zero_zero_int),
file('NUM924+3.p',unknown),
[] ).
cnf(174,axiom,
equal(hAPP_int_int(plus_plus_int(u),u),bit0(u)),
file('NUM924+3.p',unknown),
[] ).
cnf(241,axiom,
equal(hAPP_int_int(times_times_int(u),v),hAPP_int_int(times_times_int(v),u)),
file('NUM924+3.p',unknown),
[] ).
cnf(244,axiom,
equal(hAPP_int_int(plus_plus_int(u),v),hAPP_int_int(plus_plus_int(v),u)),
file('NUM924+3.p',unknown),
[] ).
cnf(303,axiom,
equal(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),u)),u),bit1(u)),
file('NUM924+3.p',unknown),
[] ).
cnf(367,axiom,
equal(hAPP_int_int(times_times_int(bit0(u)),v),bit0(hAPP_int_int(times_times_int(u),v))),
file('NUM924+3.p',unknown),
[] ).
cnf(398,axiom,
equal(hAPP_int_bool(cOMBC_int_int_bool(u,v),w),hAPP_int_bool(hAPP_i1948725293t_bool(u,w),v)),
file('NUM924+3.p',unknown),
[] ).
cnf(417,axiom,
equal(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(u)),number_number_of_int(bit0(u))),
file('NUM924+3.p',unknown),
[] ).
cnf(440,axiom,
equal(hAPP_int_int(times_times_int(u),u),hAPP_nat_int(power_power_int(u),number_number_of_nat(bit0(bit1(pls))))),
file('NUM924+3.p',unknown),
[] ).
cnf(445,axiom,
equal(hAPP_int_int(plus_plus_int(u),u),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),u)),
file('NUM924+3.p',unknown),
[] ).
cnf(481,axiom,
equal(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(u))),number_number_of_int(u)),number_number_of_int(bit1(u))),
file('NUM924+3.p',unknown),
[] ).
cnf(756,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
file('NUM924+3.p',unknown),
[] ).
cnf(1058,axiom,
equal(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
file('NUM924+3.p',unknown),
[] ).
cnf(1359,axiom,
equal(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),
file('NUM924+3.p',unknown),
[] ).
cnf(1583,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
file('NUM924+3.p',unknown),
[] ).
cnf(1702,plain,
equal(number_number_of_int(pls),pls),
inference(rew,[status(thm),theory(equality)],[15,36]),
[iquote('0:Rew:15.0,36.0')] ).
cnf(1712,plain,
equal(hAPP_int_int(times_times_int(pls),u),pls),
inference(rew,[status(thm),theory(equality)],[15,126]),
[iquote('0:Rew:15.0,126.0')] ).
cnf(1764,plain,
equal(hAPP_int_int(plus_plus_int(u),hAPP_int_int(plus_plus_int(one_one_int),u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[244,303]),
[iquote('0:Rew:244.0,303.0')] ).
cnf(1784,plain,
equal(bit0(hAPP_int_int(times_times_int(one_one_int),u)),bit0(u)),
inference(rew,[status(thm),theory(equality)],[174,445,367]),
[iquote('0:Rew:174.0,445.0,367.0,445.0,174.0,445.0')] ).
cnf(1794,plain,
equal(number_number_of_int(bit0(u)),bit0(number_number_of_int(u))),
inference(rew,[status(thm),theory(equality)],[1784,417,367,174]),
[iquote('0:Rew:1784.0,417.0,367.0,417.0,174.0,417.0')] ).
cnf(1819,plain,
equal(number_number_of_int(bit1(u)),bit1(number_number_of_int(u))),
inference(rew,[status(thm),theory(equality)],[1764,481,244]),
[iquote('0:Rew:1764.0,481.0,244.0,481.0')] ).
cnf(1821,plain,
equal(bit1(number_number_of_int(pls)),one_one_int),
inference(rew,[status(thm),theory(equality)],[1819,68]),
[iquote('0:Rew:1819.0,68.0')] ).
cnf(1822,plain,
equal(bit1(pls),one_one_int),
inference(rew,[status(thm),theory(equality)],[1702,1821]),
[iquote('0:Rew:1702.0,1821.0')] ).
cnf(1831,plain,
equal(hAPP_int_int(times_times_int(u),u),hAPP_nat_int(power_power_int(u),number_number_of_nat(bit0(one_one_int)))),
inference(rew,[status(thm),theory(equality)],[1822,440]),
[iquote('0:Rew:1822.0,440.0')] ).
cnf(1992,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)))),
inference(rew,[status(thm),theory(equality)],[398,756,244,1831,1822,15]),
[iquote('0:Rew:398.0,756.0,244.0,756.0,1831.0,756.0,1822.0,756.0,15.0,756.0')] ).
cnf(2027,plain,
equal(hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),bit0(bit0(hAPP_int_int(times_times_int(m),number_number_of_int(one_one_int)))))),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
inference(rew,[status(thm),theory(equality)],[241,1058,244,367,1794,1822]),
[iquote('0:Rew:241.0,1058.0,244.0,1058.0,241.0,1058.0,367.0,1058.0,367.0,1058.0,1794.0,1058.0,1794.0,1058.0,1822.0,1058.0')] ).
cnf(2150,plain,
equal(hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s)),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),
inference(rew,[status(thm),theory(equality)],[2027,1359,241,244,367,1794,1831,1822]),
[iquote('0:Rew:2027.0,1359.0,241.0,1359.0,244.0,1359.0,241.0,1359.0,367.0,1359.0,367.0,1359.0,1794.0,1359.0,1794.0,1359.0,244.0,1359.0,1831.0,1359.0,1822.0,1359.0')] ).
cnf(2152,plain,
~ hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(rew,[status(thm),theory(equality)],[2150,1992]),
[iquote('0:Rew:2150.0,1992.0')] ).
cnf(2256,plain,
hBOOL(hAPP_int_bool(cOMBC_int_int_bool(ord_less_int,pls),twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int)))),
inference(rew,[status(thm),theory(equality)],[398,1583,2027,241,1712,244,367,1794,1822,15]),
[iquote('0:Rew:398.0,1583.0,2027.0,1583.0,241.0,1583.0,1712.0,1583.0,241.0,1583.0,244.0,1583.0,241.0,1583.0,367.0,1583.0,367.0,1583.0,1794.0,1583.0,1794.0,1583.0,1822.0,1583.0,15.0,1583.0')] ).
cnf(2257,plain,
$false,
inference(mrr,[status(thm)],[2256,2152]),
[iquote('0:MRR:2256.0,2152.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM924+3 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.10/0.32 % Computer : n023.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Tue Jul 5 22:46:42 EDT 2022
% 0.10/0.32 % CPUTime :
% 1.07/1.33
% 1.07/1.33 SPASS V 3.9
% 1.07/1.33 SPASS beiseite: Proof found.
% 1.07/1.33 % SZS status Theorem
% 1.07/1.33 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.33 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 1151 clauses.
% 1.07/1.33 SPASS allocated 106606 KBytes.
% 1.07/1.33 SPASS spent 0:00:00.97 on the problem.
% 1.07/1.33 0:00:00.07 for the input.
% 1.07/1.33 0:00:00.45 for the FLOTTER CNF translation.
% 1.07/1.33 0:00:00.00 for inferences.
% 1.07/1.33 0:00:00.00 for the backtracking.
% 1.07/1.33 0:00:00.36 for the reduction.
% 1.07/1.33
% 1.07/1.33
% 1.07/1.33 Here is a proof with depth 0, length 33 :
% 1.07/1.33 % SZS output start Refutation
% See solution above
% 1.07/1.33 Formulae used in the proof : fact_172_Pls__def fact_212_semiring__norm_I112_J fact_255_semiring__norm_I110_J fact_509_mult__zero__left fact_182_Bit0__def fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_236_Bit1__def fact_89_mult__Bit0 help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U fact_187_double__number__of__Bit0 fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J fact_248_number__of__Bit1 conj_0 fact_1068__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
% 1.07/1.33
%------------------------------------------------------------------------------