TSTP Solution File: NUM924+6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 14:31:40 EDT 2022
% Result : Theorem 0.53s 0.72s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(90,axiom,
equal(zero_zero(int),pls),
file('NUM924+6.p',unknown),
[] ).
cnf(99,axiom,
equal(ti(int,min),min),
file('NUM924+6.p',unknown),
[] ).
cnf(101,axiom,
equal(ti(int,m),m),
file('NUM924+6.p',unknown),
[] ).
cnf(124,axiom,
equal(times_times(int,pls,u),pls),
file('NUM924+6.p',unknown),
[] ).
cnf(140,axiom,
equal(ti(int,bit0(u)),bit0(u)),
file('NUM924+6.p',unknown),
[] ).
cnf(142,axiom,
equal(ti(int,bit1(u)),bit1(u)),
file('NUM924+6.p',unknown),
[] ).
cnf(145,axiom,
equal(ti(int,u),number_number_of(int,u)),
file('NUM924+6.p',unknown),
[] ).
cnf(148,axiom,
equal(number_number_of(int,bit1(pls)),one_one(int)),
file('NUM924+6.p',unknown),
[] ).
cnf(155,axiom,
equal(plus_plus(int,pls,u),ti(int,u)),
file('NUM924+6.p',unknown),
[] ).
cnf(170,axiom,
equal(times_times(int,u,v),times_times(int,v,u)),
file('NUM924+6.p',unknown),
[] ).
cnf(172,axiom,
equal(times_times(int,u,one_one(int)),ti(int,u)),
file('NUM924+6.p',unknown),
[] ).
cnf(174,axiom,
equal(plus_plus(int,u,v),plus_plus(int,v,u)),
file('NUM924+6.p',unknown),
[] ).
cnf(273,axiom,
equal(times_times(int,bit0(u),v),bit0(times_times(int,u,v))),
file('NUM924+6.p',unknown),
[] ).
cnf(322,axiom,
equal(plus_plus(int,bit0(u),bit1(v)),bit1(plus_plus(int,u,v))),
file('NUM924+6.p',unknown),
[] ).
cnf(500,axiom,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
file('NUM924+6.p',unknown),
[] ).
cnf(760,axiom,
equal(minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
file('NUM924+6.p',unknown),
[] ).
cnf(787,axiom,
equal(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),skc4),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
file('NUM924+6.p',unknown),
[] ).
cnf(788,axiom,
equal(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))),
file('NUM924+6.p',unknown),
[] ).
cnf(822,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('NUM924+6.p',unknown),
[] ).
cnf(861,plain,
equal(number_number_of(int,min),min),
inference(rew,[status(thm),theory(equality)],[145,99]),
[iquote('0:Rew:145.0,99.0')] ).
cnf(863,plain,
equal(number_number_of(int,m),m),
inference(rew,[status(thm),theory(equality)],[145,101]),
[iquote('0:Rew:145.0,101.0')] ).
cnf(869,plain,
equal(number_number_of(int,bit1(u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[145,142]),
[iquote('0:Rew:145.0,142.0')] ).
cnf(870,plain,
equal(one_one(int),bit1(pls)),
inference(rew,[status(thm),theory(equality)],[869,148]),
[iquote('0:Rew:869.0,148.0')] ).
cnf(878,plain,
equal(number_number_of(int,bit0(u)),bit0(u)),
inference(rew,[status(thm),theory(equality)],[145,140]),
[iquote('0:Rew:145.0,140.0')] ).
cnf(886,plain,
equal(plus_plus(int,pls,u),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[145,155]),
[iquote('0:Rew:145.0,155.0')] ).
cnf(893,plain,
equal(times_times(int,u,bit1(pls)),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[870,172,145]),
[iquote('0:Rew:870.0,172.0,145.0,172.0')] ).
cnf(985,plain,
~ ord_less(int,plus_plus(int,bit1(pls),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(rew,[status(thm),theory(equality)],[174,500,870,90]),
[iquote('0:Rew:174.0,500.0,870.0,500.0,90.0,500.0')] ).
cnf(1035,plain,
equal(plus_plus(int,bit1(pls),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),min)),
inference(rew,[status(thm),theory(equality)],[861,760,174,870]),
[iquote('0:Rew:861.0,760.0,174.0,760.0,870.0,760.0')] ).
cnf(1036,plain,
~ ord_less(int,minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),min),pls),
inference(rew,[status(thm),theory(equality)],[1035,985]),
[iquote('0:Rew:1035.0,985.0')] ).
cnf(1057,plain,
equal(minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),min),times_times(int,skc4,bit1(bit0(m)))),
inference(rew,[status(thm),theory(equality)],[170,787,878,886,174,322,863,893,273,1035,870]),
[iquote('0:Rew:170.0,787.0,878.0,787.0,886.0,787.0,174.0,787.0,322.0,787.0,863.0,787.0,893.0,787.0,170.0,787.0,273.0,787.0,273.0,787.0,878.0,787.0,1035.0,787.0,174.0,787.0,870.0,787.0')] ).
cnf(1058,plain,
equal(plus_plus(int,bit1(pls),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),times_times(int,skc4,bit1(bit0(m)))),
inference(rew,[status(thm),theory(equality)],[1057,1035]),
[iquote('0:Rew:1057.0,1035.0')] ).
cnf(1059,plain,
~ ord_less(int,times_times(int,skc4,bit1(bit0(m))),pls),
inference(rew,[status(thm),theory(equality)],[1057,1036]),
[iquote('0:Rew:1057.0,1036.0')] ).
cnf(1062,plain,
equal(times_times(int,skc4,bit1(bit0(m))),times_times(int,t,bit1(bit0(m)))),
inference(rew,[status(thm),theory(equality)],[170,788,878,886,174,322,863,893,273,1058,870]),
[iquote('0:Rew:170.0,788.0,878.0,788.0,886.0,788.0,174.0,788.0,322.0,788.0,863.0,788.0,893.0,788.0,170.0,788.0,273.0,788.0,273.0,788.0,878.0,788.0,1058.0,788.0,174.0,788.0,870.0,788.0')] ).
cnf(1064,plain,
~ ord_less(int,times_times(int,t,bit1(bit0(m))),pls),
inference(rew,[status(thm),theory(equality)],[1062,1059]),
[iquote('0:Rew:1062.0,1059.0')] ).
cnf(1077,plain,
ord_less(int,times_times(int,t,bit1(bit0(m))),pls),
inference(rew,[status(thm),theory(equality)],[170,822,124,878,886,174,322,863,893,273,870,90]),
[iquote('0:Rew:170.0,822.0,124.0,822.0,170.0,822.0,878.0,822.0,886.0,822.0,174.0,822.0,322.0,822.0,863.0,822.0,893.0,822.0,170.0,822.0,273.0,822.0,273.0,822.0,878.0,822.0,870.0,822.0,90.0,822.0')] ).
cnf(1078,plain,
$false,
inference(mrr,[status(thm)],[1077,1064]),
[iquote('0:MRR:1077.0,1064.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM924+6 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 21:31:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.72
% 0.53/0.72 SPASS V 3.9
% 0.53/0.72 SPASS beiseite: Proof found.
% 0.53/0.72 % SZS status Theorem
% 0.53/0.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.72 SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 752 clauses.
% 0.53/0.72 SPASS allocated 100649 KBytes.
% 0.53/0.72 SPASS spent 0:00:00.37 on the problem.
% 0.53/0.72 0:00:00.05 for the input.
% 0.53/0.72 0:00:00.14 for the FLOTTER CNF translation.
% 0.53/0.72 0:00:00.00 for inferences.
% 0.53/0.72 0:00:00.00 for the backtracking.
% 0.53/0.72 0:00:00.12 for the reduction.
% 0.53/0.72
% 0.53/0.72
% 0.53/0.72 Here is a proof with depth 0, length 36 :
% 0.53/0.72 % SZS output start Refutation
% See solution above
% 0.53/0.72 Formulae used in the proof : fact_120_Pls__def tsy_c_Int_OMin_res tsy_v_m_res fact_62_mult__Pls tsy_c_Int_OBit0_res tsy_c_Int_OBit1_res fact_22_number__of__is__id fact_109_one__is__num__one fact_128_add__Pls fact_23_zmult__commute fact_65_zmult__1__right fact_96_zadd__commute fact_63_mult__Bit0 fact_160_add__Bit0__Bit1 conj_0 fact_324__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096 fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_ 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
% 0.53/0.72
%------------------------------------------------------------------------------