TSTP Solution File: NUM924+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 14:31:36 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of clauses : 36 ( 31 unt; 0 nHn; 36 RR)
% Number of literals : 43 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(number_number_of_int(u),u),
file('NUM924+1.p',unknown),
[] ).
cnf(9,axiom,
equal(number_number_of_int(pls),zero_zero_int),
file('NUM924+1.p',unknown),
[] ).
cnf(10,axiom,
equal(times_times_int(pls,u),pls),
file('NUM924+1.p',unknown),
[] ).
cnf(11,axiom,
equal(times_times_int(u,one_one_int),u),
file('NUM924+1.p',unknown),
[] ).
cnf(12,axiom,
equal(times_times_int(one_one_int,u),u),
file('NUM924+1.p',unknown),
[] ).
cnf(16,axiom,
equal(times_times_int(u,v),times_times_int(v,u)),
file('NUM924+1.p',unknown),
[] ).
cnf(20,axiom,
equal(plus_plus_int(u,v),plus_plus_int(v,u)),
file('NUM924+1.p',unknown),
[] ).
cnf(42,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
file('NUM924+1.p',unknown),
[] ).
cnf(69,axiom,
equal(times_times_int(bit0(u),v),bit0(times_times_int(u,v))),
file('NUM924+1.p',unknown),
[] ).
cnf(108,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+1.p',unknown),
[] ).
cnf(112,axiom,
equal(times_times_int(times_times_int(u,v),w),times_times_int(u,times_times_int(v,w))),
file('NUM924+1.p',unknown),
[] ).
cnf(119,axiom,
( ~ equal(u,zero_zero_int)
| equal(power_power_int(u,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int) ),
file('NUM924+1.p',unknown),
[] ).
cnf(125,axiom,
equal(times_times_int(power_power_int(u,v),power_power_int(u,w)),power_power_int(u,plus_plus_nat(v,w))),
file('NUM924+1.p',unknown),
[] ).
cnf(128,axiom,
equal(times_times_int(plus_plus_int(u,v),w),plus_plus_int(times_times_int(u,w),times_times_int(v,w))),
file('NUM924+1.p',unknown),
[] ).
cnf(154,axiom,
equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),skc1)),
file('NUM924+1.p',unknown),
[] ).
cnf(155,axiom,
equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
file('NUM924+1.p',unknown),
[] ).
cnf(156,axiom,
( ~ equal(u,zero_zero_int)
| ~ equal(v,zero_zero_int)
| equal(plus_plus_int(power_power_int(v,number_number_of_nat(bit0(bit1(pls)))),power_power_int(u,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int) ),
file('NUM924+1.p',unknown),
[] ).
cnf(157,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+1.p',unknown),
[] ).
cnf(159,plain,
equal(zero_zero_int,pls),
inference(rew,[status(thm),theory(equality)],[6,9]),
[iquote('0:Rew:6.0,9.0')] ).
cnf(181,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(rew,[status(thm),theory(equality)],[20,108,42,159]),
[iquote('0:Rew:20.0,108.0,42.0,108.0,159.0,108.0')] ).
cnf(183,plain,
( ~ equal(u,pls)
| equal(power_power_int(u,plus_plus_nat(one_one_nat,one_one_nat)),pls) ),
inference(rew,[status(thm),theory(equality)],[42,119,159]),
[iquote('0:Rew:42.0,119.1,159.0,119.1,159.0,119.0')] ).
cnf(191,plain,
~ ord_less_int(plus_plus_int(one_one_int,times_times_int(power_power_int(s,one_one_nat),power_power_int(s,one_one_nat))),pls),
inference(rew,[status(thm),theory(equality)],[125,181]),
[iquote('0:Rew:125.0,181.0')] ).
cnf(222,plain,
equal(plus_plus_int(one_one_int,times_times_int(power_power_int(s,one_one_nat),power_power_int(s,one_one_nat))),plus_plus_int(skc1,bit0(bit0(times_times_int(m,times_times_int(skc1,bit1(pls))))))),
inference(rew,[status(thm),theory(equality)],[20,154,125,42,12,16,112,69,128,6]),
[iquote('0:Rew:20.0,154.0,125.0,154.0,42.0,154.0,12.0,154.0,16.0,154.0,112.0,154.0,69.0,154.0,69.0,154.0,128.0,154.0,20.0,154.0,16.0,154.0,69.0,154.0,69.0,154.0,6.0,154.0')] ).
cnf(223,plain,
~ ord_less_int(plus_plus_int(skc1,bit0(bit0(times_times_int(m,times_times_int(skc1,bit1(pls)))))),pls),
inference(rew,[status(thm),theory(equality)],[222,191]),
[iquote('0:Rew:222.0,191.0')] ).
cnf(225,plain,
equal(plus_plus_int(skc1,bit0(bit0(times_times_int(m,times_times_int(skc1,bit1(pls)))))),plus_plus_int(t,bit0(bit0(times_times_int(m,times_times_int(t,bit1(pls))))))),
inference(rew,[status(thm),theory(equality)],[222,155,20,125,42,11,16,112,69,128,6]),
[iquote('0:Rew:222.0,155.0,20.0,155.0,125.0,155.0,42.0,155.0,11.0,155.0,16.0,155.0,16.0,155.0,112.0,155.0,69.0,155.0,69.0,155.0,128.0,155.0,20.0,155.0,16.0,155.0,69.0,155.0,69.0,155.0,6.0,155.0')] ).
cnf(227,plain,
~ ord_less_int(plus_plus_int(t,bit0(bit0(times_times_int(m,times_times_int(t,bit1(pls)))))),pls),
inference(rew,[status(thm),theory(equality)],[225,223]),
[iquote('0:Rew:225.0,223.0')] ).
cnf(231,plain,
( ~ equal(u,pls)
| ~ equal(v,pls)
| equal(plus_plus_int(pls,pls),pls) ),
inference(rew,[status(thm),theory(equality)],[183,156,20,42,159]),
[iquote('0:Rew:183.1,156.2,20.0,156.2,183.1,156.2,42.0,156.2,159.0,156.2,159.0,156.1,159.0,156.0')] ).
cnf(232,plain,
( ~ equal(u,pls)
| equal(plus_plus_int(pls,pls),pls) ),
inference(con,[status(thm)],[231]),
[iquote('0:Con:231.1')] ).
cnf(233,plain,
ord_less_int(plus_plus_int(t,bit0(bit0(times_times_int(m,times_times_int(t,bit1(pls)))))),plus_plus_int(pls,bit0(bit0(pls)))),
inference(rew,[status(thm),theory(equality)],[11,157,16,112,69,128,12,10,20,6,159]),
[iquote('0:Rew:11.0,157.0,16.0,157.0,16.0,157.0,112.0,157.0,69.0,157.0,69.0,157.0,128.0,157.0,12.0,157.0,10.0,157.0,16.0,157.0,10.0,157.0,16.0,157.0,112.0,157.0,69.0,157.0,69.0,157.0,128.0,157.0,20.0,157.0,16.0,157.0,69.0,157.0,69.0,157.0,6.0,157.0,159.0,157.0')] ).
cnf(270,plain,
equal(times_times_int(u,pls),pls),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.0,10.0')] ).
cnf(317,plain,
equal(plus_plus_int(pls,pls),pls),
inference(eqr,[status(thm),theory(equality)],[232]),
[iquote('0:EqR:232.0')] ).
cnf(331,plain,
equal(bit0(times_times_int(u,pls)),pls),
inference(spr,[status(thm),theory(equality)],[69,270]),
[iquote('0:SpR:69.0,270.0')] ).
cnf(333,plain,
equal(bit0(pls),pls),
inference(rew,[status(thm),theory(equality)],[270,331]),
[iquote('0:Rew:270.0,331.0')] ).
cnf(345,plain,
ord_less_int(plus_plus_int(t,bit0(bit0(times_times_int(m,times_times_int(t,bit1(pls)))))),plus_plus_int(pls,pls)),
inference(rew,[status(thm),theory(equality)],[333,233]),
[iquote('0:Rew:333.0,233.0,333.0,233.0')] ).
cnf(346,plain,
ord_less_int(plus_plus_int(t,bit0(bit0(times_times_int(m,times_times_int(t,bit1(pls)))))),pls),
inference(rew,[status(thm),theory(equality)],[317,345]),
[iquote('0:Rew:317.0,345.0')] ).
cnf(347,plain,
$false,
inference(mrr,[status(thm)],[346,227]),
[iquote('0:MRR:346.0,227.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 00:21:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 96 clauses, backtracked 12 clauses, performed 1 splits and kept 167 clauses.
% 0.20/0.48 SPASS allocated 85533 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.48 0:00:00.04 for the input.
% 0.20/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.02 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 2, length 36 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : fact_24_number__of__is__id fact_105_zero__is__num__zero fact_66_mult__Pls fact_69_zmult__1__right fact_70_zmult__1 fact_25_zmult__commute fact_104_zadd__commute fact_65_nat__1__add__1 fact_67_mult__Bit0 conj_0 fact_30_zmult__assoc fact_16_zero__eq__power2 fact_33_zpower__zadd__distrib fact_72_zadd__zmult__distrib fact_20__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_9_sum__power2__eq__zero__iff 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
% 0.20/0.48
%------------------------------------------------------------------------------