TSTP Solution File: NUM926+6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM926+6 : 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 14:31:50 EDT 2022
% Result : Theorem 2.97s 3.20s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of clauses : 71 ( 41 unt; 4 nHn; 71 RR)
% Number of literals : 104 ( 0 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(97,axiom,
equal(ti(int,min),min),
file('NUM926+6.p',unknown),
[] ).
cnf(99,axiom,
equal(ti(int,m),m),
file('NUM926+6.p',unknown),
[] ).
cnf(102,axiom,
equal(ti(int,t),t),
file('NUM926+6.p',unknown),
[] ).
cnf(103,axiom,
ord_less_eq(int,one_one(int),t),
file('NUM926+6.p',unknown),
[] ).
cnf(116,axiom,
zcong(u,v,one_one(int)),
file('NUM926+6.p',unknown),
[] ).
cnf(135,axiom,
equal(bit0(ti(int,u)),bit0(u)),
file('NUM926+6.p',unknown),
[] ).
cnf(136,axiom,
equal(ti(int,bit0(u)),bit0(u)),
file('NUM926+6.p',unknown),
[] ).
cnf(137,axiom,
equal(bit1(ti(int,u)),bit1(u)),
file('NUM926+6.p',unknown),
[] ).
cnf(138,axiom,
equal(ti(int,bit1(u)),bit1(u)),
file('NUM926+6.p',unknown),
[] ).
cnf(144,axiom,
equal(ti(int,u),number_number_of(int,u)),
file('NUM926+6.p',unknown),
[] ).
cnf(146,axiom,
equal(number_number_of(int,bit1(pls)),one_one(int)),
file('NUM926+6.p',unknown),
[] ).
cnf(152,axiom,
equal(plus_plus(int,pls,u),ti(int,u)),
file('NUM926+6.p',unknown),
[] ).
cnf(171,axiom,
equal(times_times(int,u,v),times_times(int,v,u)),
file('NUM926+6.p',unknown),
[] ).
cnf(172,axiom,
equal(plus_plus(int,u,v),plus_plus(int,v,u)),
file('NUM926+6.p',unknown),
[] ).
cnf(173,axiom,
equal(times_times(int,u,one_one(int)),ti(int,u)),
file('NUM926+6.p',unknown),
[] ).
cnf(210,axiom,
( ~ ord_less_eq(int,u,pls)
| ord_less_eq(int,bit0(u),pls) ),
file('NUM926+6.p',unknown),
[] ).
cnf(290,axiom,
equal(times_times(int,bit0(u),v),bit0(times_times(int,u,v))),
file('NUM926+6.p',unknown),
[] ).
cnf(320,axiom,
equal(plus_plus(int,bit1(u),bit0(v)),bit1(plus_plus(int,u,v))),
file('NUM926+6.p',unknown),
[] ).
cnf(321,axiom,
equal(plus_plus(int,bit0(u),bit1(v)),bit1(plus_plus(int,u,v))),
file('NUM926+6.p',unknown),
[] ).
cnf(361,axiom,
( ~ ord_less(int,u,plus_plus(int,v,one_one(int)))
| ord_less_eq(int,u,v) ),
file('NUM926+6.p',unknown),
[] ).
cnf(362,axiom,
( ~ ord_less_eq(int,u,v)
| ord_less(int,u,plus_plus(int,v,one_one(int))) ),
file('NUM926+6.p',unknown),
[] ).
cnf(428,axiom,
( ~ ord_less_eq(int,u,v)
| ~ ord_less_eq(int,v,w)
| ord_less_eq(int,u,w) ),
file('NUM926+6.p',unknown),
[] ).
cnf(442,axiom,
( ord_less(int,u,v)
| equal(ti(int,u),ti(int,v))
| ord_less(int,v,u) ),
file('NUM926+6.p',unknown),
[] ).
cnf(524,axiom,
( ~ ord_less(int,number_number_of(int,bit0(bit1(pls))),u)
| ~ zcong(one_one(int),number_number_of(int,min),u) ),
file('NUM926+6.p',unknown),
[] ).
cnf(820,axiom,
~ equal(plus_plus(int,power_power(int,u,number_number_of(nat,bit0(bit1(pls)))),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('NUM926+6.p',unknown),
[] ).
cnf(827,axiom,
( ~ equal(one_one(int),t)
| equal(plus_plus(int,power_power(int,skc9,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc8,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
file('NUM926+6.p',unknown),
[] ).
cnf(832,axiom,
( ~ ord_less(int,one_one(int),t)
| equal(plus_plus(int,power_power(int,skc11,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc10,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
file('NUM926+6.p',unknown),
[] ).
cnf(864,plain,
equal(number_number_of(int,min),min),
inference(rew,[status(thm),theory(equality)],[144,97]),
[iquote('0:Rew:144.0,97.0')] ).
cnf(866,plain,
equal(number_number_of(int,m),m),
inference(rew,[status(thm),theory(equality)],[144,99]),
[iquote('0:Rew:144.0,99.0')] ).
cnf(869,plain,
equal(number_number_of(int,t),t),
inference(rew,[status(thm),theory(equality)],[144,102]),
[iquote('0:Rew:144.0,102.0')] ).
cnf(873,plain,
equal(number_number_of(int,bit1(u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[144,138]),
[iquote('0:Rew:144.0,138.0')] ).
cnf(874,plain,
equal(one_one(int),bit1(pls)),
inference(rew,[status(thm),theory(equality)],[873,146]),
[iquote('0:Rew:873.0,146.0')] ).
cnf(875,plain,
zcong(u,v,bit1(pls)),
inference(rew,[status(thm),theory(equality)],[874,116]),
[iquote('0:Rew:874.0,116.0')] ).
cnf(876,plain,
ord_less_eq(int,bit1(pls),t),
inference(rew,[status(thm),theory(equality)],[874,103]),
[iquote('0:Rew:874.0,103.0')] ).
cnf(880,plain,
equal(bit1(number_number_of(int,u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[144,137]),
[iquote('0:Rew:144.0,137.0')] ).
cnf(881,plain,
equal(number_number_of(int,bit0(u)),bit0(u)),
inference(rew,[status(thm),theory(equality)],[144,136]),
[iquote('0:Rew:144.0,136.0')] ).
cnf(883,plain,
equal(bit0(number_number_of(int,u)),bit0(u)),
inference(rew,[status(thm),theory(equality)],[144,135]),
[iquote('0:Rew:144.0,135.0')] ).
cnf(889,plain,
equal(plus_plus(int,pls,u),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[144,152]),
[iquote('0:Rew:144.0,152.0')] ).
cnf(896,plain,
equal(times_times(int,u,bit1(pls)),number_number_of(int,u)),
inference(rew,[status(thm),theory(equality)],[874,173,144]),
[iquote('0:Rew:874.0,173.0,144.0,173.0')] ).
cnf(950,plain,
( ~ ord_less_eq(int,u,v)
| ord_less(int,u,plus_plus(int,v,bit1(pls))) ),
inference(rew,[status(thm),theory(equality)],[874,362]),
[iquote('0:Rew:874.0,362.1')] ).
cnf(951,plain,
( ~ ord_less(int,u,plus_plus(int,v,bit1(pls)))
| ord_less_eq(int,u,v) ),
inference(rew,[status(thm),theory(equality)],[874,361]),
[iquote('0:Rew:874.0,361.0')] ).
cnf(968,plain,
( equal(number_number_of(int,u),number_number_of(int,v))
| ord_less(int,v,u)
| ord_less(int,u,v) ),
inference(rew,[status(thm),theory(equality)],[144,442]),
[iquote('0:Rew:144.0,442.1,144.0,442.1')] ).
cnf(983,plain,
( ~ ord_less(int,bit0(bit1(pls)),u)
| ~ zcong(bit1(pls),min,u) ),
inference(rew,[status(thm),theory(equality)],[874,524,864,881]),
[iquote('0:Rew:874.0,524.1,864.0,524.1,881.0,524.0')] ).
cnf(1072,plain,
~ equal(plus_plus(int,power_power(int,u,number_number_of(nat,bit0(bit1(pls)))),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),bit1(bit0(m))),
inference(rew,[status(thm),theory(equality)],[881,820,889,172,321,866,896,171,290,874]),
[iquote('0:Rew:881.0,820.0,889.0,820.0,172.0,820.0,321.0,820.0,866.0,820.0,896.0,820.0,171.0,820.0,290.0,820.0,290.0,820.0,881.0,820.0,874.0,820.0')] ).
cnf(1078,plain,
( ~ equal(bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc9,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
inference(rew,[status(thm),theory(equality)],[172,827,874,881,171]),
[iquote('0:Rew:172.0,827.1,874.0,827.1,881.0,827.1,171.0,827.1,172.0,827.1,874.0,827.0')] ).
cnf(1081,plain,
( ~ ord_less(int,bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc10,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc11,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
inference(rew,[status(thm),theory(equality)],[172,832,874,881,171]),
[iquote('0:Rew:172.0,832.1,874.0,832.1,881.0,832.1,171.0,832.1,172.0,832.1,874.0,832.0')] ).
cnf(2582,plain,
equal(times_times(int,u,bit0(v)),bit0(times_times(int,v,u))),
inference(spr,[status(thm),theory(equality)],[290,171]),
[iquote('0:SpR:290.0,171.0')] ).
cnf(2609,plain,
( ~ equal(bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc9,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),bit0(times_times(int,bit0(bit1(pls)),m)))) ),
inference(rew,[status(thm),theory(equality)],[2582,1078]),
[iquote('0:Rew:2582.0,1078.1')] ).
cnf(2610,plain,
( ~ ord_less(int,bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc10,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc11,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),bit0(times_times(int,bit0(bit1(pls)),m)))) ),
inference(rew,[status(thm),theory(equality)],[2582,1081]),
[iquote('0:Rew:2582.0,1081.1')] ).
cnf(2621,plain,
( ~ equal(bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc9,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),bit0(bit0(m)))) ),
inference(rew,[status(thm),theory(equality)],[883,2609,896,171,290]),
[iquote('0:Rew:883.0,2609.1,896.0,2609.1,171.0,2609.1,290.0,2609.1')] ).
cnf(2622,plain,
( ~ equal(bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc9,number_number_of(nat,bit0(bit1(pls))))),bit1(plus_plus(int,pls,bit0(m)))) ),
inference(rew,[status(thm),theory(equality)],[320,2621]),
[iquote('0:Rew:320.0,2621.1')] ).
cnf(2623,plain,
( ~ equal(bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc9,number_number_of(nat,bit0(bit1(pls))))),bit1(bit0(m))) ),
inference(rew,[status(thm),theory(equality)],[880,2622,889]),
[iquote('0:Rew:880.0,2622.1,889.0,2622.1')] ).
cnf(2624,plain,
~ equal(bit1(pls),t),
inference(mrr,[status(thm)],[2623,1072]),
[iquote('0:MRR:2623.1,1072.0')] ).
cnf(2625,plain,
( ~ ord_less(int,bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc10,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc11,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,bit1(pls),bit0(bit0(m)))) ),
inference(rew,[status(thm),theory(equality)],[883,2610,896,171,290]),
[iquote('0:Rew:883.0,2610.1,896.0,2610.1,171.0,2610.1,290.0,2610.1')] ).
cnf(2626,plain,
( ~ ord_less(int,bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc10,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc11,number_number_of(nat,bit0(bit1(pls))))),bit1(plus_plus(int,pls,bit0(m)))) ),
inference(rew,[status(thm),theory(equality)],[320,2625]),
[iquote('0:Rew:320.0,2625.1')] ).
cnf(2627,plain,
( ~ ord_less(int,bit1(pls),t)
| equal(plus_plus(int,power_power(int,skc10,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc11,number_number_of(nat,bit0(bit1(pls))))),bit1(bit0(m))) ),
inference(rew,[status(thm),theory(equality)],[880,2626,889]),
[iquote('0:Rew:880.0,2626.1,889.0,2626.1')] ).
cnf(2628,plain,
~ ord_less(int,bit1(pls),t),
inference(mrr,[status(thm)],[2627,1072]),
[iquote('0:MRR:2627.1,1072.0')] ).
cnf(9933,plain,
( ~ ord_less_eq(int,u,pls)
| ord_less(int,u,number_number_of(int,bit1(pls))) ),
inference(spr,[status(thm),theory(equality)],[889,950]),
[iquote('0:SpR:889.0,950.1')] ).
cnf(9943,plain,
( ~ ord_less_eq(int,u,pls)
| ord_less(int,u,bit1(pls)) ),
inference(rew,[status(thm),theory(equality)],[873,9933]),
[iquote('0:Rew:873.0,9933.1')] ).
cnf(9990,plain,
( ~ ord_less_eq(int,bit0(bit1(pls)),pls)
| ~ zcong(bit1(pls),min,bit1(pls)) ),
inference(res,[status(thm),theory(equality)],[9943,983]),
[iquote('0:Res:9943.1,983.0')] ).
cnf(9991,plain,
~ ord_less_eq(int,bit0(bit1(pls)),pls),
inference(mrr,[status(thm)],[9990,875]),
[iquote('0:MRR:9990.1,875.0')] ).
cnf(10011,plain,
~ ord_less_eq(int,bit1(pls),pls),
inference(res,[status(thm),theory(equality)],[210,9991]),
[iquote('0:Res:210.1,9991.0')] ).
cnf(10563,plain,
( ~ ord_less(int,u,number_number_of(int,bit1(pls)))
| ord_less_eq(int,u,pls) ),
inference(spl,[status(thm),theory(equality)],[889,951]),
[iquote('0:SpL:889.0,951.0')] ).
cnf(10581,plain,
( ~ ord_less(int,u,bit1(pls))
| ord_less_eq(int,u,pls) ),
inference(rew,[status(thm),theory(equality)],[873,10563]),
[iquote('0:Rew:873.0,10563.0')] ).
cnf(12285,plain,
( ~ ord_less_eq(int,t,u)
| ord_less_eq(int,bit1(pls),u) ),
inference(res,[status(thm),theory(equality)],[876,428]),
[iquote('0:Res:876.0,428.0')] ).
cnf(18916,plain,
~ ord_less_eq(int,t,pls),
inference(res,[status(thm),theory(equality)],[12285,10011]),
[iquote('0:Res:12285.1,10011.0')] ).
cnf(20030,plain,
( equal(number_number_of(int,bit1(pls)),number_number_of(int,t))
| ord_less(int,t,bit1(pls)) ),
inference(res,[status(thm),theory(equality)],[968,2628]),
[iquote('0:Res:968.1,2628.0')] ).
cnf(20144,plain,
( equal(bit1(pls),t)
| ord_less(int,t,bit1(pls)) ),
inference(rew,[status(thm),theory(equality)],[873,20030,869]),
[iquote('0:Rew:873.0,20030.0,869.0,20030.0')] ).
cnf(20145,plain,
ord_less(int,t,bit1(pls)),
inference(mrr,[status(thm)],[20144,2624]),
[iquote('0:MRR:20144.0,2624.0')] ).
cnf(20224,plain,
ord_less_eq(int,t,pls),
inference(res,[status(thm),theory(equality)],[20145,10581]),
[iquote('0:Res:20145.0,10581.0')] ).
cnf(20226,plain,
$false,
inference(mrr,[status(thm)],[20224,18916]),
[iquote('0:MRR:20224.0,18916.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM926+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.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 : Thu Jul 7 17:20:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.97/3.20
% 2.97/3.20 SPASS V 3.9
% 2.97/3.20 SPASS beiseite: Proof found.
% 2.97/3.20 % SZS status Theorem
% 2.97/3.20 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.97/3.20 SPASS derived 14948 clauses, backtracked 0 clauses, performed 0 splits and kept 4249 clauses.
% 2.97/3.20 SPASS allocated 109805 KBytes.
% 2.97/3.20 SPASS spent 0:00:02.84 on the problem.
% 2.97/3.20 0:00:00.05 for the input.
% 2.97/3.20 0:00:00.15 for the FLOTTER CNF translation.
% 2.97/3.20 0:00:00.13 for inferences.
% 2.97/3.20 0:00:00.00 for the backtracking.
% 2.97/3.20 0:00:02.36 for the reduction.
% 2.97/3.20
% 2.97/3.20
% 2.97/3.20 Here is a proof with depth 4, length 71 :
% 2.97/3.20 % SZS output start Refutation
% See solution above
% 3.07/3.26 Formulae used in the proof : tsy_c_Int_OMin_res tsy_v_m_res tsy_v_t_____res fact_0_tpos fact_330_zcong__1 tsy_c_Int_OBit0_arg1 tsy_c_Int_OBit0_res tsy_c_Int_OBit1_arg1 tsy_c_Int_OBit1_res fact_86_number__of__is__id fact_158_one__is__num__one fact_124_add__Pls fact_85_zmult__commute fact_89_zadd__commute fact_127_zmult__1__right fact_98_rel__simps_I27_J fact_122_mult__Bit0 fact_149_add__Bit1__Bit0 fact_150_add__Bit0__Bit1 fact_63_zle__add1__eq__le fact_24_zle__trans fact_23_zless__linear fact_380_one__not__neg__one__mod__m conj_0 fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06 fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 3.07/3.26
%------------------------------------------------------------------------------