TSTP Solution File: NUM926+5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 9 unt; 1 nHn; 15 RR)
% Number of literals : 22 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(22,axiom,
ord_less_eq(int,one_one(int),t),
file('NUM926+5.p',unknown),
[] ).
cnf(24,axiom,
equal(number_number_of(int,u),u),
file('NUM926+5.p',unknown),
[] ).
cnf(44,axiom,
equal(times_times(int,u,v),times_times(int,v,u)),
file('NUM926+5.p',unknown),
[] ).
cnf(45,axiom,
equal(plus_plus(int,u,v),plus_plus(int,v,u)),
file('NUM926+5.p',unknown),
[] ).
cnf(96,axiom,
( ~ ord_less_eq(int,u,v)
| equal(u,v)
| ord_less(int,u,v) ),
file('NUM926+5.p',unknown),
[] ).
cnf(180,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+5.p',unknown),
[] ).
cnf(181,axiom,
( ~ equal(one_one(int),t)
| equal(plus_plus(int,power_power(int,skc6,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc5,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+5.p',unknown),
[] ).
cnf(182,axiom,
( ~ ord_less(int,one_one(int),t)
| equal(plus_plus(int,power_power(int,skc8,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc7,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+5.p',unknown),
[] ).
cnf(202,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))))),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),
inference(rew,[status(thm),theory(equality)],[45,180,44,24]),
[iquote('0:Rew:45.0,180.0,44.0,180.0,24.0,180.0')] ).
cnf(203,plain,
( ~ equal(one_one(int),t)
| equal(plus_plus(int,power_power(int,skc5,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc6,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
inference(rew,[status(thm),theory(equality)],[45,181,24,44]),
[iquote('0:Rew:45.0,181.1,24.0,181.1,44.0,181.1,45.0,181.1')] ).
cnf(204,plain,
~ equal(one_one(int),t),
inference(mrr,[status(thm)],[203,202]),
[iquote('0:MRR:203.1,202.0')] ).
cnf(205,plain,
( ~ ord_less(int,one_one(int),t)
| equal(plus_plus(int,power_power(int,skc7,number_number_of(nat,bit0(bit1(pls)))),power_power(int,skc8,number_number_of(nat,bit0(bit1(pls))))),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) ),
inference(rew,[status(thm),theory(equality)],[45,182,24,44]),
[iquote('0:Rew:45.0,182.1,24.0,182.1,44.0,182.1,45.0,182.1')] ).
cnf(206,plain,
~ ord_less(int,one_one(int),t),
inference(mrr,[status(thm)],[205,202]),
[iquote('0:MRR:205.1,202.0')] ).
cnf(222,plain,
( ~ ord_less_eq(int,one_one(int),t)
| equal(one_one(int),t) ),
inference(res,[status(thm),theory(equality)],[96,206]),
[iquote('0:Res:96.2,206.0')] ).
cnf(245,plain,
$false,
inference(mrr,[status(thm)],[222,22,204]),
[iquote('0:MRR:222.0,222.1,22.0,204.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jul 7 16:21:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 161 clauses.
% 0.20/0.49 SPASS allocated 98251 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.04 for the input.
% 0.20/0.49 0:00:00.05 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.00 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.01 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 1, length 15 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : fact_0_tpos fact_86_number__of__is__id fact_85_zmult__commute fact_89_zadd__commute fact_22_zless__le 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
% 0.20/0.49
%------------------------------------------------------------------------------