TSTP Solution File: NUM925_3 by SPASS+T---2.2.22
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%------------------------------------------------------------------------------
% File : SPASS+T---2.2.22
% Problem : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : spasst-tptp-script %s %d
% 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 14:39:34 EDT 2022
% Result : Theorem 16.16s 14.09s
% Output : Refutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 20 unt; 0 nHn; 34 RR)
% Number of literals : 57 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(17,axiom,
nat(n),
file('NUM925_3.p',unknown),
[] ).
cnf(33,axiom,
fun_nat_int(semiri1621563631at_int),
file('NUM925_3.p',unknown),
[] ).
cnf(42,axiom,
int(one_one_int),
file('NUM925_3.p',unknown),
[] ).
cnf(66,axiom,
equal(zero_zero_int,pls),
file('NUM925_3.p',unknown),
[] ).
cnf(81,axiom,
equal(nat_1(one_one_int),one_one_nat),
file('NUM925_3.p',unknown),
[] ).
cnf(91,axiom,
~ equal(zero_zero_nat,one_one_nat),
file('NUM925_3.p',unknown),
[] ).
cnf(110,axiom,
equal(bit1(pls),succ(pls)),
file('NUM925_3.p',unknown),
[] ).
cnf(259,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
file('NUM925_3.p',unknown),
[] ).
cnf(318,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),nat_1(number_number_of_int(bit0(bit1(pls))))),
file('NUM925_3.p',unknown),
[] ).
cnf(342,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('NUM925_3.p',unknown),
[] ).
cnf(348,axiom,
( ~ fun_nat_int(U)
| ~ nat(V)
| int(hAPP_nat_int(U,V)) ),
file('NUM925_3.p',unknown),
[] ).
cnf(359,axiom,
( ~ int(U)
| ~ int(V)
| int(plus_plus_int(U,V)) ),
file('NUM925_3.p',unknown),
[] ).
cnf(462,axiom,
equal(hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('NUM925_3.p',unknown),
[] ).
cnf(489,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U),zero_zero_int))
| ~ int(U)
| equal(nat_1(U),zero_zero_nat) ),
file('NUM925_3.p',unknown),
[] ).
cnf(572,axiom,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U))
| ~ int(U)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U)) ),
file('NUM925_3.p',unknown),
[] ).
cnf(610,axiom,
( ~ equal(hAPP_nat_int(power_power_int(U),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int)
| ~ int(U)
| equal(U,zero_zero_int) ),
file('NUM925_3.p',unknown),
[] ).
cnf(1865,plain,
equal(number_number_of_nat(bit0(succ(pls))),plus_plus_nat(one_one_nat,one_one_nat)),
inference(rew,[status(thm),theory(equality)],[110,259]),
[iquote('0:Rew:110.0,259.0')] ).
cnf(1903,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rew,[status(thm),theory(equality)],[66,342]),
[iquote('0:Rew:66.0,342.0')] ).
cnf(1908,plain,
equal(plus_plus_nat(one_one_nat,one_one_nat),nat_1(number_number_of_int(bit0(succ(pls))))),
inference(rew,[status(thm),theory(equality)],[1865,318,110]),
[iquote('0:Rew:1865.0,318.0,110.0,318.0')] ).
cnf(1909,plain,
equal(number_number_of_nat(bit0(succ(pls))),nat_1(number_number_of_int(bit0(succ(pls))))),
inference(rew,[status(thm),theory(equality)],[1908,1865]),
[iquote('0:Rew:1908.0,1865.0')] ).
cnf(1948,plain,
equal(hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat_1(number_number_of_int(bit0(succ(pls))))),pls),
inference(rew,[status(thm),theory(equality)],[1909,462,110,66]),
[iquote('0:Rew:1909.0,462.0,110.0,462.0,66.0,462.0')] ).
cnf(1962,plain,
( ~ int(U)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U),pls))
| equal(nat_1(U),zero_zero_nat) ),
inference(rew,[status(thm),theory(equality)],[66,489]),
[iquote('0:Rew:66.0,489.0')] ).
cnf(2006,plain,
( ~ int(U)
| ~ equal(hAPP_nat_int(power_power_int(U),nat_1(number_number_of_int(bit0(succ(pls))))),pls)
| equal(U,pls) ),
inference(rew,[status(thm),theory(equality)],[66,610,1909,110]),
[iquote('0:Rew:66.0,610.2,1909.0,610.0,110.0,610.0,66.0,610.0')] ).
cnf(2030,plain,
( ~ int(U)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U)) ),
inference(rew,[status(thm),theory(equality)],[66,572]),
[iquote('0:Rew:66.0,572.0')] ).
cnf(2522,plain,
( ~ int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| equal(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)),pls) ),
inference(res,[status(thm),theory(equality)],[1948,2006]),
[iquote('0:Res:1948.0,2006.0')] ).
cnf(8144,plain,
( ~ int(one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls))
| equal(zero_zero_nat,one_one_nat) ),
inference(spr,[status(thm),theory(equality)],[1962,81]),
[iquote('0:SpR:1962.2,81.0')] ).
cnf(8190,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)),
inference(mrr,[status(thm)],[8144,42,91]),
[iquote('0:MRR:8144.0,8144.2,42.0,91.0')] ).
cnf(14623,plain,
( ~ int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(res,[status(thm),theory(equality)],[1903,2030]),
[iquote('0:Res:1903.0,2030.1')] ).
cnf(14632,plain,
( ~ int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)) ),
inference(rew,[status(thm),theory(equality)],[2522,14623]),
[iquote('0:Rew:2522.1,14623.1')] ).
cnf(14633,plain,
~ int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),
inference(mrr,[status(thm)],[14632,8190]),
[iquote('0:MRR:14632.1,8190.0')] ).
cnf(14637,plain,
( ~ int(one_one_int)
| ~ int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(res,[status(thm),theory(equality)],[359,14633]),
[iquote('0:Res:359.2,14633.0')] ).
cnf(14638,plain,
~ int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(mrr,[status(thm)],[14637,42]),
[iquote('0:MRR:14637.0,42.0')] ).
cnf(14641,plain,
( ~ fun_nat_int(semiri1621563631at_int)
| ~ nat(n) ),
inference(res,[status(thm),theory(equality)],[348,14638]),
[iquote('0:Res:348.2,14638.0')] ).
cnf(14642,plain,
$false,
inference(mrr,[status(thm)],[14641,33,17]),
[iquote('0:MRR:14641.0,14641.1,33.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : spasst-tptp-script %s %d
% 0.12/0.34 % Computer : n023.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 21:10:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55 % Using EUF theory
% 16.16/14.09
% 16.16/14.09
% 16.16/14.09 % SZS status Theorem for /tmp/SPASST_4450_n023.cluster.edu
% 16.16/14.09
% 16.16/14.09 SPASS V 2.2.22 in combination with yices.
% 16.16/14.09 SPASS beiseite: Proof found by SPASS.
% 16.16/14.09 Problem: /tmp/SPASST_4450_n023.cluster.edu
% 16.16/14.09 SPASS derived 8550 clauses, backtracked 0 clauses and kept 3973 clauses.
% 16.16/14.09 SPASS backtracked 1 times (0 times due to theory inconsistency).
% 16.16/14.09 SPASS allocated 19991 KBytes.
% 16.16/14.09 SPASS spent 0:00:02.76 on the problem.
% 16.16/14.09 0:00:00.06 for the input.
% 16.16/14.09 0:00:00.36 for the FLOTTER CNF translation.
% 16.16/14.09 0:00:00.08 for inferences.
% 16.16/14.09 0:00:00.02 for the backtracking.
% 16.16/14.09 0:00:01.90 for the reduction.
% 16.16/14.09 0:00:00.09 for interacting with the SMT procedure.
% 16.16/14.09
% 16.16/14.09
% 16.16/14.09 % SZS output start CNFRefutation for /tmp/SPASST_4450_n023.cluster.edu
% See solution above
% 16.16/14.09
% 16.16/14.09 Formulae used in the proof : fof_sy_v_n____ fof_sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint fof_sy_c_Groups_Oone__class_Oone_000tc__Int__Oint fof_fact_98_Pls__def fof_fact_768_transfer__nat__int__numerals_I2_J fof_fact_226_one__neq__zero fof_fact_808_succ__Pls fof_fact_19_semiring__one__add__one__is__two fof_fact_822_transfer__nat__int__numerals_I3_J fof_fact_0_n1pos fof_sy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint fof_sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint fof_conj_0 fof_fact_583_nat__le__0 fof_fact_806_int__one__le__iff__zero__less fof_fact_10_zero__eq__power2
% 16.29/14.30
% 16.29/14.30 SPASS+T ended
%------------------------------------------------------------------------------