TSTP Solution File: NUM925_2 by SPASS+T---2.2.22
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS+T---2.2.22
% Problem : NUM925_2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : spasst-tptp-script %s %d
% Computer : n020.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 14:39:33 EDT 2022
% Result : Theorem 6.35s 5.83s
% Output : Refutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 32 ( 16 unt; 0 nHn; 32 RR)
% Number of literals : 61 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
nat(n),
file('NUM925_2.p',unknown),
[] ).
cnf(15,axiom,
fun_nat_int(semiri1621563631at_int),
file('NUM925_2.p',unknown),
[] ).
cnf(22,axiom,
int(one_one_int),
file('NUM925_2.p',unknown),
[] ).
cnf(50,axiom,
equal(zero_zero_int,pls),
file('NUM925_2.p',unknown),
[] ).
cnf(80,axiom,
equal(bit1(pls),succ(pls)),
file('NUM925_2.p',unknown),
[] ).
cnf(127,axiom,
( ~ int(U)
| fun_int_int(plus_plus_int(U)) ),
file('NUM925_2.p',unknown),
[] ).
cnf(129,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
file('NUM925_2.p',unknown),
[] ).
cnf(202,axiom,
equal(number_number_of_nat(bit0(bit1(pls))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
file('NUM925_2.p',unknown),
[] ).
cnf(249,axiom,
( ~ fun_nat_int(U)
| ~ nat(V)
| int(hAPP_nat_int(U,V)) ),
file('NUM925_2.p',unknown),
[] ).
cnf(252,axiom,
( ~ fun_int_int(U)
| ~ int(V)
| int(hAPP_int_int(U,V)) ),
file('NUM925_2.p',unknown),
[] ).
cnf(276,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('NUM925_2.p',unknown),
[] ).
cnf(321,axiom,
equal(hAPP_nat_int(power_power_int(hAPP_int_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_2.p',unknown),
[] ).
cnf(335,axiom,
( ~ int(U)
| ~ int(V)
| equal(hAPP_int_int(plus_plus_int(U),V),hAPP_int_int(plus_plus_int(V),U)) ),
file('NUM925_2.p',unknown),
[] ).
cnf(365,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_2.p',unknown),
[] ).
cnf(396,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_2.p',unknown),
[] ).
cnf(1069,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)),
inference(rew,[status(thm),theory(equality)],[50,129]),
[iquote('0:Rew:50.0,129.0')] ).
cnf(1080,plain,
equal(number_number_of_nat(bit0(succ(pls))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),
inference(rew,[status(thm),theory(equality)],[80,202]),
[iquote('0:Rew:80.0,202.0')] ).
cnf(1109,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(rew,[status(thm),theory(equality)],[50,276]),
[iquote('0:Rew:50.0,276.0')] ).
cnf(1130,plain,
equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),pls),
inference(rew,[status(thm),theory(equality)],[1080,321,80,50]),
[iquote('0:Rew:1080.0,321.0,80.0,321.0,50.0,321.0')] ).
cnf(1147,plain,
( ~ int(U)
| ~ equal(hAPP_nat_int(power_power_int(U),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),pls)
| equal(U,pls) ),
inference(rew,[status(thm),theory(equality)],[50,396,1080,80]),
[iquote('0:Rew:50.0,396.2,1080.0,396.0,80.0,396.0,50.0,396.0')] ).
cnf(1162,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)],[50,365]),
[iquote('0:Rew:50.0,365.0')] ).
cnf(1363,plain,
( ~ int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| equal(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),pls) ),
inference(res,[status(thm),theory(equality)],[1130,1147]),
[iquote('0:Res:1130.0,1147.0')] ).
cnf(5494,plain,
( ~ int(U)
| ~ int(V)
| ~ fun_int_int(plus_plus_int(U))
| ~ int(V)
| int(hAPP_int_int(plus_plus_int(V),U)) ),
inference(spr,[status(thm),theory(equality)],[335,252]),
[iquote('0:SpR:335.2,252.2')] ).
cnf(5522,plain,
( ~ int(U)
| ~ fun_int_int(plus_plus_int(U))
| ~ int(V)
| int(hAPP_int_int(plus_plus_int(V),U)) ),
inference(obv,[status(thm),theory(equality)],[5494]),
[iquote('0:Obv:5494.1')] ).
cnf(5523,plain,
( ~ int(U)
| ~ int(V)
| int(hAPP_int_int(plus_plus_int(V),U)) ),
inference(mrr,[status(thm)],[5522,127]),
[iquote('0:MRR:5522.1,127.1')] ).
cnf(7950,plain,
( ~ int(hAPP_int_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),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(res,[status(thm),theory(equality)],[1109,1162]),
[iquote('0:Res:1109.0,1162.1')] ).
cnf(7956,plain,
( ~ int(hAPP_int_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)],[1363,7950]),
[iquote('0:Rew:1363.1,7950.1')] ).
cnf(7957,plain,
~ int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
inference(mrr,[status(thm)],[7956,1069]),
[iquote('0:MRR:7956.1,1069.0')] ).
cnf(7961,plain,
( ~ int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ int(one_one_int) ),
inference(res,[status(thm),theory(equality)],[5523,7957]),
[iquote('0:Res:5523.2,7957.0')] ).
cnf(7962,plain,
~ int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(mrr,[status(thm)],[7961,22]),
[iquote('0:MRR:7961.1,22.0')] ).
cnf(7964,plain,
( ~ fun_nat_int(semiri1621563631at_int)
| ~ nat(n) ),
inference(res,[status(thm),theory(equality)],[249,7962]),
[iquote('0:Res:249.2,7962.0')] ).
cnf(7965,plain,
$false,
inference(mrr,[status(thm)],[7964,15,3]),
[iquote('0:MRR:7964.0,7964.1,15.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM925_2 : TPTP v8.1.0. Released v5.3.0.
% 0.04/0.12 % Command : spasst-tptp-script %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jul 7 06:38:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.51 % Using EUF theory
% 6.35/5.83
% 6.35/5.83
% 6.35/5.83 % SZS status Theorem for /tmp/SPASST_28774_n020.cluster.edu
% 6.35/5.83
% 6.35/5.83 SPASS V 2.2.22 in combination with yices.
% 6.35/5.83 SPASS beiseite: Proof found by SPASS.
% 6.35/5.83 Problem: /tmp/SPASST_28774_n020.cluster.edu
% 6.35/5.83 SPASS derived 5129 clauses, backtracked 0 clauses and kept 1816 clauses.
% 6.35/5.83 SPASS backtracked 1 times (0 times due to theory inconsistency).
% 6.35/5.83 SPASS allocated 13971 KBytes.
% 6.35/5.83 SPASS spent 0:00:01.02 on the problem.
% 6.35/5.83 0:00:00.03 for the input.
% 6.35/5.83 0:00:00.13 for the FLOTTER CNF translation.
% 6.35/5.83 0:00:00.06 for inferences.
% 6.35/5.83 0:00:00.02 for the backtracking.
% 6.35/5.83 0:00:00.63 for the reduction.
% 6.35/5.83 0:00:00.06 for interacting with the SMT procedure.
% 6.35/5.83
% 6.35/5.83
% 6.35/5.83 % SZS output start CNFRefutation for /tmp/SPASST_28774_n020.cluster.edu
% See solution above
% 6.35/5.83
% 6.35/5.83 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_567_succ__Pls fof_sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint fof_fact_494_not__one__le__zero fof_fact_19_semiring__one__add__one__is__two fof_sy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint fof_sy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint fof_fact_0_n1pos fof_conj_0 fof_fact_67_zadd__commute fof_fact_565_int__one__le__iff__zero__less fof_fact_10_zero__eq__power2
% 6.51/5.95
% 6.51/5.95 SPASS+T ended
%------------------------------------------------------------------------------