TSTP Solution File: NUM925+5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM925+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:31:45 EDT 2022
% Result : Theorem 1.60s 1.80s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of clauses : 49 ( 39 unt; 0 nHn; 49 RR)
% Number of literals : 63 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
linord219039673up_add(int),
file('NUM925+5.p',unknown),
[] ).
cnf(2,axiom,
ring_11004092258visors(int),
file('NUM925+5.p',unknown),
[] ).
cnf(3,axiom,
no_zero_divisors(int),
file('NUM925+5.p',unknown),
[] ).
cnf(4,axiom,
linordered_idom(int),
file('NUM925+5.p',unknown),
[] ).
cnf(5,axiom,
number_semiring(int),
file('NUM925+5.p',unknown),
[] ).
cnf(6,axiom,
zero_neq_one(int),
file('NUM925+5.p',unknown),
[] ).
cnf(7,axiom,
semiring_1(int),
file('NUM925+5.p',unknown),
[] ).
cnf(8,axiom,
semiring_0(int),
file('NUM925+5.p',unknown),
[] ).
cnf(9,axiom,
mult_zero(int),
file('NUM925+5.p',unknown),
[] ).
cnf(10,axiom,
ring_char_0(int),
file('NUM925+5.p',unknown),
[] ).
cnf(11,axiom,
number_ring(int),
file('NUM925+5.p',unknown),
[] ).
cnf(12,axiom,
power(int),
file('NUM925+5.p',unknown),
[] ).
cnf(13,axiom,
number(int),
file('NUM925+5.p',unknown),
[] ).
cnf(23,axiom,
equal(zero_zero(int),pls),
file('NUM925+5.p',unknown),
[] ).
cnf(29,axiom,
~ ord_less(int,pls,pls),
file('NUM925+5.p',unknown),
[] ).
cnf(41,axiom,
equal(plus_plus(int,pls,u),u),
file('NUM925+5.p',unknown),
[] ).
cnf(43,axiom,
equal(bit0(ti(int,u)),bit0(u)),
file('NUM925+5.p',unknown),
[] ).
cnf(47,axiom,
equal(semiring_1_of_nat(int,one_one(nat)),one_one(int)),
file('NUM925+5.p',unknown),
[] ).
cnf(59,axiom,
( ~ equal(pls,u)
| equal(bit0(u),pls) ),
file('NUM925+5.p',unknown),
[] ).
cnf(62,axiom,
( ~ equal(bit0(u),bit0(v))
| equal(u,v) ),
file('NUM925+5.p',unknown),
[] ).
cnf(64,axiom,
equal(plus_plus(int,u,v),plus_plus(int,v,u)),
file('NUM925+5.p',unknown),
[] ).
cnf(77,axiom,
( ~ ord_less(int,pls,u)
| ord_less(int,pls,bit0(u)) ),
file('NUM925+5.p',unknown),
[] ).
cnf(82,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('NUM925+5.p',unknown),
[] ).
cnf(100,axiom,
equal(plus_plus(int,plus_plus(int,one_one(int),u),u),bit1(u)),
file('NUM925+5.p',unknown),
[] ).
cnf(140,axiom,
equal(plus_plus(int,semiring_1_of_nat(int,u),semiring_1_of_nat(int,v)),semiring_1_of_nat(int,plus_plus(nat,u,v))),
file('NUM925+5.p',unknown),
[] ).
cnf(146,axiom,
equal(power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),zero_zero(int)),
file('NUM925+5.p',unknown),
[] ).
cnf(180,axiom,
( ~ ring_11004092258visors(u)
| ~ equal(power_power(u,v,number_number_of(nat,bit0(bit1(pls)))),zero_zero(u))
| equal(ti(u,v),zero_zero(u)) ),
file('NUM925+5.p',unknown),
[] ).
cnf(207,plain,
equal(plus_plus(int,u,plus_plus(int,one_one(int),u)),bit1(u)),
inference(rew,[status(thm),theory(equality)],[64,100]),
[iquote('0:Rew:64.0,100.0')] ).
cnf(210,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(rew,[status(thm),theory(equality)],[23,82]),
[iquote('0:Rew:23.0,82.0')] ).
cnf(218,plain,
equal(power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),pls),
inference(rew,[status(thm),theory(equality)],[23,146]),
[iquote('0:Rew:23.0,146.0')] ).
cnf(348,plain,
( ~ equal(bit0(u),bit0(v))
| equal(ti(int,u),v) ),
inference(spl,[status(thm),theory(equality)],[43,62]),
[iquote('0:SpL:43.0,62.0')] ).
cnf(385,plain,
( ~ equal(pls,u)
| ~ ord_less(int,pls,u)
| ord_less(int,pls,pls) ),
inference(spr,[status(thm),theory(equality)],[59,77]),
[iquote('0:SpR:59.1,77.1')] ).
cnf(388,plain,
( ~ equal(pls,u)
| ~ ord_less(int,pls,u) ),
inference(mrr,[status(thm)],[385,29]),
[iquote('0:MRR:385.2,29.0')] ).
cnf(396,plain,
~ equal(plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),pls),
inference(res,[status(thm),theory(equality)],[210,388]),
[iquote('0:Res:210.0,388.1')] ).
cnf(521,plain,
equal(plus_plus(int,one_one(int),pls),bit1(pls)),
inference(spr,[status(thm),theory(equality)],[207,41]),
[iquote('0:SpR:207.0,41.0')] ).
cnf(528,plain,
equal(one_one(int),bit1(pls)),
inference(rew,[status(thm),theory(equality)],[41,521,64]),
[iquote('0:Rew:41.0,521.0,64.0,521.0')] ).
cnf(533,plain,
equal(semiring_1_of_nat(int,one_one(nat)),bit1(pls)),
inference(rew,[status(thm),theory(equality)],[528,47]),
[iquote('0:Rew:528.0,47.0')] ).
cnf(536,plain,
~ equal(plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),pls),
inference(rew,[status(thm),theory(equality)],[528,396]),
[iquote('0:Rew:528.0,396.0')] ).
cnf(541,plain,
equal(power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),pls),
inference(rew,[status(thm),theory(equality)],[528,218]),
[iquote('0:Rew:528.0,218.0')] ).
cnf(1260,plain,
equal(ti(int,u),u),
inference(eqr,[status(thm),theory(equality)],[348]),
[iquote('0:EqR:348.0')] ).
cnf(3489,plain,
equal(plus_plus(int,semiring_1_of_nat(int,u),bit1(pls)),semiring_1_of_nat(int,plus_plus(nat,u,one_one(nat)))),
inference(spr,[status(thm),theory(equality)],[533,140]),
[iquote('0:SpR:533.0,140.0')] ).
cnf(3508,plain,
equal(plus_plus(int,bit1(pls),semiring_1_of_nat(int,u)),semiring_1_of_nat(int,plus_plus(nat,u,one_one(nat)))),
inference(rew,[status(thm),theory(equality)],[64,3489]),
[iquote('0:Rew:64.0,3489.0')] ).
cnf(3510,plain,
~ equal(semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat))),pls),
inference(rew,[status(thm),theory(equality)],[3508,536]),
[iquote('0:Rew:3508.0,536.0')] ).
cnf(3521,plain,
equal(power_power(int,semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat))),number_number_of(nat,bit0(bit1(pls)))),pls),
inference(rew,[status(thm),theory(equality)],[3508,541]),
[iquote('0:Rew:3508.0,541.0')] ).
cnf(9465,plain,
( ~ ring_11004092258visors(int)
| ~ equal(zero_zero(int),pls)
| equal(ti(int,semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat)))),zero_zero(int)) ),
inference(spl,[status(thm),theory(equality)],[3521,180]),
[iquote('0:SpL:3521.0,180.1')] ).
cnf(9470,plain,
( ~ ring_11004092258visors(int)
| ~ equal(pls,pls)
| equal(semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat))),pls) ),
inference(rew,[status(thm),theory(equality)],[1260,9465,23]),
[iquote('0:Rew:1260.0,9465.2,23.0,9465.2,23.0,9465.1')] ).
cnf(9471,plain,
( ~ ring_11004092258visors(int)
| equal(semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat))),pls) ),
inference(obv,[status(thm),theory(equality)],[9470]),
[iquote('0:Obv:9470.1')] ).
cnf(9472,plain,
equal(semiring_1_of_nat(int,plus_plus(nat,n,one_one(nat))),pls),
inference(ssi,[status(thm)],[9471,10,2,7,13,1,9,8,6,3,5,12,11,4]),
[iquote('0:SSi:9471.0,10.0,2.0,7.0,13.0,1.0,9.0,8.0,6.0,3.0,5.0,12.0,11.0,4.0')] ).
cnf(9473,plain,
$false,
inference(mrr,[status(thm)],[9472,3510]),
[iquote('0:MRR:9472.0,3510.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jul 6 17:12:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.60/1.80
% 1.60/1.80 SPASS V 3.9
% 1.60/1.80 SPASS beiseite: Proof found.
% 1.60/1.80 % SZS status Theorem
% 1.60/1.80 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.60/1.80 SPASS derived 6925 clauses, backtracked 0 clauses, performed 0 splits and kept 2132 clauses.
% 1.60/1.80 SPASS allocated 104102 KBytes.
% 1.60/1.80 SPASS spent 0:00:01.40 on the problem.
% 1.60/1.80 0:00:00.04 for the input.
% 1.60/1.80 0:00:00.05 for the FLOTTER CNF translation.
% 1.60/1.80 0:00:00.08 for inferences.
% 1.60/1.80 0:00:00.00 for the backtracking.
% 1.60/1.80 0:00:01.20 for the reduction.
% 1.60/1.80
% 1.60/1.80
% 1.60/1.80 Here is a proof with depth 2, length 49 :
% 1.60/1.80 % SZS output start Refutation
% See solution above
% 1.60/1.80 Formulae used in the proof : arity_Int_Oint___Groups_Olinordered__ab__group__add arity_Int_Oint___Rings_Oring__1__no__zero__divisors arity_Int_Oint___Rings_Ono__zero__divisors arity_Int_Oint___Rings_Olinordered__idom arity_Int_Oint___Int_Onumber__semiring arity_Int_Oint___Rings_Ozero__neq__one arity_Int_Oint___Rings_Osemiring__1 arity_Int_Oint___Rings_Osemiring__0 arity_Int_Oint___Rings_Omult__zero arity_Int_Oint___Int_Oring__char__0 arity_Int_Oint___Int_Onumber__ring arity_Int_Oint___Power_Opower arity_Int_Oint___Int_Onumber fact_73_Pls__def fact_32_rel__simps_I2_J fact_76_add__Pls tsy_c_Int_OBit0_arg1 fact_24_int__1 fact_71_rel__simps_I38_J fact_43_rel__simps_I48_J fact_47_zadd__commute fact_55_rel__simps_I4_J fact_0_n1pos fact_92_Bit1__def fact_23_zadd__int conj_0 fact_5_zero__eq__power2
% 1.60/1.80
%------------------------------------------------------------------------------