TSTP Solution File: SEU342+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 : Tue Jul 19 14:36:26 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of clauses : 82 ( 33 unt; 30 nHn; 82 RR)
% Number of literals : 208 ( 0 equ; 102 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
lattice(skc10),
file('SEU342+1.p',unknown),
[] ).
cnf(2,axiom,
latt_str(skc10),
file('SEU342+1.p',unknown),
[] ).
cnf(10,axiom,
~ empty_carrier(skc10),
file('SEU342+1.p',unknown),
[] ).
cnf(13,axiom,
element(skc12,the_carrier(skc10)),
file('SEU342+1.p',unknown),
[] ).
cnf(14,axiom,
element(skc11,the_carrier(skc10)),
file('SEU342+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ meet_semilatt_str(u)
| one_sorted_str(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ latt_str(u)
| meet_semilatt_str(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ latt_str(u)
| join_semilatt_str(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(22,axiom,
element(skf6(u,v),the_carrier(v)),
file('SEU342+1.p',unknown),
[] ).
cnf(23,axiom,
element(skf5(u,v),the_carrier(v)),
file('SEU342+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ one_sorted_str(u)
| ~ empty(the_carrier(u))
| empty_carrier(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU342+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_commutative(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_associative(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_commutative(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_associative(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_absorbing(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_absorbing(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ equal(ordered_pair(u,v),ordered_pair(w,x))
| equal(u,w) ),
file('SEU342+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ equal(ordered_pair(u,v),ordered_pair(w,x))
| equal(v,x) ),
file('SEU342+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| equal(a_1_0_filter_1(u),relation_of_lattice(u)) ),
file('SEU342+1.p',unknown),
[] ).
cnf(46,axiom,
( in(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skc11,skc12),relation_of_lattice(skc10))
| below_refl(skc10,skc11,skc12) ),
file('SEU342+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ in(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skc11,skc12),relation_of_lattice(skc10))
| ~ below_refl(skc10,skc11,skc12) ),
file('SEU342+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ element(u,v)
| ~ element(w,x)
| empty(v)
| empty(x)
| equal(ordered_pair_as_product_element(x,v,w,u),ordered_pair(w,u)) ),
file('SEU342+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ in(v,a_1_0_filter_1(u))
| below_refl(u,skf6(v,u),skf5(v,u))
| empty_carrier(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ in(v,a_1_0_filter_1(u))
| equal(ordered_pair_as_product_element(the_carrier(u),the_carrier(u),skf6(v,u),skf5(v,u)),v)
| empty_carrier(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ below_refl(u,v,w)
| ~ element(w,the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(x,ordered_pair_as_product_element(the_carrier(u),the_carrier(u),v,w))
| in(x,a_1_0_filter_1(u))
| empty_carrier(u) ),
file('SEU342+1.p',unknown),
[] ).
cnf(58,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ in(v,relation_of_lattice(u))
| empty_carrier(u)
| below_refl(u,skf6(v,u),skf5(v,u)) ),
inference(rew,[status(thm),theory(equality)],[44,49]),
[iquote('0:Rew:44.3,49.2')] ).
cnf(60,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ in(v,relation_of_lattice(u))
| empty_carrier(u)
| equal(ordered_pair_as_product_element(the_carrier(u),the_carrier(u),skf6(v,u),skf5(v,u)),v) ),
inference(rew,[status(thm),theory(equality)],[44,53]),
[iquote('0:Rew:44.3,53.2')] ).
cnf(61,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ equal(x,ordered_pair_as_product_element(the_carrier(u),the_carrier(u),v,w))
| ~ below_refl(u,v,w)
| empty_carrier(u)
| in(x,relation_of_lattice(u)) ),
inference(rew,[status(thm),theory(equality)],[44,56]),
[iquote('0:Rew:44.3,56.6')] ).
cnf(68,plain,
( ~ lattice(skc10)
| ~ in(u,relation_of_lattice(skc10))
| below_refl(skc10,skf6(u,skc10),skf5(u,skc10))
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,58]),
[iquote('0:Res:2.0,58.0')] ).
cnf(71,plain,
( ~ lattice(skc10)
| join_commutative(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,33]),
[iquote('0:Res:2.0,33.0')] ).
cnf(72,plain,
( ~ lattice(skc10)
| join_associative(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,34]),
[iquote('0:Res:2.0,34.0')] ).
cnf(73,plain,
( ~ lattice(skc10)
| meet_commutative(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,35]),
[iquote('0:Res:2.0,35.0')] ).
cnf(74,plain,
( ~ lattice(skc10)
| meet_associative(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,36]),
[iquote('0:Res:2.0,36.0')] ).
cnf(75,plain,
( ~ lattice(skc10)
| meet_absorbing(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,37]),
[iquote('0:Res:2.0,37.0')] ).
cnf(76,plain,
( ~ lattice(skc10)
| join_absorbing(skc10)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[2,38]),
[iquote('0:Res:2.0,38.0')] ).
cnf(77,plain,
meet_semilatt_str(skc10),
inference(res,[status(thm),theory(equality)],[2,19]),
[iquote('0:Res:2.0,19.0')] ).
cnf(78,plain,
join_semilatt_str(skc10),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(80,plain,
( ~ latt_str(skc10)
| ~ in(u,relation_of_lattice(skc10))
| equal(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skf6(u,skc10),skf5(u,skc10)),u)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[1,60]),
[iquote('0:Res:1.0,60.1')] ).
cnf(105,plain,
( ~ one_sorted_str(skc10)
| ~ empty(the_carrier(skc10)) ),
inference(res,[status(thm),theory(equality)],[29,10]),
[iquote('0:Res:29.2,10.0')] ).
cnf(127,plain,
( empty(the_carrier(skc10))
| in(skc12,the_carrier(skc10)) ),
inference(res,[status(thm),theory(equality)],[13,31]),
[iquote('0:Res:13.0,31.0')] ).
cnf(130,plain,
join_commutative(skc10),
inference(mrr,[status(thm)],[71,1,10]),
[iquote('0:MRR:71.0,71.2,1.0,10.0')] ).
cnf(131,plain,
join_associative(skc10),
inference(mrr,[status(thm)],[72,1,10]),
[iquote('0:MRR:72.0,72.2,1.0,10.0')] ).
cnf(132,plain,
meet_commutative(skc10),
inference(mrr,[status(thm)],[73,1,10]),
[iquote('0:MRR:73.0,73.2,1.0,10.0')] ).
cnf(133,plain,
meet_associative(skc10),
inference(mrr,[status(thm)],[74,1,10]),
[iquote('0:MRR:74.0,74.2,1.0,10.0')] ).
cnf(134,plain,
meet_absorbing(skc10),
inference(mrr,[status(thm)],[75,1,10]),
[iquote('0:MRR:75.0,75.2,1.0,10.0')] ).
cnf(135,plain,
join_absorbing(skc10),
inference(mrr,[status(thm)],[76,1,10]),
[iquote('0:MRR:76.0,76.2,1.0,10.0')] ).
cnf(138,plain,
( ~ in(u,relation_of_lattice(skc10))
| below_refl(skc10,skf6(u,skc10),skf5(u,skc10)) ),
inference(mrr,[status(thm)],[68,1,10]),
[iquote('0:MRR:68.0,68.3,1.0,10.0')] ).
cnf(142,plain,
( ~ in(u,relation_of_lattice(skc10))
| equal(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skf6(u,skc10),skf5(u,skc10)),u) ),
inference(mrr,[status(thm)],[80,2,10]),
[iquote('0:MRR:80.0,80.3,2.0,10.0')] ).
cnf(163,plain,
empty(the_carrier(skc10)),
inference(spt,[spt(split,[position(s1)])],[127]),
[iquote('1:Spt:127.0')] ).
cnf(164,plain,
~ one_sorted_str(skc10),
inference(mrr,[status(thm)],[105,163]),
[iquote('1:MRR:105.1,163.0')] ).
cnf(165,plain,
$false,
inference(ssi,[status(thm)],[164,17,1,2,133,131,130,78,77,135,134,132]),
[iquote('1:SSi:164.0,17.0,1.0,2.0,133.0,131.0,130.0,78.0,77.0,135.0,134.0,132.1')] ).
cnf(166,plain,
~ empty(the_carrier(skc10)),
inference(spt,[spt(split,[position(sa)])],[165,163]),
[iquote('1:Spt:165.0,127.0,163.0')] ).
cnf(167,plain,
in(skc12,the_carrier(skc10)),
inference(spt,[spt(split,[position(s2)])],[127]),
[iquote('1:Spt:165.0,127.1')] ).
cnf(169,plain,
~ empty(the_carrier(skc10)),
inference(res,[status(thm),theory(equality)],[167,27]),
[iquote('1:Res:167.0,27.1')] ).
cnf(236,plain,
in(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skc11,skc12),relation_of_lattice(skc10)),
inference(spt,[spt(split,[position(s2s1)])],[46]),
[iquote('2:Spt:46.0')] ).
cnf(237,plain,
~ below_refl(skc10,skc11,skc12),
inference(mrr,[status(thm)],[47,236]),
[iquote('2:MRR:47.0,236.0')] ).
cnf(274,plain,
( ~ element(skc12,the_carrier(skc10))
| ~ element(skc11,the_carrier(skc10))
| empty(the_carrier(skc10))
| empty(the_carrier(skc10))
| in(ordered_pair(skc11,skc12),relation_of_lattice(skc10)) ),
inference(spr,[status(thm),theory(equality)],[48,236]),
[iquote('2:SpR:48.4,236.0')] ).
cnf(277,plain,
( ~ element(skc12,the_carrier(skc10))
| ~ element(skc11,the_carrier(skc10))
| empty(the_carrier(skc10))
| in(ordered_pair(skc11,skc12),relation_of_lattice(skc10)) ),
inference(obv,[status(thm),theory(equality)],[274]),
[iquote('2:Obv:274.2')] ).
cnf(278,plain,
in(ordered_pair(skc11,skc12),relation_of_lattice(skc10)),
inference(mrr,[status(thm)],[277,13,14,169]),
[iquote('2:MRR:277.0,277.1,277.2,13.0,14.0,169.0')] ).
cnf(372,plain,
( ~ in(u,relation_of_lattice(skc10))
| ~ element(skf5(u,skc10),the_carrier(skc10))
| ~ element(skf6(u,skc10),the_carrier(skc10))
| empty(the_carrier(skc10))
| empty(the_carrier(skc10))
| equal(ordered_pair(skf6(u,skc10),skf5(u,skc10)),u) ),
inference(spr,[status(thm),theory(equality)],[142,48]),
[iquote('0:SpR:142.1,48.4')] ).
cnf(373,plain,
( ~ in(u,relation_of_lattice(skc10))
| ~ element(skf5(u,skc10),the_carrier(skc10))
| ~ element(skf6(u,skc10),the_carrier(skc10))
| empty(the_carrier(skc10))
| equal(ordered_pair(skf6(u,skc10),skf5(u,skc10)),u) ),
inference(obv,[status(thm),theory(equality)],[372]),
[iquote('0:Obv:372.3')] ).
cnf(374,plain,
( ~ in(u,relation_of_lattice(skc10))
| equal(ordered_pair(skf6(u,skc10),skf5(u,skc10)),u) ),
inference(mrr,[status(thm)],[373,23,22,169]),
[iquote('1:MRR:373.1,373.2,373.3,23.0,22.0,169.0')] ).
cnf(381,plain,
( ~ in(u,relation_of_lattice(skc10))
| ~ equal(u,ordered_pair(v,w))
| equal(skf6(u,skc10),v) ),
inference(spl,[status(thm),theory(equality)],[374,41]),
[iquote('1:SpL:374.1,41.0')] ).
cnf(416,plain,
( ~ in(ordered_pair(u,v),relation_of_lattice(skc10))
| equal(skf6(ordered_pair(u,v),skc10),u) ),
inference(eqr,[status(thm),theory(equality)],[381]),
[iquote('1:EqR:381.1')] ).
cnf(423,plain,
equal(skf6(ordered_pair(skc11,skc12),skc10),skc11),
inference(res,[status(thm),theory(equality)],[278,416]),
[iquote('2:Res:278.0,416.0')] ).
cnf(432,plain,
( ~ in(ordered_pair(skc11,skc12),relation_of_lattice(skc10))
| below_refl(skc10,skc11,skf5(ordered_pair(skc11,skc12),skc10)) ),
inference(spr,[status(thm),theory(equality)],[423,138]),
[iquote('2:SpR:423.0,138.1')] ).
cnf(434,plain,
( ~ in(ordered_pair(skc11,skc12),relation_of_lattice(skc10))
| equal(ordered_pair(skc11,skf5(ordered_pair(skc11,skc12),skc10)),ordered_pair(skc11,skc12)) ),
inference(spr,[status(thm),theory(equality)],[423,374]),
[iquote('2:SpR:423.0,374.1')] ).
cnf(440,plain,
below_refl(skc10,skc11,skf5(ordered_pair(skc11,skc12),skc10)),
inference(mrr,[status(thm)],[432,278]),
[iquote('2:MRR:432.0,278.0')] ).
cnf(441,plain,
equal(ordered_pair(skc11,skf5(ordered_pair(skc11,skc12),skc10)),ordered_pair(skc11,skc12)),
inference(mrr,[status(thm)],[434,278]),
[iquote('2:MRR:434.0,278.0')] ).
cnf(450,plain,
( ~ equal(ordered_pair(skc11,skc12),ordered_pair(u,v))
| equal(skf5(ordered_pair(skc11,skc12),skc10),v) ),
inference(spl,[status(thm),theory(equality)],[441,42]),
[iquote('2:SpL:441.0,42.0')] ).
cnf(463,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below_refl(u,v,w)
| empty_carrier(u)
| in(ordered_pair_as_product_element(the_carrier(u),the_carrier(u),v,w),relation_of_lattice(u)) ),
inference(eqr,[status(thm),theory(equality)],[61]),
[iquote('0:EqR:61.4')] ).
cnf(531,plain,
equal(skf5(ordered_pair(skc11,skc12),skc10),skc12),
inference(eqr,[status(thm),theory(equality)],[450]),
[iquote('2:EqR:450.0')] ).
cnf(536,plain,
below_refl(skc10,skc11,skc12),
inference(rew,[status(thm),theory(equality)],[531,440]),
[iquote('2:Rew:531.0,440.0')] ).
cnf(546,plain,
$false,
inference(mrr,[status(thm)],[536,237]),
[iquote('2:MRR:536.0,237.0')] ).
cnf(554,plain,
~ in(ordered_pair_as_product_element(the_carrier(skc10),the_carrier(skc10),skc11,skc12),relation_of_lattice(skc10)),
inference(spt,[spt(split,[position(s2sa)])],[546,236]),
[iquote('2:Spt:546.0,46.0,236.0')] ).
cnf(555,plain,
below_refl(skc10,skc11,skc12),
inference(spt,[spt(split,[position(s2s2)])],[46]),
[iquote('2:Spt:546.0,46.1')] ).
cnf(807,plain,
( ~ lattice(skc10)
| ~ latt_str(skc10)
| ~ element(skc11,the_carrier(skc10))
| ~ element(skc12,the_carrier(skc10))
| ~ below_refl(skc10,skc11,skc12)
| empty_carrier(skc10) ),
inference(res,[status(thm),theory(equality)],[463,554]),
[iquote('2:Res:463.6,554.0')] ).
cnf(809,plain,
( ~ element(skc11,the_carrier(skc10))
| ~ element(skc12,the_carrier(skc10))
| ~ below_refl(skc10,skc11,skc12)
| empty_carrier(skc10) ),
inference(ssi,[status(thm)],[807,1,2,133,131,130,78,77,135,134,132]),
[iquote('2:SSi:807.1,807.0,1.0,2.0,133.0,131.0,130.0,78.0,77.0,135.0,134.0,132.0,1.0,2.0,133.0,131.0,130.0,78.0,77.0,135.0,134.0,132.0')] ).
cnf(810,plain,
$false,
inference(mrr,[status(thm)],[809,14,13,555,10]),
[iquote('2:MRR:809.0,809.1,809.2,809.3,14.0,13.0,555.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 04:13:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 569 clauses, backtracked 9 clauses, performed 3 splits and kept 321 clauses.
% 0.19/0.52 SPASS allocated 98498 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.18 on the problem.
% 0.19/0.52 0:00:00.03 for the input.
% 0.19/0.52 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.06 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 8, length 82 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : t32_filter_1 dt_l1_lattices dt_l3_lattices fraenkel_a_1_0_filter_1 existence_m1_subset_1 t7_boole fc1_struct_0 t2_subset cc1_lattices t33_zfmisc_1 d8_filter_1 redefinition_k1_domain_1
% 0.19/0.53
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