TSTP Solution File: SEU325+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:36:17 EDT 2022
% Result : Theorem 80.64s 80.81s
% Output : Refutation 80.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of clauses : 65 ( 46 unt; 1 nHn; 65 RR)
% Number of literals : 94 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
one_sorted_str(skc30),
file('SEU325+2.p',unknown),
[] ).
cnf(15,axiom,
relation_empty_yielding(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(19,axiom,
epsilon_transitive(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(20,axiom,
epsilon_connected(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(21,axiom,
ordinal(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(25,axiom,
v1_membered(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(26,axiom,
v2_membered(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(27,axiom,
v3_membered(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(28,axiom,
v4_membered(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(29,axiom,
v5_membered(empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(49,axiom,
relation(skc326),
file('SEU325+2.p',unknown),
[] ).
cnf(50,axiom,
function(skc326),
file('SEU325+2.p',unknown),
[] ).
cnf(51,axiom,
one_to_one(skc326),
file('SEU325+2.p',unknown),
[] ).
cnf(52,axiom,
empty(skc326),
file('SEU325+2.p',unknown),
[] ).
cnf(84,axiom,
~ empty_carrier(skc30),
file('SEU325+2.p',unknown),
[] ).
cnf(85,axiom,
is_a_cover_of_carrier(skc30,empty_set),
file('SEU325+2.p',unknown),
[] ).
cnf(101,axiom,
empty(skf367(u)),
file('SEU325+2.p',unknown),
[] ).
cnf(108,axiom,
natural(skf367(u)),
file('SEU325+2.p',unknown),
[] ).
cnf(109,axiom,
finite(skf367(u)),
file('SEU325+2.p',unknown),
[] ).
cnf(214,axiom,
equal(set_difference(u,empty_set),u),
file('SEU325+2.p',unknown),
[] ).
cnf(220,axiom,
element(empty_set,powerset(powerset(the_carrier(skc30)))),
file('SEU325+2.p',unknown),
[] ).
cnf(285,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU325+2.p',unknown),
[] ).
cnf(304,axiom,
( ~ being_limit_ordinal(u)
| equal(union(u),u) ),
file('SEU325+2.p',unknown),
[] ).
cnf(431,axiom,
( ~ one_sorted_str(u)
| equal(cast_as_carrier_subset(u),the_carrier(u)) ),
file('SEU325+2.p',unknown),
[] ).
cnf(488,axiom,
( ~ one_sorted_str(u)
| ~ empty(cast_as_carrier_subset(u))
| empty_carrier(u) ),
file('SEU325+2.p',unknown),
[] ).
cnf(523,axiom,
( ~ ordinal(u)
| being_limit_ordinal(u)
| in(skf575(u),u) ),
file('SEU325+2.p',unknown),
[] ).
cnf(712,axiom,
( ~ element(u,powerset(v))
| equal(set_difference(v,u),subset_complement(v,u)) ),
file('SEU325+2.p',unknown),
[] ).
cnf(723,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| in(u,w) ),
file('SEU325+2.p',unknown),
[] ).
cnf(729,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(union_of_subsets(v,u),union(u)) ),
file('SEU325+2.p',unknown),
[] ).
cnf(872,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| ~ in(u,subset_complement(w,v)) ),
file('SEU325+2.p',unknown),
[] ).
cnf(1054,axiom,
( ~ one_sorted_str(u)
| ~ is_a_cover_of_carrier(u,v)
| ~ element(v,powerset(powerset(the_carrier(u))))
| equal(union_of_subsets(the_carrier(u),v),cast_as_carrier_subset(u)) ),
file('SEU325+2.p',unknown),
[] ).
cnf(1324,plain,
( ~ one_sorted_str(u)
| ~ empty(the_carrier(u))
| empty_carrier(u) ),
inference(rew,[status(thm),theory(equality)],[431,488]),
[iquote('0:Rew:431.1,488.1')] ).
cnf(1397,plain,
( ~ one_sorted_str(u)
| ~ is_a_cover_of_carrier(u,v)
| ~ element(v,powerset(powerset(the_carrier(u))))
| equal(union(v),the_carrier(u)) ),
inference(rew,[status(thm),theory(equality)],[729,1054,431]),
[iquote('0:Rew:729.1,1054.3,431.1,1054.3')] ).
cnf(1472,plain,
( ~ empty(the_carrier(skc30))
| empty_carrier(skc30) ),
inference(res,[status(thm),theory(equality)],[1,1324]),
[iquote('0:Res:1.0,1324.0')] ).
cnf(1529,plain,
( ~ one_sorted_str(skc30)
| ~ is_a_cover_of_carrier(skc30,empty_set)
| equal(union(empty_set),the_carrier(skc30)) ),
inference(res,[status(thm),theory(equality)],[220,1397]),
[iquote('0:Res:220.0,1397.2')] ).
cnf(1580,plain,
( ~ in(u,subset_complement(powerset(the_carrier(skc30)),empty_set))
| ~ in(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[220,872]),
[iquote('0:Res:220.0,872.0')] ).
cnf(1582,plain,
equal(set_difference(powerset(the_carrier(skc30)),empty_set),subset_complement(powerset(the_carrier(skc30)),empty_set)),
inference(res,[status(thm),theory(equality)],[220,712]),
[iquote('0:Res:220.0,712.0')] ).
cnf(1584,plain,
( ~ in(u,empty_set)
| in(u,powerset(the_carrier(skc30))) ),
inference(res,[status(thm),theory(equality)],[220,723]),
[iquote('0:Res:220.0,723.0')] ).
cnf(1604,plain,
~ empty(the_carrier(skc30)),
inference(mrr,[status(thm)],[1472,84]),
[iquote('0:MRR:1472.1,84.0')] ).
cnf(1608,plain,
equal(subset_complement(powerset(the_carrier(skc30)),empty_set),powerset(the_carrier(skc30))),
inference(rew,[status(thm),theory(equality)],[214,1582]),
[iquote('0:Rew:214.0,1582.0')] ).
cnf(1610,plain,
equal(union(empty_set),the_carrier(skc30)),
inference(mrr,[status(thm)],[1529,1,85]),
[iquote('0:MRR:1529.0,1529.1,1.0,85.0')] ).
cnf(1613,plain,
( ~ in(u,powerset(the_carrier(skc30)))
| ~ in(u,empty_set) ),
inference(rew,[status(thm),theory(equality)],[1608,1580]),
[iquote('0:Rew:1608.0,1580.0')] ).
cnf(1614,plain,
~ in(u,empty_set),
inference(mrr,[status(thm)],[1613,1584]),
[iquote('0:MRR:1613.0,1584.1')] ).
cnf(1775,plain,
equal(skf367(u),empty_set),
inference(ems,[status(thm)],[285,101]),
[iquote('0:EmS:285.0,101.0')] ).
cnf(1778,plain,
equal(empty_set,skc326),
inference(ems,[status(thm)],[285,52]),
[iquote('0:EmS:285.0,52.0')] ).
cnf(1784,plain,
relation_empty_yielding(skc326),
inference(rew,[status(thm),theory(equality)],[1778,15]),
[iquote('0:Rew:1778.0,15.0')] ).
cnf(1785,plain,
epsilon_transitive(skc326),
inference(rew,[status(thm),theory(equality)],[1778,19]),
[iquote('0:Rew:1778.0,19.0')] ).
cnf(1786,plain,
epsilon_connected(skc326),
inference(rew,[status(thm),theory(equality)],[1778,20]),
[iquote('0:Rew:1778.0,20.0')] ).
cnf(1788,plain,
v1_membered(skc326),
inference(rew,[status(thm),theory(equality)],[1778,25]),
[iquote('0:Rew:1778.0,25.0')] ).
cnf(1789,plain,
v2_membered(skc326),
inference(rew,[status(thm),theory(equality)],[1778,26]),
[iquote('0:Rew:1778.0,26.0')] ).
cnf(1790,plain,
v3_membered(skc326),
inference(rew,[status(thm),theory(equality)],[1778,27]),
[iquote('0:Rew:1778.0,27.0')] ).
cnf(1791,plain,
v4_membered(skc326),
inference(rew,[status(thm),theory(equality)],[1778,28]),
[iquote('0:Rew:1778.0,28.0')] ).
cnf(1792,plain,
v5_membered(skc326),
inference(rew,[status(thm),theory(equality)],[1778,29]),
[iquote('0:Rew:1778.0,29.0')] ).
cnf(1794,plain,
ordinal(skc326),
inference(rew,[status(thm),theory(equality)],[1778,21]),
[iquote('0:Rew:1778.0,21.0')] ).
cnf(1802,plain,
~ in(u,skc326),
inference(rew,[status(thm),theory(equality)],[1778,1614]),
[iquote('0:Rew:1778.0,1614.0')] ).
cnf(1805,plain,
equal(union(skc326),the_carrier(skc30)),
inference(rew,[status(thm),theory(equality)],[1778,1610]),
[iquote('0:Rew:1778.0,1610.0')] ).
cnf(1949,plain,
equal(skf367(u),skc326),
inference(rew,[status(thm),theory(equality)],[1778,1775]),
[iquote('0:Rew:1778.0,1775.0')] ).
cnf(1950,plain,
natural(skc326),
inference(rew,[status(thm),theory(equality)],[1949,108]),
[iquote('0:Rew:1949.0,108.0')] ).
cnf(1954,plain,
finite(skc326),
inference(rew,[status(thm),theory(equality)],[1949,109]),
[iquote('0:Rew:1949.0,109.0')] ).
cnf(2073,plain,
( ~ being_limit_ordinal(skc326)
| equal(the_carrier(skc30),skc326) ),
inference(spr,[status(thm),theory(equality)],[304,1805]),
[iquote('0:SpR:304.1,1805.0')] ).
cnf(3575,plain,
( ~ ordinal(skc326)
| being_limit_ordinal(skc326) ),
inference(res,[status(thm),theory(equality)],[523,1802]),
[iquote('0:Res:523.2,1802.0')] ).
cnf(3584,plain,
being_limit_ordinal(skc326),
inference(ssi,[status(thm)],[3575,51,52,50,49,1784,1785,1786,1788,1789,1790,1791,1792,1794,1950,1954]),
[iquote('0:SSi:3575.0,51.0,52.0,50.0,49.0,1784.0,1785.0,1786.0,1788.0,1789.0,1790.0,1791.0,1792.0,1794.0,1950.0,1954.0')] ).
cnf(3585,plain,
equal(the_carrier(skc30),skc326),
inference(mrr,[status(thm)],[2073,3584]),
[iquote('0:MRR:2073.0,3584.0')] ).
cnf(3586,plain,
~ empty(skc326),
inference(rew,[status(thm),theory(equality)],[3585,1604]),
[iquote('0:Rew:3585.0,1604.0')] ).
cnf(3683,plain,
$false,
inference(mrr,[status(thm)],[3586,52]),
[iquote('0:MRR:3586.0,52.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU325+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Sun Jun 19 18:22:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 80.64/80.81
% 80.64/80.81 SPASS V 3.9
% 80.64/80.81 SPASS beiseite: Proof found.
% 80.64/80.81 % SZS status Theorem
% 80.64/80.81 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.64/80.81 SPASS derived 2088 clauses, backtracked 38 clauses, performed 12 splits and kept 2412 clauses.
% 80.64/80.81 SPASS allocated 165622 KBytes.
% 80.64/80.81 SPASS spent 0:1:20.41 on the problem.
% 80.64/80.81 0:00:00.04 for the input.
% 80.64/80.81 0:1:18.87 for the FLOTTER CNF translation.
% 80.64/80.81 0:00:00.03 for inferences.
% 80.64/80.81 0:00:00.01 for the backtracking.
% 80.64/80.81 0:00:01.13 for the reduction.
% 80.64/80.81
% 80.64/80.81
% 80.64/80.81 Here is a proof with depth 2, length 65 :
% 80.64/80.81 % SZS output start Refutation
% See solution above
% 80.64/80.81 Formulae used in the proof : t5_tops_2 fc2_ordinal1 fc6_membered rc1_partfun1 rc2_finset_1 t3_boole t6_boole d6_ordinal1 t12_pre_topc fc2_pre_topc t41_ordinal1 rc3_ordinal1 d5_subset_1 l3_subset_1 redefinition_k5_setfam_1 t54_subset_1 d8_pre_topc
% 80.64/80.81
%------------------------------------------------------------------------------