%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 14:36:24 EDT 2022
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 23
% Syntax : Number of clauses : 65 ( 29 unt; 6 nHn; 65 RR)
% Number of literals : 130 ( 0 equ; 69 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
antisymmetric_relstr(skc7),
file('SEU339+1.p',unknown),
[] ).
cnf(2,axiom,
rel_str(skc7),
file('SEU339+1.p',unknown),
[] ).
cnf(5,axiom,
empty(empty_set),
file('SEU339+1.p',unknown),
[] ).
cnf(7,axiom,
empty(skf13(u)),
file('SEU339+1.p',unknown),
[] ).
cnf(10,axiom,
element(skc9,the_carrier(skc7)),
file('SEU339+1.p',unknown),
[] ).
cnf(11,axiom,
element(skc8,the_carrier(skc7)),
file('SEU339+1.p',unknown),
[] ).
cnf(12,axiom,
related(skc7,skc8,skc9),
file('SEU339+1.p',unknown),
[] ).
cnf(13,axiom,
related(skc7,skc9,skc8),
file('SEU339+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(skc9,skc8),
file('SEU339+1.p',unknown),
[] ).
cnf(21,axiom,
element(skf13(u),powerset(u)),
file('SEU339+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU339+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ element(u,powerset(v))
| subset(u,v) ),
file('SEU339+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ subset(u,v)
| element(u,powerset(v)) ),
file('SEU339+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ element(u,powerset(cartesian_product2(v,w)))
| relation(u) ),
file('SEU339+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU339+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ rel_str(u)
| relation_of2_as_subset(the_InternalRel(u),the_carrier(u),the_carrier(u)) ),
file('SEU339+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ rel_str(u)
| ~ antisymmetric_relstr(u)
| is_antisymmetric_in(the_InternalRel(u),the_carrier(u)) ),
file('SEU339+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ relation_of2_as_subset(u,v,w)
| element(u,powerset(cartesian_product2(v,w))) ),
file('SEU339+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SEU339+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| element(u,w) ),
file('SEU339+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU339+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ rel_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ related(u,w,v)
| in(ordered_pair(w,v),the_InternalRel(u)) ),
file('SEU339+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ relation(u)
| ~ is_antisymmetric_in(u,v)
| ~ in(w,v)
| ~ in(x,v)
| ~ in(ordered_pair(w,x),u)
| ~ in(ordered_pair(x,w),u)
| equal(x,w) ),
file('SEU339+1.p',unknown),
[] ).
cnf(59,plain,
( ~ antisymmetric_relstr(skc7)
| is_antisymmetric_in(the_InternalRel(skc7),the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[2,42]),
[iquote('0:Res:2.0,42.1')] ).
cnf(61,plain,
relation_of2_as_subset(the_InternalRel(skc7),the_carrier(skc7),the_carrier(skc7)),
inference(res,[status(thm),theory(equality)],[2,39]),
[iquote('0:Res:2.0,39.0')] ).
cnf(68,plain,
( ~ rel_str(skc7)
| ~ element(skc9,the_carrier(skc7))
| ~ element(skc8,the_carrier(skc7))
| in(ordered_pair(skc9,skc8),the_InternalRel(skc7)) ),
inference(res,[status(thm),theory(equality)],[13,54]),
[iquote('0:Res:13.0,54.1')] ).
cnf(69,plain,
( ~ rel_str(skc7)
| ~ element(skc8,the_carrier(skc7))
| ~ element(skc9,the_carrier(skc7))
| in(ordered_pair(skc8,skc9),the_InternalRel(skc7)) ),
inference(res,[status(thm),theory(equality)],[12,54]),
[iquote('0:Res:12.0,54.1')] ).
cnf(74,plain,
( empty(the_carrier(skc7))
| in(skc8,the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[11,36]),
[iquote('0:Res:11.0,36.0')] ).
cnf(79,plain,
( empty(the_carrier(skc7))
| in(skc9,the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[10,36]),
[iquote('0:Res:10.0,36.0')] ).
cnf(80,plain,
is_antisymmetric_in(the_InternalRel(skc7),the_carrier(skc7)),
inference(mrr,[status(thm)],[59,1]),
[iquote('0:MRR:59.0,1.0')] ).
cnf(81,plain,
in(ordered_pair(skc9,skc8),the_InternalRel(skc7)),
inference(mrr,[status(thm)],[68,2,10,11]),
[iquote('0:MRR:68.0,68.1,68.2,2.0,10.0,11.0')] ).
cnf(82,plain,
in(ordered_pair(skc8,skc9),the_InternalRel(skc7)),
inference(mrr,[status(thm)],[69,2,11,10]),
[iquote('0:MRR:69.0,69.1,69.2,2.0,11.0,10.0')] ).
cnf(121,plain,
equal(skf13(u),empty_set),
inference(ems,[status(thm)],[25,7]),
[iquote('0:EmS:25.0,7.0')] ).
cnf(126,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[121,21]),
[iquote('0:Rew:121.0,21.0')] ).
cnf(151,plain,
relation(empty_set),
inference(res,[status(thm),theory(equality)],[126,32]),
[iquote('0:Res:126.0,32.0')] ).
cnf(222,plain,
( ~ relation_of2_as_subset(u,v,w)
| subset(u,cartesian_product2(v,w)) ),
inference(res,[status(thm),theory(equality)],[44,30]),
[iquote('0:Res:44.1,30.0')] ).
cnf(223,plain,
( ~ relation_of2_as_subset(u,v,w)
| relation(u) ),
inference(res,[status(thm),theory(equality)],[44,32]),
[iquote('0:Res:44.1,32.0')] ).
cnf(227,plain,
relation(the_InternalRel(skc7)),
inference(res,[status(thm),theory(equality)],[61,223]),
[iquote('0:Res:61.0,223.0')] ).
cnf(235,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[126,48]),
[iquote('0:Res:126.0,48.2')] ).
cnf(237,plain,
( ~ empty(u)
| ~ subset(v,u)
| ~ in(w,v) ),
inference(res,[status(thm),theory(equality)],[31,48]),
[iquote('0:Res:31.1,48.2')] ).
cnf(239,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[235,5]),
[iquote('0:EmS:235.0,5.0')] ).
cnf(251,plain,
( ~ relation_of2_as_subset(u,v,w)
| ~ in(x,u)
| element(x,cartesian_product2(v,w)) ),
inference(res,[status(thm),theory(equality)],[44,47]),
[iquote('0:Res:44.1,47.1')] ).
cnf(422,plain,
( ~ relation(the_InternalRel(skc7))
| ~ is_antisymmetric_in(the_InternalRel(skc7),u)
| ~ in(skc9,u)
| ~ in(skc8,u)
| ~ in(ordered_pair(skc8,skc9),the_InternalRel(skc7))
| equal(skc9,skc8) ),
inference(res,[status(thm),theory(equality)],[81,55]),
[iquote('0:Res:81.0,55.4')] ).
cnf(429,plain,
( ~ is_antisymmetric_in(the_InternalRel(skc7),u)
| ~ in(skc9,u)
| ~ in(skc8,u)
| ~ in(ordered_pair(skc8,skc9),the_InternalRel(skc7))
| equal(skc9,skc8) ),
inference(ssi,[status(thm)],[422,227]),
[iquote('0:SSi:422.0,227.0')] ).
cnf(430,plain,
( ~ is_antisymmetric_in(the_InternalRel(skc7),u)
| ~ in(skc9,u)
| ~ in(skc8,u) ),
inference(mrr,[status(thm)],[429,82,14]),
[iquote('0:MRR:429.3,429.4,82.0,14.0')] ).
cnf(825,plain,
( ~ in(u,the_InternalRel(skc7))
| element(u,cartesian_product2(the_carrier(skc7),the_carrier(skc7))) ),
inference(res,[status(thm),theory(equality)],[61,251]),
[iquote('0:Res:61.0,251.0')] ).
cnf(832,plain,
( ~ in(u,the_InternalRel(skc7))
| empty(cartesian_product2(the_carrier(skc7),the_carrier(skc7)))
| in(u,cartesian_product2(the_carrier(skc7),the_carrier(skc7))) ),
inference(res,[status(thm),theory(equality)],[825,36]),
[iquote('0:Res:825.1,36.0')] ).
cnf(890,plain,
( ~ in(skc9,the_carrier(skc7))
| ~ in(skc8,the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[80,430]),
[iquote('0:Res:80.0,430.0')] ).
cnf(895,plain,
( ~ in(skc8,the_carrier(skc7))
| empty(the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[79,890]),
[iquote('0:Res:79.1,890.0')] ).
cnf(896,plain,
empty(the_carrier(skc7)),
inference(mrr,[status(thm)],[895,74]),
[iquote('0:MRR:895.0,74.1')] ).
cnf(898,plain,
equal(the_carrier(skc7),empty_set),
inference(ems,[status(thm)],[25,896]),
[iquote('0:EmS:25.0,896.0')] ).
cnf(904,plain,
relation_of2_as_subset(the_InternalRel(skc7),empty_set,empty_set),
inference(rew,[status(thm),theory(equality)],[898,61]),
[iquote('0:Rew:898.0,61.0')] ).
cnf(918,plain,
( ~ in(u,the_InternalRel(skc7))
| empty(cartesian_product2(empty_set,empty_set))
| in(u,cartesian_product2(the_carrier(skc7),the_carrier(skc7))) ),
inference(rew,[status(thm),theory(equality)],[898,832]),
[iquote('0:Rew:898.0,832.1')] ).
cnf(921,plain,
( ~ in(u,the_InternalRel(skc7))
| empty(cartesian_product2(empty_set,empty_set))
| in(u,cartesian_product2(empty_set,empty_set)) ),
inference(rew,[status(thm),theory(equality)],[898,918]),
[iquote('0:Rew:898.0,918.2')] ).
cnf(1210,plain,
( ~ in(u,the_InternalRel(skc7))
| in(u,cartesian_product2(empty_set,empty_set)) ),
inference(spt,[spt(split,[position(s1)])],[921]),
[iquote('1:Spt:921.0,921.2')] ).
cnf(1212,plain,
( ~ in(ordered_pair(u,v),the_InternalRel(skc7))
| in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[1210,46]),
[iquote('1:Res:1210.1,46.0')] ).
cnf(1220,plain,
~ in(ordered_pair(u,v),the_InternalRel(skc7)),
inference(mrr,[status(thm)],[1212,239]),
[iquote('1:MRR:1212.1,239.0')] ).
cnf(1221,plain,
$false,
inference(unc,[status(thm)],[1220,81]),
[iquote('1:UnC:1220.0,81.0')] ).
cnf(1224,plain,
empty(cartesian_product2(empty_set,empty_set)),
inference(spt,[spt(split,[position(s2)])],[921]),
[iquote('1:Spt:1221.0,921.1')] ).
cnf(1226,plain,
equal(cartesian_product2(empty_set,empty_set),empty_set),
inference(ems,[status(thm)],[25,1224]),
[iquote('1:EmS:25.0,1224.0')] ).
cnf(1254,plain,
( ~ relation_of2_as_subset(u,empty_set,empty_set)
| subset(u,empty_set) ),
inference(spr,[status(thm),theory(equality)],[1226,222]),
[iquote('1:SpR:1226.0,222.1')] ).
cnf(1439,plain,
subset(the_InternalRel(skc7),empty_set),
inference(res,[status(thm),theory(equality)],[904,1254]),
[iquote('1:Res:904.0,1254.0')] ).
cnf(1442,plain,
( ~ empty(empty_set)
| ~ in(u,the_InternalRel(skc7)) ),
inference(res,[status(thm),theory(equality)],[1439,237]),
[iquote('1:Res:1439.0,237.1')] ).
cnf(1443,plain,
~ in(u,the_InternalRel(skc7)),
inference(ssi,[status(thm)],[1442,5,151]),
[iquote('1:SSi:1442.0,5.0,151.0')] ).
cnf(1444,plain,
$false,
inference(unc,[status(thm)],[1443,81]),
[iquote('1:UnC:1443.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08 % Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.08 % Command : run_spass %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Mon Jun 20 03:25:18 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.10/0.45
% 0.10/0.45 SPASS V 3.9
% 0.10/0.45 SPASS beiseite: Proof found.
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 SPASS derived 1242 clauses, backtracked 1 clauses, performed 1 splits and kept 692 clauses.
% 0.10/0.45 SPASS allocated 98928 KBytes.
% 0.10/0.45 SPASS spent 0:00:00.17 on the problem.
% 0.10/0.45 0:00:00.03 for the input.
% 0.10/0.45 0:00:00.02 for the FLOTTER CNF translation.
% 0.10/0.45 0:00:00.01 for inferences.
% 0.10/0.45 0:00:00.00 for the backtracking.
% 0.10/0.45 0:00:00.07 for the reduction.
% 0.10/0.45
% 0.10/0.45
% 0.10/0.45 Here is a proof with depth 8, length 65 :
% 0.10/0.45 % SZS output start Refutation
% See solution above
% 0.10/0.45 Formulae used in the proof : t25_orders_2 fc1_xboole_0 rc2_subset_1 t6_boole t3_subset cc1_relset_1 t2_subset dt_u1_orders_2 d6_orders_2 dt_m2_relset_1 t106_zfmisc_1 t4_subset t5_subset d9_orders_2 d4_relat_2
% 0.10/0.45
%------------------------------------------------------------------------------