%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET260-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:25:20 EDT 2022
% Result : Unsatisfiable 45.36s 45.54s
% Output : Refutation 45.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of clauses : 66 ( 23 unt; 16 nHn; 66 RR)
% Number of literals : 123 ( 0 equ; 50 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(x__dfg,y__dfg),xr),
file('SET260-6.p',unknown),
[] ).
cnf(2,axiom,
member(ordered_pair(x__dfg,y__dfg),cross_product(universal_class,universal_class)),
file('SET260-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(x__dfg,domain_of(xr)),
file('SET260-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET260-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET260-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET260-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET260-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET260-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET260-6.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET260-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET260-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
file('SET260-6.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET260-6.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
file('SET260-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET260-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET260-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET260-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET260-6.p',unknown),
[] ).
cnf(31,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET260-6.p',unknown),
[] ).
cnf(34,axiom,
( ~ member(u,universal_class)
| member(u,domain_of(v))
| equal(restrict(v,singleton(u),universal_class),null_class) ),
file('SET260-6.p',unknown),
[] ).
cnf(69,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET260-6.p',unknown),
[] ).
cnf(123,plain,
( ~ member(x__dfg,universal_class)
| equal(restrict(xr,singleton(x__dfg),universal_class),null_class) ),
inference(res,[status(thm),theory(equality)],[34,3]),
[iquote('0:Res:34.2,3.0')] ).
cnf(130,plain,
( ~ member(ordered_pair(x__dfg,y__dfg),u)
| member(ordered_pair(x__dfg,y__dfg),intersection(xr,u)) ),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.0')] ).
cnf(134,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,17]),
[iquote('0:Res:2.0,17.0')] ).
cnf(135,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(149,plain,
equal(restrict(xr,singleton(x__dfg),universal_class),null_class),
inference(mrr,[status(thm)],[123,134]),
[iquote('0:MRR:123.0,134.0')] ).
cnf(193,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[15,13]),
[iquote('0:SpR:15.0,13.1')] ).
cnf(207,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[69,27]),
[iquote('0:Res:69.1,27.1')] ).
cnf(221,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[5,25]),
[iquote('0:Res:5.1,25.0')] ).
cnf(429,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[69,4]),
[iquote('0:Res:69.1,4.0')] ).
cnf(575,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[15,11]),
[iquote('0:SpL:15.0,11.0')] ).
cnf(589,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[575]),
[iquote('0:Obv:575.1')] ).
cnf(592,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[69,589]),
[iquote('0:Res:69.1,589.0')] ).
cnf(593,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[5,589]),
[iquote('0:Res:5.1,589.0')] ).
cnf(800,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(804,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[592,69]),
[iquote('0:SpR:592.1,69.1')] ).
cnf(807,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[804]),
[iquote('0:Obv:804.0')] ).
cnf(2715,plain,
( subclass(singleton(u),v)
| subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[593,5]),
[iquote('0:SpR:593.1,5.1')] ).
cnf(2719,plain,
( subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[2715]),
[iquote('0:Obv:2715.0')] ).
cnf(2720,plain,
( subclass(null_class,u)
| member(v,singleton(v)) ),
inference(rew,[status(thm),theory(equality)],[807,2719]),
[iquote('0:Rew:807.0,2719.0')] ).
cnf(2723,plain,
subclass(null_class,u),
inference(spt,[spt(split,[position(s1)])],[2720]),
[iquote('1:Spt:2720.0')] ).
cnf(2725,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[2723,10]),
[iquote('1:Res:2723.0,10.0')] ).
cnf(3359,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[429,207]),
[iquote('0:Res:429.2,207.0')] ).
cnf(3377,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3359]),
[iquote('0:Obv:3359.1')] ).
cnf(3386,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[7,3377]),
[iquote('0:Res:7.0,3377.0')] ).
cnf(3411,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[3386,27]),
[iquote('0:SpL:3386.0,27.1')] ).
cnf(4313,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[221,6]),
[iquote('0:Res:221.1,6.0')] ).
cnf(4315,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[4313]),
[iquote('0:Obv:4313.0')] ).
cnf(4347,plain,
equal(intersection(u,null_class),null_class),
inference(res,[status(thm),theory(equality)],[4315,2725]),
[iquote('1:Res:4315.0,2725.0')] ).
cnf(4578,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[4347,24]),
[iquote('1:SpL:4347.0,24.0')] ).
cnf(4596,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[3411,4578]),
[iquote('1:MRR:3411.0,4578.1')] ).
cnf(5762,plain,
( ~ member(ordered_pair(x__dfg,y__dfg),cross_product(u,v))
| member(ordered_pair(x__dfg,y__dfg),restrict(xr,u,v)) ),
inference(spr,[status(thm),theory(equality)],[31,130]),
[iquote('0:SpR:31.0,130.1')] ).
cnf(10270,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,800]),
[iquote('0:Res:7.0,800.2')] ).
cnf(10277,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[10270]),
[iquote('0:Con:10270.1')] ).
cnf(54208,plain,
( ~ member(ordered_pair(x__dfg,y__dfg),cross_product(singleton(x__dfg),universal_class))
| member(ordered_pair(x__dfg,y__dfg),null_class) ),
inference(spr,[status(thm),theory(equality)],[149,5762]),
[iquote('0:SpR:149.0,5762.1')] ).
cnf(54231,plain,
~ member(ordered_pair(x__dfg,y__dfg),cross_product(singleton(x__dfg),universal_class)),
inference(mrr,[status(thm)],[54208,4596]),
[iquote('1:MRR:54208.1,4596.0')] ).
cnf(59375,plain,
( ~ member(y__dfg,universal_class)
| ~ member(x__dfg,singleton(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[19,54231]),
[iquote('1:Res:19.2,54231.0')] ).
cnf(59380,plain,
~ member(x__dfg,singleton(x__dfg)),
inference(mrr,[status(thm)],[59375,135]),
[iquote('1:MRR:59375.0,135.0')] ).
cnf(59385,plain,
~ member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[193,59380]),
[iquote('1:Res:193.1,59380.0')] ).
cnf(59387,plain,
$false,
inference(mrr,[status(thm)],[59385,134]),
[iquote('1:MRR:59385.0,134.0')] ).
cnf(59388,plain,
member(u,singleton(u)),
inference(spt,[spt(split,[position(s2)])],[2720]),
[iquote('1:Spt:59387.0,2720.1')] ).
cnf(59401,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[3411,10277]),
[iquote('0:MRR:3411.0,10277.1')] ).
cnf(59547,plain,
~ member(ordered_pair(x__dfg,y__dfg),cross_product(singleton(x__dfg),universal_class)),
inference(mrr,[status(thm)],[54208,59401]),
[iquote('0:MRR:54208.1,59401.0')] ).
cnf(59682,plain,
member(u,universal_class),
inference(res,[status(thm),theory(equality)],[59388,10277]),
[iquote('1:Res:59388.0,10277.0')] ).
cnf(69606,plain,
( ~ member(y__dfg,universal_class)
| ~ member(x__dfg,singleton(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[19,59547]),
[iquote('0:Res:19.2,59547.0')] ).
cnf(69613,plain,
$false,
inference(mrr,[status(thm)],[69606,59682,59388]),
[iquote('1:MRR:69606.0,69606.1,59682.0,59388.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET260-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 02:35:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 45.36/45.54
% 45.36/45.54 SPASS V 3.9
% 45.36/45.54 SPASS beiseite: Proof found.
% 45.36/45.54 % SZS status Theorem
% 45.36/45.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.36/45.54 SPASS derived 52572 clauses, backtracked 5046 clauses, performed 11 splits and kept 22811 clauses.
% 45.36/45.54 SPASS allocated 126622 KBytes.
% 45.36/45.54 SPASS spent 0:0:44.46 on the problem.
% 45.36/45.54 0:00:00.04 for the input.
% 45.36/45.54 0:00:00.00 for the FLOTTER CNF translation.
% 45.36/45.54 0:00:00.62 for inferences.
% 45.36/45.54 0:00:04.17 for the backtracking.
% 45.36/45.54 0:0:38.95 for the reduction.
% 45.36/45.54
% 45.36/45.54
% 45.36/45.54 Here is a proof with depth 7, length 66 :
% 45.36/45.54 % SZS output start Refutation
% See solution above
% 45.36/45.54 Formulae used in the proof : prove_domain_alternate_defn3_1 prove_domain_alternate_defn3_2 prove_domain_alternate_defn3_3 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal unordered_pair_member unordered_pair3 singleton_set cartesian_product1 cartesian_product2 cartesian_product3 intersection1 intersection2 intersection3 complement1 restriction1 domain2 regularity1
% 45.36/45.54
%------------------------------------------------------------------------------