TSTP Solution File: NUM030-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM030-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:23:46 EDT 2022
% Result : Unsatisfiable 134.80s 135.02s
% Output : Refutation 134.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of clauses : 46 ( 15 unt; 16 nHn; 46 RR)
% Number of literals : 90 ( 0 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(symmetrization_of(x__dfg),x__dfg),
file('NUM030-1.p',unknown),
[] ).
cnf(2,axiom,
~ subclass(inverse(x__dfg),x__dfg),
file('NUM030-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('NUM030-1.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('NUM030-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('NUM030-1.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('NUM030-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('NUM030-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('NUM030-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('NUM030-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('NUM030-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('NUM030-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('NUM030-1.p',unknown),
[] ).
cnf(28,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('NUM030-1.p',unknown),
[] ).
cnf(115,axiom,
equal(union(u,inverse(u)),symmetrization_of(u)),
file('NUM030-1.p',unknown),
[] ).
cnf(288,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.1,26.1')] ).
cnf(339,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[4,23]),
[iquote('0:Res:4.1,23.0')] ).
cnf(967,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[27,5]),
[iquote('0:Res:27.2,5.0')] ).
cnf(1012,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[27,288]),
[iquote('0:Res:27.2,288.0')] ).
cnf(1406,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.1,3.0')] ).
cnf(5246,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[25,3]),
[iquote('0:Res:25.2,3.0')] ).
cnf(13514,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[339,5]),
[iquote('0:Res:339.1,5.0')] ).
cnf(13518,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[13514]),
[iquote('0:Obv:13514.0')] ).
cnf(38518,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[1406,967]),
[iquote('0:Res:1406.2,967.0')] ).
cnf(38529,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[38518]),
[iquote('0:Obv:38518.1')] ).
cnf(38985,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[6,5246]),
[iquote('0:Res:6.0,5246.2')] ).
cnf(38992,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[38985]),
[iquote('0:Con:38985.1')] ).
cnf(39040,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[4,38992]),
[iquote('0:Res:4.1,38992.0')] ).
cnf(39264,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1012,39040]),
[iquote('0:MRR:1012.0,39040.1')] ).
cnf(56491,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[38529,6]),
[iquote('0:MRR:38529.0,6.0')] ).
cnf(131215,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[39264,5]),
[iquote('0:Res:39264.0,5.0')] ).
cnf(131219,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[131215]),
[iquote('0:Obv:131215.0')] ).
cnf(131241,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[28,131219]),
[iquote('0:SpR:28.0,131219.0')] ).
cnf(132555,plain,
subclass(complement(symmetrization_of(u)),intersection(complement(u),complement(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[115,131241]),
[iquote('0:SpR:115.0,131241.0')] ).
cnf(132610,plain,
subclass(complement(x__dfg),intersection(complement(x__dfg),complement(inverse(x__dfg)))),
inference(spr,[status(thm),theory(equality)],[1,132555]),
[iquote('0:SpR:1.0,132555.0')] ).
cnf(132656,plain,
( ~ subclass(intersection(complement(x__dfg),complement(inverse(x__dfg))),complement(x__dfg))
| equal(intersection(complement(x__dfg),complement(inverse(x__dfg))),complement(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[132610,9]),
[iquote('0:Res:132610.0,9.0')] ).
cnf(132659,plain,
equal(intersection(complement(x__dfg),complement(inverse(x__dfg))),complement(x__dfg)),
inference(mrr,[status(thm)],[132656,13518]),
[iquote('0:MRR:132656.0,13518.0')] ).
cnf(132668,plain,
equal(union(x__dfg,inverse(x__dfg)),complement(complement(x__dfg))),
inference(spr,[status(thm),theory(equality)],[132659,28]),
[iquote('0:SpR:132659.0,28.0')] ).
cnf(132709,plain,
( ~ member(u,complement(x__dfg))
| member(u,complement(inverse(x__dfg))) ),
inference(spl,[status(thm),theory(equality)],[132659,24]),
[iquote('0:SpL:132659.0,24.0')] ).
cnf(132716,plain,
equal(complement(complement(x__dfg)),x__dfg),
inference(rew,[status(thm),theory(equality)],[1,132668,115]),
[iquote('0:Rew:1.0,132668.0,115.0,132668.0')] ).
cnf(132775,plain,
( member(not_subclass_element(u,x__dfg),complement(x__dfg))
| subclass(u,complement(complement(x__dfg))) ),
inference(spr,[status(thm),theory(equality)],[132716,56491]),
[iquote('0:SpR:132716.0,56491.0')] ).
cnf(132840,plain,
( member(not_subclass_element(u,x__dfg),complement(x__dfg))
| subclass(u,x__dfg) ),
inference(rew,[status(thm),theory(equality)],[132716,132775]),
[iquote('0:Rew:132716.0,132775.1')] ).
cnf(150945,plain,
( ~ member(u,complement(x__dfg))
| ~ member(u,inverse(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[132709,26]),
[iquote('0:Res:132709.1,26.1')] ).
cnf(151416,plain,
( ~ member(not_subclass_element(u,x__dfg),inverse(x__dfg))
| subclass(u,x__dfg) ),
inference(res,[status(thm),theory(equality)],[132840,150945]),
[iquote('0:Res:132840.0,150945.0')] ).
cnf(152476,plain,
( subclass(inverse(x__dfg),x__dfg)
| subclass(inverse(x__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[4,151416]),
[iquote('0:Res:4.1,151416.0')] ).
cnf(152482,plain,
subclass(inverse(x__dfg),x__dfg),
inference(obv,[status(thm),theory(equality)],[152476]),
[iquote('0:Obv:152476.0')] ).
cnf(152483,plain,
$false,
inference(mrr,[status(thm)],[152482,2]),
[iquote('0:MRR:152482.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : NUM030-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.02/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n011.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Thu Jul 7 08:19:38 EDT 2022
% 0.08/0.28 % CPUTime :
% 134.80/135.02
% 134.80/135.02 SPASS V 3.9
% 134.80/135.02 SPASS beiseite: Proof found.
% 134.80/135.02 % SZS status Theorem
% 134.80/135.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 134.80/135.02 SPASS derived 122564 clauses, backtracked 21901 clauses, performed 57 splits and kept 60283 clauses.
% 134.80/135.02 SPASS allocated 172922 KBytes.
% 134.80/135.02 SPASS spent 0:2:10.94 on the problem.
% 134.80/135.02 0:00:00.03 for the input.
% 134.80/135.02 0:00:00.00 for the FLOTTER CNF translation.
% 134.80/135.02 0:00:01.82 for inferences.
% 134.80/135.02 0:0:13.80 for the backtracking.
% 134.80/135.02 0:1:53.20 for the reduction.
% 134.80/135.02
% 134.80/135.02
% 134.80/135.02 Here is a proof with depth 11, length 46 :
% 134.80/135.02 % SZS output start Refutation
% See solution above
% 134.80/135.02 Formulae used in the proof : prove_symmetrization_property3_1 prove_symmetrization_property3_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection1 intersection2 intersection3 complement1 complement2 union symmetrization
% 134.80/135.02
%------------------------------------------------------------------------------