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  
%------------------------------------------------------------------------------