TSTP Solution File: SET257-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET257-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 05:25:19 EDT 2022

% Result   : Unsatisfiable 11.42s 11.61s
% Output   : Refutation 11.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   20 (   8 unt;   5 nHn;  20 RR)
%            Number of literals    :   36 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg),cross_product(x__dfg,y__dfg)),
    file('SET257-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET257-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET257-6.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subclass(u,v)
    | ~ subclass(v,u)
    | equal(v,u) ),
    file('SET257-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET257-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET257-6.p',unknown),
    [] ).

cnf(30,axiom,
    equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
    file('SET257-6.p',unknown),
    [] ).

cnf(120,plain,
    ( ~ subclass(cross_product(x__dfg,y__dfg),restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg))
    | ~ subclass(restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg),cross_product(x__dfg,y__dfg)) ),
    inference(res,[status(thm),theory(equality)],[8,1]),
    [iquote('0:Res:8.2,1.0')] ).

cnf(167,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),v) ),
    inference(res,[status(thm),theory(equality)],[3,23]),
    [iquote('0:Res:3.1,23.0')] ).

cnf(793,plain,
    ( ~ member(not_subclass_element(u,intersection(v,w)),w)
    | ~ member(not_subclass_element(u,intersection(v,w)),v)
    | subclass(u,intersection(v,w)) ),
    inference(res,[status(thm),theory(equality)],[24,4]),
    [iquote('0:Res:24.2,4.0')] ).

cnf(2772,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[167,4]),
    [iquote('0:Res:167.1,4.0')] ).

cnf(2774,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[2772]),
    [iquote('0:Obv:2772.0')] ).

cnf(2794,plain,
    subclass(restrict(u,v,w),u),
    inference(spr,[status(thm),theory(equality)],[30,2774]),
    [iquote('0:SpR:30.0,2774.0')] ).

cnf(2918,plain,
    ~ subclass(cross_product(x__dfg,y__dfg),restrict(cross_product(x__dfg,y__dfg),x__dfg,y__dfg)),
    inference(mrr,[status(thm)],[120,2794]),
    [iquote('0:MRR:120.1,2794.0')] ).

cnf(11094,plain,
    ( ~ member(not_subclass_element(u,intersection(v,u)),v)
    | subclass(u,intersection(v,u))
    | subclass(u,intersection(v,u)) ),
    inference(res,[status(thm),theory(equality)],[3,793]),
    [iquote('0:Res:3.1,793.0')] ).

cnf(11111,plain,
    ( ~ member(not_subclass_element(u,intersection(v,u)),v)
    | subclass(u,intersection(v,u)) ),
    inference(obv,[status(thm),theory(equality)],[11094]),
    [iquote('0:Obv:11094.1')] ).

cnf(24220,plain,
    ( subclass(u,intersection(u,u))
    | subclass(u,intersection(u,u)) ),
    inference(res,[status(thm),theory(equality)],[3,11111]),
    [iquote('0:Res:3.1,11111.0')] ).

cnf(24247,plain,
    subclass(u,intersection(u,u)),
    inference(obv,[status(thm),theory(equality)],[24220]),
    [iquote('0:Obv:24220.0')] ).

cnf(26326,plain,
    subclass(cross_product(u,v),restrict(cross_product(u,v),u,v)),
    inference(spr,[status(thm),theory(equality)],[30,24247]),
    [iquote('0:SpR:30.0,24247.0')] ).

cnf(26374,plain,
    $false,
    inference(unc,[status(thm)],[26326,2918]),
    [iquote('0:UnC:26326.0,2918.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET257-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n012.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 Jul 10 09:22:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 11.42/11.61  
% 11.42/11.61  SPASS V 3.9 
% 11.42/11.61  SPASS beiseite: Proof found.
% 11.42/11.61  % SZS status Theorem
% 11.42/11.61  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 11.42/11.61  SPASS derived 20524 clauses, backtracked 208 clauses, performed 5 splits and kept 9444 clauses.
% 11.42/11.61  SPASS allocated 99163 KBytes.
% 11.42/11.61  SPASS spent	0:0:11.06 on the problem.
% 11.42/11.61  		0:00:00.04 for the input.
% 11.42/11.61  		0:00:00.00 for the FLOTTER CNF translation.
% 11.42/11.61  		0:00:00.22 for inferences.
% 11.42/11.61  		0:00:00.86 for the backtracking.
% 11.42/11.61  		0:00:09.77 for the reduction.
% 11.42/11.61  
% 11.42/11.61  
% 11.42/11.61  Here is a proof with depth 4, length 20 :
% 11.42/11.61  % SZS output start Refutation
% See solution above
% 11.42/11.61  Formulae used in the proof : prove_restriction_property5_1 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection2 intersection3 restriction2
% 11.42/11.61  
%------------------------------------------------------------------------------