TSTP Solution File: SET144-6 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET144-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:24:29 EDT 2022

% Result   : Unsatisfiable 44.62s 44.83s
% Output   : Refutation 44.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   3 unt;   5 nHn;  16 RR)
%            Number of literals    :   33 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(intersection(y__dfg,x__dfg),intersection(x__dfg,y__dfg)),
    file('SET144-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subclass(u,v)
    | ~ subclass(v,u)
    | equal(v,u) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET144-6.p',unknown),
    [] ).

cnf(117,plain,
    ( ~ subclass(intersection(x__dfg,y__dfg),intersection(y__dfg,x__dfg))
    | ~ subclass(intersection(y__dfg,x__dfg),intersection(x__dfg,y__dfg)) ),
    inference(res,[status(thm),theory(equality)],[8,1]),
    [iquote('0:Res:8.2,1.0')] ).

cnf(163,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(169,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),u) ),
    inference(res,[status(thm),theory(equality)],[3,22]),
    [iquote('0:Res:3.1,22.0')] ).

cnf(789,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(11001,plain,
    ( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
    | subclass(intersection(u,v),intersection(w,u))
    | subclass(intersection(u,v),intersection(w,u)) ),
    inference(res,[status(thm),theory(equality)],[169,789]),
    [iquote('0:Res:169.1,789.0')] ).

cnf(11022,plain,
    ( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
    | subclass(intersection(u,v),intersection(w,u)) ),
    inference(obv,[status(thm),theory(equality)],[11001]),
    [iquote('0:Obv:11001.1')] ).

cnf(67649,plain,
    ( subclass(intersection(u,v),intersection(v,u))
    | subclass(intersection(u,v),intersection(v,u)) ),
    inference(res,[status(thm),theory(equality)],[163,11022]),
    [iquote('0:Res:163.1,11022.0')] ).

cnf(67664,plain,
    subclass(intersection(u,v),intersection(v,u)),
    inference(obv,[status(thm),theory(equality)],[67649]),
    [iquote('0:Obv:67649.0')] ).

cnf(67665,plain,
    $false,
    inference(mrr,[status(thm)],[117,67664]),
    [iquote('0:MRR:117.1,117.0,67664.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET144-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n020.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 : Sun Jul 10 14:45:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 44.62/44.83  
% 44.62/44.83  SPASS V 3.9 
% 44.62/44.83  SPASS beiseite: Proof found.
% 44.62/44.83  % SZS status Theorem
% 44.62/44.83  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 44.62/44.83  SPASS derived 49812 clauses, backtracked 239 clauses, performed 8 splits and kept 17890 clauses.
% 44.62/44.83  SPASS allocated 132652 KBytes.
% 44.62/44.83  SPASS spent	0:0:43.66 on the problem.
% 44.62/44.83  		0:00:00.04 for the input.
% 44.62/44.83  		0:00:00.00 for the FLOTTER CNF translation.
% 44.62/44.83  		0:00:00.52 for inferences.
% 44.62/44.83  		0:00:05.16 for the backtracking.
% 44.62/44.83  		0:0:37.45 for the reduction.
% 44.62/44.83  
% 44.62/44.83  
% 44.62/44.83  Here is a proof with depth 3, length 16 :
% 44.62/44.83  % SZS output start Refutation
% See solution above
% 44.62/44.83  Formulae used in the proof : prove_commutativity_of_intersection_1 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection2 intersection3
% 44.62/44.83  
%------------------------------------------------------------------------------