%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET074-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 05:23:36 EDT 2022

% Result   : Unsatisfiable 0.20s 0.48s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   8 unt;   3 nHn;  14 RR)
%            Number of literals    :   21 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(y__dfg,universal_class),
    file('SET074-6.p',unknown),
    [] ).

cnf(2,axiom,
    equal(unordered_pair(x__dfg,y__dfg),null_class),
    file('SET074-6.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(v,u)) ),
    file('SET074-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET074-6.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET074-6.p',unknown),
    [] ).

cnf(69,axiom,
    ( equal(u,null_class)
    | equal(intersection(u,regular(u)),null_class) ),
    file('SET074-6.p',unknown),
    [] ).

cnf(100,plain,
    member(y__dfg,unordered_pair(u,y__dfg)),
    inference(res,[status(thm),theory(equality)],[1,12]),
    [iquote('0:Res:1.0,12.0')] ).

cnf(108,plain,
    ~ member(y__dfg,complement(universal_class)),
    inference(res,[status(thm),theory(equality)],[1,26]),
    [iquote('0:Res:1.0,26.1')] ).

cnf(334,plain,
    member(y__dfg,null_class),
    inference(spr,[status(thm),theory(equality)],[2,100]),
    [iquote('0:SpR:2.0,100.0')] ).

cnf(351,plain,
    ( ~ member(u,null_class)
    | equal(v,null_class)
    | member(u,v) ),
    inference(spl,[status(thm),theory(equality)],[69,23]),
    [iquote('0:SpL:69.1,23.0')] ).

cnf(456,plain,
    ( equal(u,null_class)
    | member(y__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[334,351]),
    [iquote('0:Res:334.0,351.0')] ).

cnf(461,plain,
    equal(complement(universal_class),null_class),
    inference(res,[status(thm),theory(equality)],[456,108]),
    [iquote('0:Res:456.1,108.0')] ).

cnf(469,plain,
    ~ member(y__dfg,null_class),
    inference(rew,[status(thm),theory(equality)],[461,108]),
    [iquote('0:Rew:461.0,108.0')] ).

cnf(470,plain,
    $false,
    inference(mrr,[status(thm)],[469,334]),
    [iquote('0:MRR:469.0,334.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET074-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n022.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 : Sat Jul  9 17:02:55 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.48  
% 0.20/0.48  SPASS V 3.9 
% 0.20/0.48  SPASS beiseite: Proof found.
% 0.20/0.48  % SZS status Theorem
% 0.20/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.48  SPASS derived 349 clauses, backtracked 21 clauses, performed 1 splits and kept 330 clauses.
% 0.20/0.48  SPASS allocated 76108 KBytes.
% 0.20/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.20/0.48  		0:00:00.04 for the input.
% 0.20/0.48  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48  		0:00:00.01 for inferences.
% 0.20/0.48  		0:00:00.00 for the backtracking.
% 0.20/0.48  		0:00:00.05 for the reduction.
% 0.20/0.48  
% 0.20/0.48  
% 0.20/0.48  Here is a proof with depth 4, length 14 :
% 0.20/0.48  % SZS output start Refutation
% See solution above
% 0.20/0.48  Formulae used in the proof : prove_corollary_to_unordered_pair_axiom2_1 prove_corollary_to_unordered_pair_axiom2_2 unordered_pair3 intersection1 complement1 regularity2
% 0.20/0.48  
%------------------------------------------------------------------------------