%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:27:33 EDT 2022

% Result   : Theorem 2.66s 2.87s
% Output   : Refutation 2.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (  17 unt;   0 nHn;  17 RR)
%            Number of literals    :   17 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    equal(union(u,v),union(v,u)),
    file('SET620+3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(intersection(u,v),intersection(v,u)),
    file('SET620+3.p',unknown),
    [] ).

cnf(6,axiom,
    equal(symmetric_difference(u,v),symmetric_difference(v,u)),
    file('SET620+3.p',unknown),
    [] ).

cnf(8,axiom,
    equal(difference(u,intersection(u,v)),difference(u,v)),
    file('SET620+3.p',unknown),
    [] ).

cnf(16,axiom,
    equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
    file('SET620+3.p',unknown),
    [] ).

cnf(21,axiom,
    ~ equal(difference(union(skc3,skc2),intersection(skc3,skc2)),symmetric_difference(skc3,skc2)),
    file('SET620+3.p',unknown),
    [] ).

cnf(24,axiom,
    equal(union(difference(u,v),difference(w,v)),difference(union(u,w),v)),
    file('SET620+3.p',unknown),
    [] ).

cnf(28,plain,
    ~ equal(difference(union(skc2,skc3),intersection(skc2,skc3)),symmetric_difference(skc2,skc3)),
    inference(rew,[status(thm),theory(equality)],[4,21,5,6]),
    [iquote('0:Rew:4.0,21.0,5.0,21.0,6.0,21.0')] ).

cnf(48,plain,
    equal(difference(u,intersection(v,u)),difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[5,8]),
    [iquote('0:SpR:5.0,8.0')] ).

cnf(145,plain,
    equal(union(difference(u,v),difference(w,v)),difference(union(w,u),v)),
    inference(spr,[status(thm),theory(equality)],[24,4]),
    [iquote('0:SpR:24.0,4.0')] ).

cnf(151,plain,
    equal(union(difference(u,intersection(v,w)),difference(v,w)),difference(union(u,v),intersection(v,w))),
    inference(spr,[status(thm),theory(equality)],[8,24]),
    [iquote('0:SpR:8.0,24.0')] ).

cnf(156,plain,
    equal(difference(union(u,v),w),difference(union(v,u),w)),
    inference(rew,[status(thm),theory(equality)],[24,145]),
    [iquote('0:Rew:24.0,145.0')] ).

cnf(158,plain,
    equal(union(difference(u,v),difference(w,intersection(u,v))),difference(union(w,u),intersection(u,v))),
    inference(rew,[status(thm),theory(equality)],[4,151]),
    [iquote('0:Rew:4.0,151.0')] ).

cnf(2235,plain,
    equal(union(difference(u,v),difference(v,u)),difference(union(v,u),intersection(u,v))),
    inference(spr,[status(thm),theory(equality)],[48,158]),
    [iquote('0:SpR:48.0,158.0')] ).

cnf(2268,plain,
    equal(difference(union(u,v),intersection(v,u)),symmetric_difference(v,u)),
    inference(rew,[status(thm),theory(equality)],[16,2235]),
    [iquote('0:Rew:16.0,2235.0')] ).

cnf(11512,plain,
    equal(difference(union(u,v),intersection(u,v)),symmetric_difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[2268,156]),
    [iquote('0:SpR:2268.0,156.0')] ).

cnf(11573,plain,
    $false,
    inference(unc,[status(thm)],[11512,28]),
    [iquote('0:UnC:11512.0,28.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.15  % Command  : run_spass %d %s
% 0.14/0.37  % Computer : n027.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 600
% 0.14/0.37  % DateTime : Mon Jul 11 06:05:18 EDT 2022
% 0.14/0.37  % CPUTime  : 
% 2.66/2.87  
% 2.66/2.87  SPASS V 3.9 
% 2.66/2.87  SPASS beiseite: Proof found.
% 2.66/2.87  % SZS status Theorem
% 2.66/2.87  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 2.66/2.87  SPASS derived 9370 clauses, backtracked 0 clauses, performed 0 splits and kept 2655 clauses.
% 2.66/2.87  SPASS allocated 94423 KBytes.
% 2.66/2.87  SPASS spent	0:00:02.43 on the problem.
% 2.66/2.87  		0:00:00.04 for the input.
% 2.66/2.87  		0:00:00.03 for the FLOTTER CNF translation.
% 2.66/2.87  		0:00:00.08 for inferences.
% 2.66/2.87  		0:00:00.00 for the backtracking.
% 2.66/2.87  		0:00:02.25 for the reduction.
% 2.66/2.87  
% 2.66/2.87  
% 2.66/2.87  Here is a proof with depth 3, length 17 :
% 2.66/2.87  % SZS output start Refutation
% See solution above
% 2.66/2.87  Formulae used in the proof : commutativity_of_union commutativity_of_intersection commutativity_of_symmetric_difference difference_into_intersection symmetric_difference_defn prove_th96 difference_distributes_over_union
% 2.66/2.87  
%------------------------------------------------------------------------------