%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET630+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 05:27:40 EDT 2022

% Result   : Theorem 0.47s 0.69s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (  11 unt;   4 nHn;  17 RR)
%            Number of literals    :   25 (   0 equ;   8 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; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( disjoint(u,v)
    | intersect(u,v) ),
    file('SET630+3.p',unknown),
    [] ).

cnf(2,axiom,
    disjoint(intersection(u,v),difference(u,v)),
    file('SET630+3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(intersection(u,v),intersection(v,u)),
    file('SET630+3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(symmetric_difference(u,v),symmetric_difference(v,u)),
    file('SET630+3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ disjoint(intersection(skc3,skc2),symmetric_difference(skc3,skc2)),
    file('SET630+3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ intersect(u,v)
    | ~ disjoint(u,v) ),
    file('SET630+3.p',unknown),
    [] ).

cnf(15,axiom,
    equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
    file('SET630+3.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ intersect(u,union(v,w))
    | intersect(u,v)
    | intersect(u,w) ),
    file('SET630+3.p',unknown),
    [] ).

cnf(23,plain,
    ~ disjoint(intersection(skc2,skc3),symmetric_difference(skc2,skc3)),
    inference(rew,[status(thm),theory(equality)],[4,7,5]),
    [iquote('0:Rew:4.0,7.0,5.0,7.0')] ).

cnf(24,plain,
    intersect(intersection(skc2,skc3),symmetric_difference(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[1,23]),
    [iquote('0:Res:1.1,23.0')] ).

cnf(29,plain,
    disjoint(intersection(u,v),difference(v,u)),
    inference(spr,[status(thm),theory(equality)],[4,2]),
    [iquote('0:SpR:4.0,2.0')] ).

cnf(160,plain,
    ( ~ intersect(u,symmetric_difference(v,w))
    | intersect(u,difference(v,w))
    | intersect(u,difference(w,v)) ),
    inference(spl,[status(thm),theory(equality)],[15,19]),
    [iquote('0:SpL:15.0,19.0')] ).

cnf(565,plain,
    ( intersect(intersection(skc2,skc3),difference(skc2,skc3))
    | intersect(intersection(skc2,skc3),difference(skc3,skc2)) ),
    inference(res,[status(thm),theory(equality)],[24,160]),
    [iquote('0:Res:24.0,160.0')] ).

cnf(3712,plain,
    ( ~ disjoint(intersection(skc2,skc3),difference(skc3,skc2))
    | intersect(intersection(skc2,skc3),difference(skc2,skc3)) ),
    inference(res,[status(thm),theory(equality)],[565,8]),
    [iquote('0:Res:565.1,8.0')] ).

cnf(3727,plain,
    intersect(intersection(skc2,skc3),difference(skc2,skc3)),
    inference(mrr,[status(thm)],[3712,29]),
    [iquote('0:MRR:3712.0,29.0')] ).

cnf(3735,plain,
    ~ disjoint(intersection(skc2,skc3),difference(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[3727,8]),
    [iquote('0:Res:3727.0,8.0')] ).

cnf(3750,plain,
    $false,
    inference(mrr,[status(thm)],[3735,2]),
    [iquote('0:MRR:3735.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET630+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n029.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul 10 19:13:01 EDT 2022
% 0.11/0.34  % CPUTime  : 
% 0.47/0.69  
% 0.47/0.69  SPASS V 3.9 
% 0.47/0.69  SPASS beiseite: Proof found.
% 0.47/0.69  % SZS status Theorem
% 0.47/0.69  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.69  SPASS derived 3457 clauses, backtracked 0 clauses, performed 2 splits and kept 985 clauses.
% 0.47/0.69  SPASS allocated 87086 KBytes.
% 0.47/0.69  SPASS spent	0:00:00.33 on the problem.
% 0.47/0.69  		0:00:00.04 for the input.
% 0.47/0.69  		0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.69  		0:00:00.03 for inferences.
% 0.47/0.69  		0:00:00.00 for the backtracking.
% 0.47/0.69  		0:00:00.21 for the reduction.
% 0.47/0.69  
% 0.47/0.69  
% 0.47/0.69  Here is a proof with depth 4, length 17 :
% 0.47/0.69  % SZS output start Refutation
% See solution above
% 0.47/0.69  Formulae used in the proof : disjoint_defn intersection_and_union_disjoint commutativity_of_intersection commutativity_of_symmetric_difference prove_intersection_and_symmetric_difference_disjoint symmetric_difference_defn intersect_with_union
% 0.47/0.69  
%------------------------------------------------------------------------------