%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 05:27:39 EDT 2022

% Result   : Theorem 0.17s 0.45s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (   9 unt;   1 nHn;  15 RR)
%            Number of literals    :   21 (   0 equ;  11 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( disjoint(u,v)
    | intersect(u,v) ),
    file('SET629+3.p',unknown),
    [] ).

cnf(2,axiom,
    equal(intersection(u,v),intersection(v,u)),
    file('SET629+3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ disjoint(intersection(skc3,skc2),difference(skc3,skc2)),
    file('SET629+3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET629+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ intersect(u,v)
    | member(skf2(v,u),u) ),
    file('SET629+3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ intersect(u,v)
    | member(skf2(v,w),v) ),
    file('SET629+3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ member(u,v)
    | ~ member(u,difference(w,v)) ),
    file('SET629+3.p',unknown),
    [] ).

cnf(19,plain,
    ~ disjoint(intersection(skc2,skc3),difference(skc3,skc2)),
    inference(rew,[status(thm),theory(equality)],[2,4]),
    [iquote('0:Rew:2.0,4.0')] ).

cnf(20,plain,
    intersect(intersection(skc2,skc3),difference(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[1,19]),
    [iquote('0:Res:1.1,19.0')] ).

cnf(34,plain,
    member(skf2(difference(skc3,skc2),u),difference(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[20,10]),
    [iquote('0:Res:20.0,10.0')] ).

cnf(45,plain,
    ( ~ intersect(intersection(u,v),w)
    | member(skf2(w,intersection(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[9,7]),
    [iquote('0:Res:9.1,7.0')] ).

cnf(58,plain,
    ~ member(skf2(difference(skc3,skc2),u),skc2),
    inference(res,[status(thm),theory(equality)],[34,11]),
    [iquote('0:Res:34.0,11.1')] ).

cnf(164,plain,
    ~ intersect(intersection(u,skc2),difference(skc3,skc2)),
    inference(res,[status(thm),theory(equality)],[45,58]),
    [iquote('0:Res:45.1,58.0')] ).

cnf(173,plain,
    ~ intersect(intersection(skc2,u),difference(skc3,skc2)),
    inference(spl,[status(thm),theory(equality)],[2,164]),
    [iquote('0:SpL:2.0,164.0')] ).

cnf(177,plain,
    $false,
    inference(unc,[status(thm)],[173,20]),
    [iquote('0:UnC:173.0,20.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n005.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 09:57:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.17/0.45  
% 0.17/0.45  SPASS V 3.9 
% 0.17/0.45  SPASS beiseite: Proof found.
% 0.17/0.45  % SZS status Theorem
% 0.17/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.17/0.45  SPASS derived 157 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.17/0.45  SPASS allocated 85324 KBytes.
% 0.17/0.45  SPASS spent	0:00:00.11 on the problem.
% 0.17/0.45  		0:00:00.04 for the input.
% 0.17/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.17/0.45  		0:00:00.00 for inferences.
% 0.17/0.45  		0:00:00.00 for the backtracking.
% 0.17/0.45  		0:00:00.01 for the reduction.
% 0.17/0.45  
% 0.17/0.45  
% 0.17/0.45  Here is a proof with depth 5, length 15 :
% 0.17/0.45  % SZS output start Refutation
% See solution above
% 0.17/0.45  Formulae used in the proof : disjoint_defn commutativity_of_intersection prove_intersection_and_difference_disjoint intersection_defn intersect_defn difference_defn
% 0.17/0.45  
%------------------------------------------------------------------------------