%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET002+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 05:22:19 EDT 2022

% Result   : Theorem 2.20s 2.36s
% Output   : Refutation 2.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   5 unt;   6 nHn;  16 RR)
%            Number of literals    :   30 (   0 equ;  10 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ equal_set(union(skc1,skc1),skc1),
    file('SET002+4.p',unknown),
    [] ).

cnf(7,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET002+4.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(skf3(u,v),u)
    | subset(w,u) ),
    file('SET002+4.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ member(u,v)
    | member(u,union(w,v)) ),
    file('SET002+4.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal_set(v,u) ),
    file('SET002+4.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,union(v,w))
    | member(u,v)
    | member(u,w) ),
    file('SET002+4.p',unknown),
    [] ).

cnf(31,plain,
    ( ~ subset(skc1,union(skc1,skc1))
    | ~ subset(union(skc1,skc1),skc1) ),
    inference(res,[status(thm),theory(equality)],[24,3]),
    [iquote('0:Res:24.2,3.0')] ).

cnf(45,plain,
    ( ~ member(skf3(union(u,v),w),v)
    | subset(x,union(u,v)) ),
    inference(res,[status(thm),theory(equality)],[16,12]),
    [iquote('0:Res:16.1,12.0')] ).

cnf(177,plain,
    ( subset(union(u,v),w)
    | member(skf3(w,union(u,v)),u)
    | member(skf3(w,union(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[7,25]),
    [iquote('0:Res:7.1,25.0')] ).

cnf(774,plain,
    ( subset(u,union(v,u))
    | subset(w,union(v,u)) ),
    inference(res,[status(thm),theory(equality)],[7,45]),
    [iquote('0:Res:7.1,45.0')] ).

cnf(779,plain,
    subset(u,union(v,u)),
    inference(con,[status(thm)],[774]),
    [iquote('0:Con:774.1')] ).

cnf(780,plain,
    ~ subset(union(skc1,skc1),skc1),
    inference(mrr,[status(thm)],[31,779]),
    [iquote('0:MRR:31.0,779.0')] ).

cnf(3203,plain,
    ( subset(union(u,u),v)
    | member(skf3(v,union(u,u)),u) ),
    inference(fac,[status(thm)],[177]),
    [iquote('0:Fac:177.1,177.2')] ).

cnf(6749,plain,
    ( subset(union(u,u),u)
    | subset(v,u) ),
    inference(res,[status(thm),theory(equality)],[3203,12]),
    [iquote('0:Res:3203.1,12.0')] ).

cnf(6766,plain,
    subset(union(u,u),u),
    inference(con,[status(thm)],[6749]),
    [iquote('0:Con:6749.1')] ).

cnf(6767,plain,
    $false,
    inference(unc,[status(thm)],[6766,780]),
    [iquote('0:UnC:6766.0,780.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET002+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 02:35:43 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 2.20/2.36  
% 2.20/2.36  SPASS V 3.9 
% 2.20/2.36  SPASS beiseite: Proof found.
% 2.20/2.36  % SZS status Theorem
% 2.20/2.36  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.20/2.36  SPASS derived 5837 clauses, backtracked 0 clauses, performed 0 splits and kept 3598 clauses.
% 2.20/2.36  SPASS allocated 90852 KBytes.
% 2.20/2.36  SPASS spent	0:00:01.97 on the problem.
% 2.20/2.36  		0:00:00.04 for the input.
% 2.20/2.36  		0:00:00.04 for the FLOTTER CNF translation.
% 2.20/2.36  		0:00:00.07 for inferences.
% 2.20/2.36  		0:00:00.00 for the backtracking.
% 2.20/2.36  		0:00:01.77 for the reduction.
% 2.20/2.36  
% 2.20/2.36  
% 2.20/2.36  Here is a proof with depth 3, length 16 :
% 2.20/2.36  % SZS output start Refutation
% See solution above
% 2.20/2.36  Formulae used in the proof : thI14 subset union equal_set
% 2.20/2.36  
%------------------------------------------------------------------------------