%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 05:28:45 EDT 2022

% Result   : Theorem 0.51s 0.70s
% Output   : Refutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   9 unt;   0 nHn;  15 RR)
%            Number of literals    :   23 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;  10 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    subset(skc9,skc8),
    file('SET800+4.p',unknown),
    [] ).

cnf(6,axiom,
    greatest_lower_bound(skc11,skc9,skc6,skc7),
    file('SET800+4.p',unknown),
    [] ).

cnf(7,axiom,
    ~ apply(skc6,skc10,skc11),
    file('SET800+4.p',unknown),
    [] ).

cnf(8,axiom,
    greatest_lower_bound(skc10,skc8,skc6,skc7),
    file('SET800+4.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ greatest_lower_bound(u,v,w,x)
    | member(u,v) ),
    file('SET800+4.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ greatest_lower_bound(u,v,w,x)
    | lower_bound(u,w,v) ),
    file('SET800+4.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ member(u,v)
    | ~ subset(v,w)
    | member(u,w) ),
    file('SET800+4.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ member(u,v)
    | ~ lower_bound(w,x,v)
    | apply(x,w,u) ),
    file('SET800+4.p',unknown),
    [] ).

cnf(109,plain,
    ( ~ member(u,skc9)
    | member(u,skc8) ),
    inference(res,[status(thm),theory(equality)],[2,45]),
    [iquote('0:Res:2.0,45.0')] ).

cnf(116,plain,
    lower_bound(skc10,skc6,skc8),
    inference(res,[status(thm),theory(equality)],[8,44]),
    [iquote('0:Res:8.0,44.0')] ).

cnf(123,plain,
    ( ~ member(skc11,u)
    | ~ lower_bound(skc10,skc6,u) ),
    inference(res,[status(thm),theory(equality)],[63,7]),
    [iquote('0:Res:63.2,7.0')] ).

cnf(129,plain,
    member(skc11,skc9),
    inference(res,[status(thm),theory(equality)],[6,38]),
    [iquote('0:Res:6.0,38.0')] ).

cnf(139,plain,
    member(skc11,skc8),
    inference(res,[status(thm),theory(equality)],[129,109]),
    [iquote('0:Res:129.0,109.0')] ).

cnf(195,plain,
    ~ member(skc11,skc8),
    inference(res,[status(thm),theory(equality)],[116,123]),
    [iquote('0:Res:116.0,123.1')] ).

cnf(196,plain,
    $false,
    inference(mrr,[status(thm)],[195,139]),
    [iquote('0:MRR:195.0,139.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n006.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 23:22:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.51/0.70  
% 0.51/0.70  SPASS V 3.9 
% 0.51/0.70  SPASS beiseite: Proof found.
% 0.51/0.70  % SZS status Theorem
% 0.51/0.70  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.51/0.70  SPASS derived 99 clauses, backtracked 0 clauses, performed 2 splits and kept 169 clauses.
% 0.51/0.70  SPASS allocated 88316 KBytes.
% 0.51/0.70  SPASS spent	0:00:00.34 on the problem.
% 0.51/0.70  		0:00:00.03 for the input.
% 0.51/0.70  		0:00:00.27 for the FLOTTER CNF translation.
% 0.51/0.70  		0:00:00.00 for inferences.
% 0.51/0.70  		0:00:00.00 for the backtracking.
% 0.51/0.70  		0:00:00.01 for the reduction.
% 0.51/0.70  
% 0.51/0.70  
% 0.51/0.70  Here is a proof with depth 2, length 15 :
% 0.51/0.70  % SZS output start Refutation
% See solution above
% 0.51/0.70  Formulae used in the proof : thIV12 greatest_lower_bound subset lower_bound
% 0.51/0.70  
%------------------------------------------------------------------------------