%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM557+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 : Mon Jul 18 14:27:28 EDT 2022

% Result   : Theorem 4.29s 4.48s
% Output   : Refutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   30 (   0 equ;  23 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    aSet0(xS),
    file('NUM557+1.p',unknown),
    [] ).

cnf(10,axiom,
    aElementOf0(xk,szNzAzT0),
    file('NUM557+1.p',unknown),
    [] ).

cnf(13,axiom,
    aSubsetOf0(xP,xS),
    file('NUM557+1.p',unknown),
    [] ).

cnf(21,axiom,
    equal(sbrdtbr0(xP),xk),
    file('NUM557+1.p',unknown),
    [] ).

cnf(23,axiom,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    file('NUM557+1.p',unknown),
    [] ).

cnf(116,axiom,
    ( ~ aSet0(u)
    | ~ aSubsetOf0(v,u)
    | ~ aElementOf0(w,szNzAzT0)
    | ~ equal(x,slbdtsldtrb0(u,w))
    | ~ equal(sbrdtbr0(v),w)
    | aElementOf0(v,x) ),
    file('NUM557+1.p',unknown),
    [] ).

cnf(2402,plain,
    ( ~ aSet0(u)
    | ~ aSubsetOf0(v,u)
    | ~ aElementOf0(w,szNzAzT0)
    | ~ equal(sbrdtbr0(v),w)
    | aElementOf0(v,slbdtsldtrb0(u,w)) ),
    inference(eqr,[status(thm),theory(equality)],[116]),
    [iquote('0:EqR:116.3')] ).

cnf(12881,plain,
    ( ~ aSet0(xS)
    | ~ aSubsetOf0(xP,xS)
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ equal(sbrdtbr0(xP),xk) ),
    inference(res,[status(thm),theory(equality)],[2402,23]),
    [iquote('0:Res:2402.4,23.0')] ).

cnf(12890,plain,
    ( ~ aSet0(xS)
    | ~ aSubsetOf0(xP,xS)
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ equal(xk,xk) ),
    inference(rew,[status(thm),theory(equality)],[21,12881]),
    [iquote('0:Rew:21.0,12881.3')] ).

cnf(12891,plain,
    ( ~ aSet0(xS)
    | ~ aSubsetOf0(xP,xS)
    | ~ aElementOf0(xk,szNzAzT0) ),
    inference(obv,[status(thm),theory(equality)],[12890]),
    [iquote('0:Obv:12890.3')] ).

cnf(12892,plain,
    ( ~ aSubsetOf0(xP,xS)
    | ~ aElementOf0(xk,szNzAzT0) ),
    inference(ssi,[status(thm)],[12891,4]),
    [iquote('0:SSi:12891.0,4.0')] ).

cnf(12893,plain,
    $false,
    inference(mrr,[status(thm)],[12892,13,10]),
    [iquote('0:MRR:12892.0,12892.1,13.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : NUM557+1 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Wed Jul  6 16:46:59 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 4.29/4.48  
% 4.29/4.48  SPASS V 3.9 
% 4.29/4.48  SPASS beiseite: Proof found.
% 4.29/4.48  % SZS status Theorem
% 4.29/4.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 4.29/4.48  SPASS derived 9592 clauses, backtracked 691 clauses, performed 20 splits and kept 4094 clauses.
% 4.29/4.48  SPASS allocated 108143 KBytes.
% 4.29/4.48  SPASS spent	0:00:03.87 on the problem.
% 4.29/4.48  		0:00:00.04 for the input.
% 4.29/4.48  		0:00:00.11 for the FLOTTER CNF translation.
% 4.29/4.48  		0:00:00.17 for inferences.
% 4.29/4.48  		0:00:00.10 for the backtracking.
% 4.29/4.48  		0:00:03.37 for the reduction.
% 4.29/4.48  
% 4.29/4.48  
% 4.29/4.48  Here is a proof with depth 2, length 12 :
% 4.29/4.48  % SZS output start Refutation
% See solution above
% 4.29/4.48  Formulae used in the proof : m__2202_02 m__2202 m__2431 m__ mDefSel
% 4.29/4.48  
%------------------------------------------------------------------------------