%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 05:28:53 EDT 2022

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   8 unt;   2 nHn;  12 RR)
%            Number of literals    :   17 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ c_in(u,c_emptyset,v),
    file('SET820-2.p',unknown),
    [] ).

cnf(2,axiom,
    c_in(u,c_insert(u,v,w),w),
    file('SET820-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_in(u,c_insert(v,w,x),x)
    | equal(u,v)
    | c_in(u,w,x) ),
    file('SET820-2.p',unknown),
    [] ).

cnf(4,axiom,
    v_P(v_a),
    file('SET820-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ c_in(u,v,tc_IntDef_Oint)
    | c_in(v_x(v),v,tc_IntDef_Oint) ),
    file('SET820-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ v_P(v_x(u))
    | ~ c_in(v,u,tc_IntDef_Oint) ),
    file('SET820-2.p',unknown),
    [] ).

cnf(7,plain,
    ~ v_P(v_x(c_insert(u,v,tc_IntDef_Oint))),
    inference(res,[status(thm),theory(equality)],[2,6]),
    [iquote('0:Res:2.0,6.1')] ).

cnf(8,plain,
    c_in(v_x(c_insert(u,v,tc_IntDef_Oint)),c_insert(u,v,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(res,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Res:2.0,5.0')] ).

cnf(12,plain,
    ( equal(v_x(c_insert(u,v,tc_IntDef_Oint)),u)
    | c_in(v_x(c_insert(u,v,tc_IntDef_Oint)),v,tc_IntDef_Oint) ),
    inference(res,[status(thm),theory(equality)],[8,3]),
    [iquote('0:Res:8.0,3.0')] ).

cnf(13,plain,
    equal(v_x(c_insert(u,c_emptyset,tc_IntDef_Oint)),u),
    inference(res,[status(thm),theory(equality)],[12,1]),
    [iquote('0:Res:12.1,1.0')] ).

cnf(20,plain,
    ~ v_P(u),
    inference(spl,[status(thm),theory(equality)],[13,7]),
    [iquote('0:SpL:13.0,7.0')] ).

cnf(21,plain,
    $false,
    inference(unc,[status(thm)],[20,4]),
    [iquote('0:UnC:20.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.14/0.33  % Computer : n014.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Sat Jul  9 18:51:35 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.40  
% 0.14/0.40  SPASS V 3.9 
% 0.14/0.40  SPASS beiseite: Proof found.
% 0.14/0.40  % SZS status Theorem
% 0.14/0.40  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.14/0.40  SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.14/0.40  SPASS allocated 63102 KBytes.
% 0.14/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.14/0.40  		0:00:00.03 for the input.
% 0.14/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.40  		0:00:00.00 for inferences.
% 0.14/0.40  		0:00:00.00 for the backtracking.
% 0.14/0.40  		0:00:00.00 for the reduction.
% 0.14/0.40  
% 0.14/0.40  
% 0.14/0.40  Here is a proof with depth 4, length 12 :
% 0.14/0.40  % SZS output start Refutation
% See solution above
% 0.14/0.40  Formulae used in the proof : cls_Set_OemptyE_0 cls_Set_OinsertCI_1 cls_Set_OinsertE_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.14/0.40  
%------------------------------------------------------------------------------