%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL431-2 : 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 : Sun Jul 17 14:36:54 EDT 2022

% Result   : Unsatisfiable 0.13s 0.41s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :    8 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_PropLog_Osat(c_emptyset,u,v)
    | c_in(u,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(u,w,v),c_PropLog_Ohyps(u,x,v),tc_set(tc_PropLog_Opl(v))),v),tc_PropLog_Opl(v)) ),
    file('LCL431-2.p',unknown),
    [] ).

cnf(2,axiom,
    equal(c_minus(u,u,tc_set(v)),c_emptyset),
    file('LCL431-2.p',unknown),
    [] ).

cnf(3,axiom,
    c_PropLog_Osat(c_emptyset,v,t_a),
    file('LCL431-2.p',unknown),
    [] ).

cnf(4,axiom,
    ~ c_in(v,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
    file('LCL431-2.p',unknown),
    [] ).

cnf(5,plain,
    c_in(v,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v,u,t_a),c_PropLog_Ohyps(v,v,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.0,1.0')] ).

cnf(7,plain,
    c_in(v,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
    inference(spr,[status(thm),theory(equality)],[2,5]),
    [iquote('0:SpR:2.0,5.0')] ).

cnf(8,plain,
    $false,
    inference(mrr,[status(thm)],[7,4]),
    [iquote('0:MRR:7.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL431-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n006.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 : Sun Jul  3 13:34:22 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.41  
% 0.13/0.41  SPASS V 3.9 
% 0.13/0.41  SPASS beiseite: Proof found.
% 0.13/0.41  % SZS status Theorem
% 0.13/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.13/0.41  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 6 clauses.
% 0.13/0.41  SPASS allocated 63091 KBytes.
% 0.13/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.13/0.41  		0:00:00.04 for the input.
% 0.13/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.41  		0:00:00.00 for inferences.
% 0.13/0.41  		0:00:00.00 for the backtracking.
% 0.13/0.41  		0:00:00.00 for the reduction.
% 0.13/0.41  
% 0.13/0.41  
% 0.13/0.41  Here is a proof with depth 2, length 7 :
% 0.13/0.41  % SZS output start Refutation
% See solution above
% 0.13/0.41  Formulae used in the proof : cls_PropLog_Ocompleteness__0__lemma__dest_0 cls_Set_ODiff__cancel_0 cls_conjecture_0 cls_conjecture_1
% 0.13/0.41  
%------------------------------------------------------------------------------