%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL176-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 14:35:07 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   8 unt;   0 nHn;  14 RR)
%            Number of literals    :   22 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(or__dfg(not__dfg(p),p)),
    file('LCL176-1.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
    file('LCL176-1.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(or__dfg(not__dfg(u),or__dfg(v,u))),
    file('LCL176-1.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
    file('LCL176-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL176-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ theorem(u)
    | ~ axiom(or__dfg(not__dfg(u),v))
    | theorem(v) ),
    file('LCL176-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(or__dfg(not__dfg(u),v))
    | ~ axiom(or__dfg(not__dfg(w),u))
    | theorem(or__dfg(not__dfg(w),v)) ),
    file('LCL176-1.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ theorem(or__dfg(not__dfg(u),p))
    | ~ axiom(or__dfg(not__dfg(p),u)) ),
    inference(res,[status(thm),theory(equality)],[9,1]),
    [iquote('0:Res:9.2,1.0')] ).

cnf(24,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(res,[status(thm),theory(equality)],[4,8]),
    [iquote('0:Res:4.0,8.1')] ).

cnf(31,plain,
    ( ~ axiom(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[24,7]),
    [iquote('0:SoR:24.0,7.1')] ).

cnf(41,plain,
    theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
    inference(sor,[status(thm)],[31,2]),
    [iquote('0:SoR:31.0,2.0')] ).

cnf(43,plain,
    theorem(or__dfg(not__dfg(or__dfg(u,u)),u)),
    inference(sor,[status(thm)],[24,41]),
    [iquote('0:SoR:24.0,41.0')] ).

cnf(59,plain,
    ~ axiom(or__dfg(not__dfg(p),or__dfg(p,p))),
    inference(res,[status(thm),theory(equality)],[43,11]),
    [iquote('0:Res:43.0,11.0')] ).

cnf(61,plain,
    $false,
    inference(mrr,[status(thm)],[59,3]),
    [iquote('0:MRR:59.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL176-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 09:56:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 42 clauses, backtracked 0 clauses, performed 0 splits and kept 39 clauses.
% 0.18/0.41  SPASS allocated 75679 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.03 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 5, length 14 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 rule_1 rule_2 rule_3
% 0.18/0.41  
%------------------------------------------------------------------------------