%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 14:34:03 EDT 2022

% Result   : Unsatisfiable 0.11s 0.39s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   4 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(equivalent(u,v))
    | is_a_theorem(v) ),
    file('LCL013-1.p',unknown),
    [] ).

cnf(2,axiom,
    is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(u,w)),equivalent(w,v)))),
    file('LCL013-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
    file('LCL013-1.p',unknown),
    [] ).

cnf(7,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(equivalent(equivalent(v,equivalent(u,w)),equivalent(w,v))) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.0,1.1')] ).

cnf(8,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(equivalent(v,equivalent(u,w)))
    | is_a_theorem(equivalent(w,v)) ),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.1,1.1')] ).

cnf(10,plain,
    ( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
    | is_a_theorem(equivalent(equivalent(w,u),v)) ),
    inference(sor,[status(thm)],[8,2]),
    [iquote('0:SoR:8.1,2.0')] ).

cnf(12,plain,
    is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(v,equivalent(w,u)))),
    inference(sor,[status(thm)],[10,2]),
    [iquote('0:SoR:10.0,2.0')] ).

cnf(13,plain,
    $false,
    inference(unc,[status(thm)],[12,3]),
    [iquote('0:UnC:12.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun Jul  3 21:17:49 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.39  
% 0.11/0.39  SPASS V 3.9 
% 0.11/0.39  SPASS beiseite: Proof found.
% 0.11/0.39  % SZS status Theorem
% 0.11/0.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.11/0.39  SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.11/0.39  SPASS allocated 75600 KBytes.
% 0.11/0.39  SPASS spent	0:00:00.06 on the problem.
% 0.11/0.39  		0:00:00.04 for the input.
% 0.11/0.39  		0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.39  		0:00:00.00 for inferences.
% 0.11/0.39  		0:00:00.00 for the backtracking.
% 0.11/0.39  		0:00:00.00 for the reduction.
% 0.11/0.39  
% 0.11/0.39  
% 0.11/0.39  Here is a proof with depth 4, length 8 :
% 0.11/0.39  % SZS output start Refutation
% See solution above
% 0.11/0.39  Formulae used in the proof : condensed_detachment xgf prove_um
% 0.11/0.39  
%------------------------------------------------------------------------------