%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 14:35:16 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   18 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(or__dfg(not__dfg(or__dfg(p,or__dfg(q,r))),or__dfg(p,or__dfg(r,q)))),
    file('LCL190-1.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
    file('LCL190-1.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(or__dfg(not__dfg(or__dfg(not__dfg(u),v)),or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v)))),
    file('LCL190-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL190-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ theorem(u)
    | ~ axiom(or__dfg(not__dfg(u),v))
    | theorem(v) ),
    file('LCL190-1.p',unknown),
    [] ).

cnf(23,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(27,plain,
    ( ~ axiom(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[23,7]),
    [iquote('0:SoR:23.0,7.1')] ).

cnf(32,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
    inference(sor,[status(thm)],[27,4]),
    [iquote('0:SoR:27.0,4.0')] ).

cnf(50,plain,
    ( ~ theorem(or__dfg(not__dfg(u),v))
    | theorem(or__dfg(not__dfg(or__dfg(w,u)),or__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Res:6.0,8.1')] ).

cnf(54,plain,
    theorem(or__dfg(not__dfg(or__dfg(u,v)),or__dfg(v,u))),
    inference(sor,[status(thm)],[23,32]),
    [iquote('0:SoR:23.0,32.0')] ).

cnf(114,plain,
    theorem(or__dfg(not__dfg(or__dfg(u,or__dfg(v,w))),or__dfg(u,or__dfg(w,v)))),
    inference(sor,[status(thm)],[50,54]),
    [iquote('0:SoR:50.0,54.0')] ).

cnf(124,plain,
    $false,
    inference(unc,[status(thm)],[114,1]),
    [iquote('0:UnC:114.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul  4 03:06:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 105 clauses, backtracked 0 clauses, performed 0 splits and kept 78 clauses.
% 0.19/0.42  SPASS allocated 75790 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 5, length 12 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : prove_this axiom_1_4 axiom_1_6 rule_1 rule_2
% 0.19/0.42  
%------------------------------------------------------------------------------