%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 : Mon Jul 18 20:01:23 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  10 unt;   1 nHn;  15 RR)
%            Number of literals    :   20 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(converse(converse(u)),u),
    file('REL003+1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(join(skc7,skc6),skc6),
    file('REL003+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(join(u,v),join(v,u)),
    file('REL003+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( equal(join(u,v),v)
    | skP0(v,u) ),
    file('REL003+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL003+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ skP0(skc4,skc5)
    | equal(join(converse(skc7),converse(skc6)),converse(skc6)) ),
    file('REL003+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ equal(join(converse(u),converse(v)),converse(v))
    | skP0(v,u) ),
    file('REL003+1.p',unknown),
    [] ).

cnf(18,plain,
    ~ equal(join(skc6,skc7),skc6),
    inference(rew,[status(thm),theory(equality)],[6,3]),
    [iquote('0:Rew:6.0,3.0')] ).

cnf(19,plain,
    ( ~ equal(converse(u),converse(u))
    | skP0(u,v) ),
    inference(rew,[status(thm),theory(equality)],[7,14,9]),
    [iquote('0:Rew:7.0,14.0,9.0,14.0')] ).

cnf(20,plain,
    skP0(u,v),
    inference(obv,[status(thm),theory(equality)],[19]),
    [iquote('0:Obv:19.0')] ).

cnf(21,plain,
    ( ~ skP0(skc4,skc5)
    | equal(converse(join(skc6,skc7)),converse(skc6)) ),
    inference(rew,[status(thm),theory(equality)],[6,13,9]),
    [iquote('0:Rew:6.0,13.1,9.0,13.1')] ).

cnf(22,plain,
    equal(converse(join(skc6,skc7)),converse(skc6)),
    inference(mrr,[status(thm)],[21,20]),
    [iquote('0:MRR:21.0,20.0')] ).

cnf(30,plain,
    equal(join(skc6,skc7),converse(converse(skc6))),
    inference(spr,[status(thm),theory(equality)],[22,2]),
    [iquote('0:SpR:22.0,2.0')] ).

cnf(32,plain,
    equal(join(skc6,skc7),skc6),
    inference(rew,[status(thm),theory(equality)],[2,30]),
    [iquote('0:Rew:2.0,30.0')] ).

cnf(33,plain,
    $false,
    inference(mrr,[status(thm)],[32,18]),
    [iquote('0:MRR:32.0,18.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 12:42:31 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.19/0.43  SPASS allocated 85112 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.00 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 1, length 15 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : converse_idempotence goals maddux1_join_commutativity converse_additivity
% 0.19/0.43  
%------------------------------------------------------------------------------