%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HWV052-1.001.001 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 : Sat Jul 16 19:15:35 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   16 (  10 unt;   6 nHn;  16 RR)
%            Number of literals    :   22 (   0 equ;   1 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( equal(u,i)
    | equal(u,o) ),
    file('HWV052-1.001.001.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(inv(u),u),
    file('HWV052-1.001.001.p',unknown),
    [] ).

cnf(3,axiom,
    equal(unpack1(u,pack1(u)),u),
    file('HWV052-1.001.001.p',unknown),
    [] ).

cnf(4,axiom,
    equal(unpack1(inv(u),pack1(u)),u),
    file('HWV052-1.001.001.p',unknown),
    [] ).

cnf(5,axiom,
    equal(unpack1(u,inv(pack1(u))),u),
    file('HWV052-1.001.001.p',unknown),
    [] ).

cnf(14,plain,
    ( equal(pack1(u),o)
    | equal(unpack1(u,i),u) ),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(16,plain,
    ( equal(pack1(u),o)
    | equal(unpack1(inv(u),i),u) ),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(20,plain,
    ( equal(inv(pack1(u)),o)
    | equal(unpack1(u,i),u) ),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(21,plain,
    ( equal(inv(o),o)
    | equal(unpack1(u,i),u) ),
    inference(rew,[status(thm),theory(equality)],[14,20]),
    [iquote('0:Rew:14.0,20.0')] ).

cnf(22,plain,
    equal(unpack1(u,i),u),
    inference(mrr,[status(thm)],[21,2]),
    [iquote('0:MRR:21.0,2.0')] ).

cnf(23,plain,
    ( equal(pack1(u),o)
    | equal(inv(u),u) ),
    inference(rew,[status(thm),theory(equality)],[22,16]),
    [iquote('0:Rew:22.0,16.1')] ).

cnf(24,plain,
    equal(pack1(u),o),
    inference(mrr,[status(thm)],[23,2]),
    [iquote('0:MRR:23.1,2.0')] ).

cnf(25,plain,
    equal(unpack1(u,o),u),
    inference(rew,[status(thm),theory(equality)],[24,3]),
    [iquote('0:Rew:24.0,3.0')] ).

cnf(26,plain,
    equal(unpack1(inv(u),o),u),
    inference(rew,[status(thm),theory(equality)],[24,4]),
    [iquote('0:Rew:24.0,4.0')] ).

cnf(29,plain,
    equal(inv(u),u),
    inference(rew,[status(thm),theory(equality)],[25,26]),
    [iquote('0:Rew:25.0,26.0')] ).

cnf(30,plain,
    $false,
    inference(mrr,[status(thm)],[29,2]),
    [iquote('0:MRR:29.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HWV052-1.001.001 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n023.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 : Fri Jun 17 04:44:19 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.19/0.41  SPASS allocated 63100 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.03 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 1, length 16 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : bit_domain bit_inverse unpack1 unpack1_01 unpack1_02
% 0.19/0.41  
%------------------------------------------------------------------------------