%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 : Thu Jul 14 18:02:54 EDT 2022

% Result   : Theorem 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   4 unt;   0 nHn;  16 RR)
%            Number of literals    :   35 (   0 equ;  22 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    sorti2(skc1),
    file('ALG202+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG202+1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(op2(skc1,skc1),skc1),
    file('ALG202+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(u)
    | equal(h(j(u)),u) ),
    file('ALG202+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sorti1(u)
    | equal(op1(u,u),u) ),
    file('ALG202+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | sorti2(op2(v,u)) ),
    file('ALG202+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op1(j(v),j(u)),j(op2(v,u))) ),
    file('ALG202+1.p',unknown),
    [] ).

cnf(25,plain,
    ( ~ sorti2(u)
    | ~ sorti2(u)
    | ~ sorti1(j(u))
    | equal(j(op2(u,u)),j(u)) ),
    inference(spr,[status(thm),theory(equality)],[11,7]),
    [iquote('0:SpR:11.2,7.1')] ).

cnf(30,plain,
    ( ~ sorti2(u)
    | ~ sorti1(j(u))
    | equal(j(op2(u,u)),j(u)) ),
    inference(obv,[status(thm),theory(equality)],[25]),
    [iquote('0:Obv:25.0')] ).

cnf(31,plain,
    ( ~ sorti2(u)
    | equal(j(op2(u,u)),j(u)) ),
    inference(ssi,[status(thm)],[30,3]),
    [iquote('0:SSi:30.1,3.1')] ).

cnf(36,plain,
    ( ~ sorti2(u)
    | ~ sorti2(op2(u,u))
    | equal(op2(u,u),h(j(u))) ),
    inference(spr,[status(thm),theory(equality)],[31,5]),
    [iquote('0:SpR:31.1,5.1')] ).

cnf(40,plain,
    ( ~ sorti2(u)
    | ~ sorti2(op2(u,u))
    | equal(op2(u,u),u) ),
    inference(rew,[status(thm),theory(equality)],[5,36]),
    [iquote('0:Rew:5.1,36.2')] ).

cnf(41,plain,
    ( ~ sorti2(u)
    | equal(op2(u,u),u) ),
    inference(ssi,[status(thm)],[40,9]),
    [iquote('0:SSi:40.1,9.2')] ).

cnf(49,plain,
    ( ~ sorti2(skc1)
    | ~ equal(skc1,skc1) ),
    inference(spl,[status(thm),theory(equality)],[41,4]),
    [iquote('0:SpL:41.1,4.0')] ).

cnf(50,plain,
    ~ sorti2(skc1),
    inference(obv,[status(thm),theory(equality)],[49]),
    [iquote('0:Obv:49.1')] ).

cnf(51,plain,
    $false,
    inference(ssi,[status(thm)],[50,1]),
    [iquote('0:SSi:50.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n022.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 : Wed Jun  8 10:54:50 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 22 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.18/0.42  SPASS allocated 103863 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.42  		0:00:00.04 for the input.
% 0.18/0.42  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.00 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 3, length 16 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : ax4 co1 ax3 ax2
% 0.18/0.42  
%------------------------------------------------------------------------------