%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   4 unt;   0 nHn;  11 RR)
%            Number of literals    :   22 (   0 equ;  17 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    sorti2(skc1),
    file('ALG201+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(op2(skc1,skc1),skc1),
    file('ALG201+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sorti1(u)
    | ~ equal(op1(u,u),u) ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op1(j(v),j(u)),j(op2(v,u))) ),
    file('ALG201+1.p',unknown),
    [] ).

cnf(29,plain,
    ( ~ sorti2(u)
    | ~ sorti2(u)
    | ~ sorti1(j(u))
    | ~ equal(j(op2(u,u)),j(u)) ),
    inference(spl,[status(thm),theory(equality)],[11,7]),
    [iquote('0:SpL: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)],[29]),
    [iquote('0:Obv:29.0')] ).

cnf(31,plain,
    ( ~ sorti2(u)
    | ~ equal(j(op2(u,u)),j(u)) ),
    inference(ssi,[status(thm)],[30,4]),
    [iquote('0:SSi:30.1,4.1')] ).

cnf(35,plain,
    ( ~ sorti2(skc1)
    | ~ equal(j(skc1),j(skc1)) ),
    inference(spl,[status(thm),theory(equality)],[2,31]),
    [iquote('0:SpL:2.0,31.1')] ).

cnf(36,plain,
    ~ sorti2(skc1),
    inference(obv,[status(thm),theory(equality)],[35]),
    [iquote('0:Obv:35.1')] ).

cnf(37,plain,
    $false,
    inference(ssi,[status(thm)],[36,1]),
    [iquote('0:SSi:36.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Wed Jun  8 11:22:47 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.21/0.43  
% 0.21/0.43  SPASS V 3.9 
% 0.21/0.43  SPASS beiseite: Proof found.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.43  SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses.
% 0.21/0.43  SPASS allocated 103852 KBytes.
% 0.21/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.21/0.43  		0:00:00.03 for the input.
% 0.21/0.43  		0:00:00.02 for the FLOTTER CNF translation.
% 0.21/0.43  		0:00:00.00 for inferences.
% 0.21/0.43  		0:00:00.00 for the backtracking.
% 0.21/0.43  		0:00:00.00 for the reduction.
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  Here is a proof with depth 2, length 11 :
% 0.21/0.43  % SZS output start Refutation
% See solution above
% 0.21/0.43  Formulae used in the proof : ax4 co1 ax3
% 0.21/0.43  
%------------------------------------------------------------------------------