%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 18:02:05 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (   4 unt;   0 nHn;  18 RR)
%            Number of literals    :   39 (   0 equ;  25 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    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    sorti1(skc1),
    file('ALG040+1.p',unknown),
    [] ).

cnf(2,axiom,
    sorti2(skf1(u)),
    file('ALG040+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ sorti1(u)
    | sorti2(h(u)) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(u)
    | equal(h(j(u)),u) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sorti1(u)
    | equal(op1(u,u),skc1) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | sorti2(op2(v,u)) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sorti2(u)
    | ~ equal(op2(skf1(u),skf1(u)),u) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ sorti2(u)
    | ~ sorti2(v)
    | equal(op1(j(v),j(u)),j(op2(v,u))) ),
    file('ALG040+1.p',unknown),
    [] ).

cnf(28,plain,
    ( ~ sorti2(u)
    | ~ sorti2(u)
    | ~ sorti1(j(u))
    | equal(j(op2(u,u)),skc1) ),
    inference(spr,[status(thm),theory(equality)],[12,7]),
    [iquote('0:SpR:12.2,7.1')] ).

cnf(33,plain,
    ( ~ sorti2(u)
    | ~ sorti1(j(u))
    | equal(j(op2(u,u)),skc1) ),
    inference(obv,[status(thm),theory(equality)],[28]),
    [iquote('0:Obv:28.0')] ).

cnf(34,plain,
    ( ~ sorti2(u)
    | equal(j(op2(u,u)),skc1) ),
    inference(ssi,[status(thm)],[33,4]),
    [iquote('0:SSi:33.1,4.1')] ).

cnf(39,plain,
    ( ~ sorti2(u)
    | ~ sorti2(op2(u,u))
    | equal(op2(u,u),h(skc1)) ),
    inference(spr,[status(thm),theory(equality)],[34,5]),
    [iquote('0:SpR:34.1,5.1')] ).

cnf(43,plain,
    ( ~ sorti2(u)
    | equal(op2(u,u),h(skc1)) ),
    inference(ssi,[status(thm)],[39,9]),
    [iquote('0:SSi:39.1,9.2')] ).

cnf(69,plain,
    ( ~ sorti2(skf1(u))
    | ~ sorti2(u)
    | ~ equal(h(skc1),u) ),
    inference(spl,[status(thm),theory(equality)],[43,10]),
    [iquote('0:SpL:43.1,10.1')] ).

cnf(71,plain,
    ( ~ sorti2(u)
    | ~ equal(h(skc1),u) ),
    inference(ssi,[status(thm)],[69,2]),
    [iquote('0:SSi:69.0,2.0')] ).

cnf(78,plain,
    ~ sorti2(h(skc1)),
    inference(eqr,[status(thm),theory(equality)],[71]),
    [iquote('0:EqR:71.1')] ).

cnf(79,plain,
    $false,
    inference(ssi,[status(thm)],[78,3,1]),
    [iquote('0:SSi:78.0,3.0,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG040+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun  8 01:37:40 EDT 2022
% 0.12/0.34  % 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/sandbox/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 40 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.19/0.43  SPASS allocated 103900 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 4, length 18 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : ax3 ax4 co1 ax2
% 0.19/0.43  
%------------------------------------------------------------------------------