%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG069+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 18:02:12 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (   4 unt;   0 nHn;  17 RR)
%            Number of literals    :   36 (   0 equ;  28 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,
    sorti2(skc1),
    file('ALG069+1.p',unknown),
    [] ).

cnf(2,axiom,
    sorti1(skf1(u)),
    file('ALG069+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ sorti1(u)
    | sorti2(h(u)) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ sorti2(u)
    | sorti1(j(u)) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ sorti2(u)
    | equal(h(j(u)),u) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sorti2(u)
    | ~ equal(op2(u,u),skc1) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sorti1(u)
    | equal(op1(skf1(u),skf1(u)),u) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sorti1(u)
    | ~ sorti1(v)
    | equal(op2(h(v),h(u)),h(op1(v,u))) ),
    file('ALG069+1.p',unknown),
    [] ).

cnf(39,plain,
    ( ~ sorti1(u)
    | ~ sorti1(u)
    | ~ sorti2(h(u))
    | ~ equal(h(op1(u,u)),skc1) ),
    inference(spl,[status(thm),theory(equality)],[11,7]),
    [iquote('0:SpL:11.2,7.1')] ).

cnf(40,plain,
    ( ~ sorti1(u)
    | ~ sorti2(h(u))
    | ~ equal(h(op1(u,u)),skc1) ),
    inference(obv,[status(thm),theory(equality)],[39]),
    [iquote('0:Obv:39.0')] ).

cnf(41,plain,
    ( ~ sorti1(u)
    | ~ equal(h(op1(u,u)),skc1) ),
    inference(ssi,[status(thm)],[40,3]),
    [iquote('0:SSi:40.1,3.1')] ).

cnf(46,plain,
    ( ~ sorti1(u)
    | ~ sorti1(skf1(u))
    | ~ equal(h(u),skc1) ),
    inference(spl,[status(thm),theory(equality)],[10,41]),
    [iquote('0:SpL:10.1,41.1')] ).

cnf(48,plain,
    ( ~ sorti1(u)
    | ~ equal(h(u),skc1) ),
    inference(ssi,[status(thm)],[46,2]),
    [iquote('0:SSi:46.1,2.0')] ).

cnf(55,plain,
    ( ~ sorti2(u)
    | ~ sorti1(j(u))
    | ~ equal(u,skc1) ),
    inference(spl,[status(thm),theory(equality)],[5,48]),
    [iquote('0:SpL:5.1,48.1')] ).

cnf(56,plain,
    ( ~ sorti2(u)
    | ~ equal(u,skc1) ),
    inference(ssi,[status(thm)],[55,4]),
    [iquote('0:SSi:55.1,4.1')] ).

cnf(60,plain,
    ~ equal(skc1,skc1),
    inference(ems,[status(thm)],[56,1]),
    [iquote('0:EmS:56.0,1.0')] ).

cnf(61,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[60]),
    [iquote('0:Obv:60.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG069+1 : TPTP v8.1.0. Released v2.7.0.
% 0.13/0.13  % 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 17:01:32 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.20/0.44  SPASS allocated 103892 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 4, length 17 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : ax4 ax3 co1
% 0.20/0.44  
%------------------------------------------------------------------------------