%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 : Mon Jul 18 16:38:48 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   18 (  12 unt;   1 nHn;  18 RR)
%            Number of literals    :   25 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    r1(skf22(u)),
    file('NUN087+2.p',unknown),
    [] ).

cnf(2,axiom,
    r1(skf24(u)),
    file('NUN087+2.p',unknown),
    [] ).

cnf(3,axiom,
    r1(skf23(u)),
    file('NUN087+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,skc1)
    | skP0(skc1,u) ),
    file('NUN087+2.p',unknown),
    [] ).

cnf(11,axiom,
    r4(u,skf24(u),skf23(u)),
    file('NUN087+2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ r1(u)
    | ~ skP0(v,u) ),
    file('NUN087+2.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r4(v,v,u) ),
    file('NUN087+2.p',unknown),
    [] ).

cnf(36,plain,
    ( ~ r1(u)
    | ~ r4(skf22(v),skf22(v),u) ),
    inference(res,[status(thm),theory(equality)],[1,26]),
    [iquote('0:Res:1.0,26.0')] ).

cnf(41,plain,
    ( ~ r1(u)
    | equal(u,skc1) ),
    inference(res,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Res:8.1,13.1')] ).

cnf(43,plain,
    equal(skf22(u),skc1),
    inference(ems,[status(thm)],[41,1]),
    [iquote('0:EmS:41.0,1.0')] ).

cnf(44,plain,
    equal(skf24(u),skc1),
    inference(ems,[status(thm)],[41,2]),
    [iquote('0:EmS:41.0,2.0')] ).

cnf(45,plain,
    equal(skf23(u),skc1),
    inference(ems,[status(thm)],[41,3]),
    [iquote('0:EmS:41.0,3.0')] ).

cnf(46,plain,
    r1(skc1),
    inference(rew,[status(thm),theory(equality)],[43,1]),
    [iquote('0:Rew:43.0,1.0')] ).

cnf(49,plain,
    ( ~ r1(u)
    | ~ r4(skc1,skc1,u) ),
    inference(rew,[status(thm),theory(equality)],[43,36]),
    [iquote('0:Rew:43.0,36.1')] ).

cnf(51,plain,
    r4(u,skc1,skf23(u)),
    inference(rew,[status(thm),theory(equality)],[44,11]),
    [iquote('0:Rew:44.0,11.0')] ).

cnf(57,plain,
    r4(u,skc1,skc1),
    inference(rew,[status(thm),theory(equality)],[45,51]),
    [iquote('0:Rew:45.0,51.0')] ).

cnf(73,plain,
    ~ r1(skc1),
    inference(res,[status(thm),theory(equality)],[57,49]),
    [iquote('0:Res:57.0,49.1')] ).

cnf(74,plain,
    $false,
    inference(ssi,[status(thm)],[73,46]),
    [iquote('0:SSi:73.0,46.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUN087+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  2 06:29:59 EDT 2022
% 0.13/0.34  % 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 39 clauses, backtracked 0 clauses, performed 0 splits and kept 58 clauses.
% 0.20/0.44  SPASS allocated 97687 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 2, length 18 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : axiom_4a axiom_5a axiom_1 zerotimeszeroeqzero
% 0.20/0.44  
%------------------------------------------------------------------------------