%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 16:38:47 EDT 2022

% Result   : Theorem 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   9 unt;   2 nHn;  18 RR)
%            Number of literals    :   30 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    r1(skf22(u)),
    file('NUN080+2.p',unknown),
    [] ).

cnf(6,axiom,
    r2(u,skf20(v,u)),
    file('NUN080+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,skc1)
    | skP0(skc1,u) ),
    file('NUN080+2.p',unknown),
    [] ).

cnf(9,axiom,
    r3(u,v,skf18(v,u)),
    file('NUN080+2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ r1(u)
    | ~ skP0(v,u) ),
    file('NUN080+2.p',unknown),
    [] ).

cnf(21,axiom,
    ( equal(u,skf13(v))
    | skP1(skf13(v),u,v) ),
    file('NUN080+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ r2(u,v)
    | ~ skP1(w,v,u) ),
    file('NUN080+2.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ r1(u)
    | ~ r2(v,w)
    | ~ r3(x,w,y)
    | ~ r2(u,v) ),
    file('NUN080+2.p',unknown),
    [] ).

cnf(41,plain,
    ( ~ r1(u)
    | ~ r2(u,v)
    | ~ r2(v,w) ),
    inference(res,[status(thm),theory(equality)],[9,33]),
    [iquote('0:Res:9.0,33.2')] ).

cnf(47,plain,
    ( ~ r1(u)
    | equal(u,skc1) ),
    inference(res,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Res:8.1,13.1')] ).

cnf(49,plain,
    equal(skf22(u),skc1),
    inference(ems,[status(thm)],[47,1]),
    [iquote('0:EmS:47.0,1.0')] ).

cnf(52,plain,
    r1(skc1),
    inference(rew,[status(thm),theory(equality)],[49,1]),
    [iquote('0:Rew:49.0,1.0')] ).

cnf(81,plain,
    ( ~ r2(u,v)
    | equal(v,skf13(u)) ),
    inference(res,[status(thm),theory(equality)],[21,22]),
    [iquote('0:Res:21.1,22.1')] ).

cnf(82,plain,
    equal(skf20(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[6,81]),
    [iquote('0:Res:6.0,81.0')] ).

cnf(89,plain,
    r2(u,skf13(u)),
    inference(rew,[status(thm),theory(equality)],[82,6]),
    [iquote('0:Rew:82.0,6.0')] ).

cnf(179,plain,
    ( ~ r1(u)
    | ~ r2(skf13(u),v) ),
    inference(res,[status(thm),theory(equality)],[89,41]),
    [iquote('0:Res:89.0,41.1')] ).

cnf(185,plain,
    ~ r1(u),
    inference(res,[status(thm),theory(equality)],[89,179]),
    [iquote('0:Res:89.0,179.1')] ).

cnf(187,plain,
    $false,
    inference(unc,[status(thm)],[185,52]),
    [iquote('0:UnC:185.0,52.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun  2 03:01:23 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 144 clauses, backtracked 0 clauses, performed 0 splits and kept 105 clauses.
% 0.19/0.44  SPASS allocated 97722 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.44  		0:00:00.04 for the input.
% 0.19/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.00 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 3, length 18 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : axiom_4a axiom_2a axiom_1 axiom_1a axiom_2 xplustwoeqy
% 0.19/0.44  
%------------------------------------------------------------------------------