%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ROB016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 20:56:15 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   9 RR)
%            Number of literals    :   12 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    8 (   3 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(negate(add(d,e)),negate(e)),
    file('ROB016-1.p',unknown),
    [] ).

cnf(2,axiom,
    positive_integer(k),
    file('ROB016-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ positive_integer(u)
    | ~ equal(negate(add(negate(v),negate(add(w,negate(v))))),w)
    | equal(negate(add(v,multiply(u,add(w,negate(add(w,negate(v))))))),negate(v)) ),
    file('ROB016-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
    file('ROB016-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
    file('ROB016-1.p',unknown),
    [] ).

cnf(12,plain,
    ( ~ positive_integer(k)
    | ~ equal(negate(add(negate(e),negate(add(d,negate(e))))),d) ),
    inference(res,[status(thm),theory(equality)],[3,4]),
    [iquote('0:Res:3.2,4.0')] ).

cnf(13,plain,
    ~ equal(negate(add(negate(e),negate(add(d,negate(e))))),d),
    inference(mrr,[status(thm)],[12,2]),
    [iquote('0:MRR:12.0,2.0')] ).

cnf(124,plain,
    equal(negate(add(negate(e),negate(add(d,negate(e))))),d),
    inference(spr,[status(thm),theory(equality)],[1,7]),
    [iquote('0:SpR:1.0,7.0')] ).

cnf(125,plain,
    $false,
    inference(mrr,[status(thm)],[124,13]),
    [iquote('0:MRR:124.0,13.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ROB016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n024.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  9 14:58:49 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 85 clauses, backtracked 0 clauses, performed 0 splits and kept 34 clauses.
% 0.19/0.42  SPASS allocated 75756 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.03 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 1, length 9 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : condition k_positive lemma_3_6 prove_result robbins_axiom
% 0.19/0.42  
%------------------------------------------------------------------------------