%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWW413-1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 21 01:28:26 EDT 2022

% Result   : Unsatisfiable 0.11s 0.32s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   1 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ equal(x3__dfg,x2__dfg),
    file('SWW413-1.p',unknown),
    [] ).

cnf(7,axiom,
    heap(sep(lseg(x3__dfg,nil),sep(next(x2__dfg,x3__dfg),emp))),
    file('SWW413-1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ heap(sep(lseg(x2__dfg,nil),emp)),
    file('SWW413-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(sep(u,sep(v,w)),sep(v,sep(u,w))),
    file('SWW413-1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ heap(sep(next(u,v),sep(lseg(v,w),x)))
    | heap(sep(lseg(u,w),x))
    | equal(u,v) ),
    file('SWW413-1.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ heap(sep(next(x2__dfg,u),sep(lseg(u,nil),emp)))
    | equal(x2__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[16,8]),
    [iquote('0:Res:16.2,8.0')] ).

cnf(22,plain,
    ( ~ heap(sep(lseg(u,nil),sep(next(x2__dfg,u),emp)))
    | equal(x2__dfg,u) ),
    inference(rew,[status(thm),theory(equality)],[9,21]),
    [iquote('0:Rew:9.0,21.0')] ).

cnf(111,plain,
    equal(x3__dfg,x2__dfg),
    inference(res,[status(thm),theory(equality)],[7,22]),
    [iquote('0:Res:7.0,22.0')] ).

cnf(112,plain,
    $false,
    inference(mrr,[status(thm)],[111,3]),
    [iquote('0:MRR:111.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SWW413-1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.08  % Command  : run_spass %d %s
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 600
% 0.07/0.27  % DateTime : Sun Jun  5 23:37:04 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.11/0.32  
% 0.11/0.32  SPASS V 3.9 
% 0.11/0.32  SPASS beiseite: Proof found.
% 0.11/0.32  % SZS status Theorem
% 0.11/0.32  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.11/0.32  SPASS derived 89 clauses, backtracked 0 clauses, performed 0 splits and kept 39 clauses.
% 0.11/0.32  SPASS allocated 63254 KBytes.
% 0.11/0.32  SPASS spent	0:00:00.05 on the problem.
% 0.11/0.32  		0:00:00.03 for the input.
% 0.11/0.32  		0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.32  		0:00:00.00 for inferences.
% 0.11/0.32  		0:00:00.00 for the backtracking.
% 0.11/0.32  		0:00:00.00 for the reduction.
% 0.11/0.32  
% 0.11/0.32  
% 0.11/0.32  Here is a proof with depth 2, length 9 :
% 0.11/0.32  % SZS output start Refutation
% See solution above
% 0.11/0.32  Formulae used in the proof : premise_3 premise_7 conclusion_1 associative_commutative unfolding_2
% 0.11/0.32  
%------------------------------------------------------------------------------