%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Tue Jul 19 05:22:22 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   7 unt;   4 nHn;  13 RR)
%            Number of literals    :   22 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    difference(b,a,bDa),
    file('SET008-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ intersection(a,bDa,aI_bDa),
    file('SET008-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(u,aI_bDa),
    file('SET008-1.p',unknown),
    [] ).

cnf(13,axiom,
    ( member(h(u,v,w),u)
    | member(h(u,v,w),w)
    | intersection(u,v,w) ),
    file('SET008-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( member(h(u,v,w),v)
    | member(h(u,v,w),w)
    | intersection(u,v,w) ),
    file('SET008-1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | ~ difference(x,w,v) ),
    file('SET008-1.p',unknown),
    [] ).

cnf(39,plain,
    ( member(h(a,bDa,aI_bDa),aI_bDa)
    | member(h(a,bDa,aI_bDa),a) ),
    inference(res,[status(thm),theory(equality)],[13,2]),
    [iquote('0:Res:13.1,2.0')] ).

cnf(40,plain,
    ( member(h(a,bDa,aI_bDa),aI_bDa)
    | member(h(a,bDa,aI_bDa),bDa) ),
    inference(res,[status(thm),theory(equality)],[14,2]),
    [iquote('0:Res:14.1,2.0')] ).

cnf(41,plain,
    member(h(a,bDa,aI_bDa),a),
    inference(mrr,[status(thm)],[39,3]),
    [iquote('0:MRR:39.0,3.0')] ).

cnf(42,plain,
    member(h(a,bDa,aI_bDa),bDa),
    inference(mrr,[status(thm)],[40,3]),
    [iquote('0:MRR:40.0,3.0')] ).

cnf(138,plain,
    ( ~ member(u,bDa)
    | ~ member(u,a) ),
    inference(res,[status(thm),theory(equality)],[1,17]),
    [iquote('0:Res:1.0,17.2')] ).

cnf(148,plain,
    ~ member(h(a,bDa,aI_bDa),bDa),
    inference(res,[status(thm),theory(equality)],[41,138]),
    [iquote('0:Res:41.0,138.1')] ).

cnf(156,plain,
    $false,
    inference(mrr,[status(thm)],[148,42]),
    [iquote('0:MRR:148.0,42.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % 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 : Sun Jul 10 20:29:16 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 123 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.19/0.42  SPASS allocated 63185 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.42  		0:00:00.04 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  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 2, length 13 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : b_minus_a a_intersection_bDa prove_aI_bDa_is_empty intersection_axiom1 intersection_axiom2 not_member_of_difference
% 0.19/0.42  
%------------------------------------------------------------------------------