%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 05:29:43 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   9 unt;   1 nHn;  16 RR)
%            Number of literals    :   26 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(set_union2(singleton(skc5),skc4),empty_set),
    file('SET908+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SET908+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( equal(u,empty_set)
    | in(skf4(u),u) ),
    file('SET908+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(u,v)
    | ~ equal(v,empty_set) ),
    file('SET908+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SET908+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ in(u,v)
    | ~ equal(w,set_union2(x,v))
    | in(u,w) ),
    file('SET908+1.p',unknown),
    [] ).

cnf(22,plain,
    equal(set_union2(skc4,singleton(skc5)),empty_set),
    inference(rew,[status(thm),theory(equality)],[6,5]),
    [iquote('0:Rew:6.0,5.0')] ).

cnf(23,plain,
    ~ in(u,set_union2(skc4,singleton(skc5))),
    inference(res,[status(thm),theory(equality)],[22,11]),
    [iquote('0:Res:22.0,11.0')] ).

cnf(26,plain,
    ( ~ in(u,singleton(skc5))
    | in(u,empty_set) ),
    inference(res,[status(thm),theory(equality)],[22,16]),
    [iquote('0:Res:22.0,16.1')] ).

cnf(29,plain,
    ~ in(u,empty_set),
    inference(rew,[status(thm),theory(equality)],[22,23]),
    [iquote('0:Rew:22.0,23.0')] ).

cnf(31,plain,
    ~ in(u,singleton(skc5)),
    inference(mrr,[status(thm)],[26,29]),
    [iquote('0:MRR:26.1,29.0')] ).

cnf(37,plain,
    equal(singleton(skc5),empty_set),
    inference(res,[status(thm),theory(equality)],[7,31]),
    [iquote('0:Res:7.1,31.0')] ).

cnf(75,plain,
    ( ~ equal(u,skc5)
    | ~ equal(v,empty_set)
    | in(u,v) ),
    inference(spl,[status(thm),theory(equality)],[37,14]),
    [iquote('0:SpL:37.0,14.1')] ).

cnf(76,plain,
    ( ~ equal(u,skc5)
    | ~ equal(v,empty_set) ),
    inference(mrr,[status(thm)],[75,11]),
    [iquote('0:MRR:75.2,11.0')] ).

cnf(77,plain,
    ~ equal(u,empty_set),
    inference(eqr,[status(thm),theory(equality)],[76]),
    [iquote('0:EqR:76.0')] ).

cnf(78,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[77]),
    [iquote('0:Obv:77.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.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 19:32:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  
% 0.20/0.46  SPASS V 3.9 
% 0.20/0.46  SPASS beiseite: Proof found.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.46  SPASS derived 49 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.20/0.46  SPASS allocated 85364 KBytes.
% 0.20/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.20/0.46  		0:00:00.04 for the input.
% 0.20/0.46  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.46  		0:00:00.00 for inferences.
% 0.20/0.46  		0:00:00.00 for the backtracking.
% 0.20/0.46  		0:00:00.00 for the reduction.
% 0.20/0.46  
% 0.20/0.46  
% 0.20/0.46  Here is a proof with depth 4, length 16 :
% 0.20/0.46  % SZS output start Refutation
% See solution above
% 0.20/0.46  Formulae used in the proof : t49_zfmisc_1 commutativity_k2_xboole_0 d1_xboole_0 d1_tarski idempotence_k2_xboole_0 d2_xboole_0
% 0.20/0.46  
%------------------------------------------------------------------------------