TSTP Solution File: SET903+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:41 EDT 2022

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   20 (  12 unt;   5 nHn;  20 RR)
%            Number of literals    :   34 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   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;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ~ equal(skc6,empty_set),
    file('SET903+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(skc6,skc5),
    file('SET903+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(skc5,empty_set),
    file('SET903+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_union2(skc6,skc5),singleton(skc7)),
    file('SET903+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SET903+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ skP1(u,v,w)
    | equal(w,empty_set) ),
    file('SET903+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ skP0(u,v,w)
    | equal(w,singleton(v)) ),
    file('SET903+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ skP0(u,v,w)
    | equal(u,singleton(v)) ),
    file('SET903+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ equal(singleton(u),set_union2(v,w))
    | equal(w,empty_set)
    | skP1(u,w,v)
    | skP0(w,u,v) ),
    file('SET903+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(singleton(u),set_union2(v,w))
    | equal(v,singleton(u))
    | skP0(w,u,v)
    | skP1(u,w,v) ),
    file('SET903+1.p',unknown),
    [] ).

cnf(18,plain,
    equal(set_union2(skc5,skc6),singleton(skc7)),
    inference(rew,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Rew:9.0,8.0')] ).

cnf(19,plain,
    ( ~ equal(singleton(u),set_union2(v,w))
    | equal(v,singleton(u))
    | skP1(u,w,v) ),
    inference(mrr,[status(thm)],[17,13]),
    [iquote('0:MRR:17.2,13.0')] ).

cnf(21,plain,
    ~ skP1(u,v,skc5),
    inference(res,[status(thm),theory(equality)],[12,6]),
    [iquote('0:Res:12.1,6.0')] ).

cnf(24,plain,
    ( equal(singleton(skc7),skc5)
    | skP1(skc7,skc6,skc5) ),
    inference(res,[status(thm),theory(equality)],[18,19]),
    [iquote('0:Res:18.0,19.0')] ).

cnf(25,plain,
    ( equal(skc6,empty_set)
    | skP0(skc6,skc7,skc5)
    | skP1(skc7,skc6,skc5) ),
    inference(res,[status(thm),theory(equality)],[18,16]),
    [iquote('0:Res:18.0,16.0')] ).

cnf(26,plain,
    equal(singleton(skc7),skc5),
    inference(mrr,[status(thm)],[24,21]),
    [iquote('0:MRR:24.1,21.0')] ).

cnf(28,plain,
    skP0(skc6,skc7,skc5),
    inference(mrr,[status(thm)],[25,4,21]),
    [iquote('0:MRR:25.0,25.2,4.0,21.0')] ).

cnf(46,plain,
    equal(singleton(skc7),skc6),
    inference(res,[status(thm),theory(equality)],[28,14]),
    [iquote('0:Res:28.0,14.0')] ).

cnf(47,plain,
    equal(skc6,skc5),
    inference(rew,[status(thm),theory(equality)],[26,46]),
    [iquote('0:Rew:26.0,46.0')] ).

cnf(48,plain,
    $false,
    inference(mrr,[status(thm)],[47,5]),
    [iquote('0:MRR:47.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat Jul  9 17:50:00 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  
% 0.20/0.45  SPASS V 3.9 
% 0.20/0.45  SPASS beiseite: Proof found.
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.45  SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.20/0.45  SPASS allocated 85118 KBytes.
% 0.20/0.45  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.45  		0:00:00.03 for the input.
% 0.20/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45  		0:00:00.00 for inferences.
% 0.20/0.45  		0:00:00.00 for the backtracking.
% 0.20/0.45  		0:00:00.00 for the reduction.
% 0.20/0.45  
% 0.20/0.45  
% 0.20/0.45  Here is a proof with depth 2, length 20 :
% 0.20/0.45  % SZS output start Refutation
% See solution above
% 0.20/0.45  Formulae used in the proof : t44_zfmisc_1 commutativity_k2_xboole_0 t43_zfmisc_1
% 0.20/0.45  
%------------------------------------------------------------------------------