TSTP Solution File: SET013-3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET013-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:22:28 EDT 2022

% Result   : Unsatisfiable 1.82s 2.01s
% Output   : Refutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   28 (  13 unt;   2 nHn;  28 RR)
%            Number of literals    :   48 (   0 equ;  23 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(intersection(as,bs),cs),
    file('SET013-3.p',unknown),
    [] ).

cnf(2,axiom,
    equal(intersection(bs,as),ds),
    file('SET013-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(ds,cs),
    file('SET013-3.p',unknown),
    [] ).

cnf(6,axiom,
    ( equal(u,v)
    | member(f1(u,v),v)
    | member(f1(u,v),u) ),
    file('SET013-3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(f1(u,v),v)
    | ~ member(f1(u,v),u)
    | equal(u,v) ),
    file('SET013-3.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET013-3.p',unknown),
    [] ).

cnf(32,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET013-3.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET013-3.p',unknown),
    [] ).

cnf(152,plain,
    ( ~ member(f1(cs,ds),ds)
    | ~ member(f1(cs,ds),cs) ),
    inference(res,[status(thm),theory(equality)],[7,3]),
    [iquote('0:Res:7.2,3.0')] ).

cnf(153,plain,
    ( member(f1(cs,ds),ds)
    | member(f1(cs,ds),cs) ),
    inference(res,[status(thm),theory(equality)],[6,3]),
    [iquote('0:Res:6.2,3.0')] ).

cnf(291,plain,
    ( ~ member(u,ds)
    | member(u,as) ),
    inference(spl,[status(thm),theory(equality)],[2,32]),
    [iquote('0:SpL:2.0,32.0')] ).

cnf(292,plain,
    ( ~ member(u,cs)
    | member(u,bs) ),
    inference(spl,[status(thm),theory(equality)],[1,32]),
    [iquote('0:SpL:1.0,32.0')] ).

cnf(311,plain,
    ( ~ member(u,ds)
    | member(u,bs) ),
    inference(spl,[status(thm),theory(equality)],[2,31]),
    [iquote('0:SpL:2.0,31.0')] ).

cnf(312,plain,
    ( ~ member(u,cs)
    | member(u,as) ),
    inference(spl,[status(thm),theory(equality)],[1,31]),
    [iquote('0:SpL:1.0,31.0')] ).

cnf(2934,plain,
    ( ~ member(u,as)
    | ~ member(u,bs)
    | member(u,ds) ),
    inference(spr,[status(thm),theory(equality)],[2,33]),
    [iquote('0:SpR:2.0,33.2')] ).

cnf(2935,plain,
    ( ~ member(u,bs)
    | ~ member(u,as)
    | member(u,cs) ),
    inference(spr,[status(thm),theory(equality)],[1,33]),
    [iquote('0:SpR:1.0,33.2')] ).

cnf(5104,plain,
    member(f1(cs,ds),ds),
    inference(spt,[spt(split,[position(s1)])],[153]),
    [iquote('1:Spt:153.0')] ).

cnf(5105,plain,
    ~ member(f1(cs,ds),cs),
    inference(mrr,[status(thm)],[152,5104]),
    [iquote('1:MRR:152.0,5104.0')] ).

cnf(5111,plain,
    member(f1(cs,ds),bs),
    inference(res,[status(thm),theory(equality)],[5104,311]),
    [iquote('1:Res:5104.0,311.0')] ).

cnf(5112,plain,
    member(f1(cs,ds),as),
    inference(res,[status(thm),theory(equality)],[5104,291]),
    [iquote('1:Res:5104.0,291.0')] ).

cnf(8079,plain,
    ( ~ member(f1(cs,ds),bs)
    | ~ member(f1(cs,ds),as) ),
    inference(res,[status(thm),theory(equality)],[2935,5105]),
    [iquote('1:Res:2935.2,5105.0')] ).

cnf(8081,plain,
    $false,
    inference(mrr,[status(thm)],[8079,5111,5112]),
    [iquote('1:MRR:8079.0,8079.1,5111.0,5112.0')] ).

cnf(8084,plain,
    ~ member(f1(cs,ds),ds),
    inference(spt,[spt(split,[position(sa)])],[8081,5104]),
    [iquote('1:Spt:8081.0,153.0,5104.0')] ).

cnf(8085,plain,
    member(f1(cs,ds),cs),
    inference(spt,[spt(split,[position(s2)])],[153]),
    [iquote('1:Spt:8081.0,153.1')] ).

cnf(8099,plain,
    member(f1(cs,ds),as),
    inference(res,[status(thm),theory(equality)],[8085,312]),
    [iquote('1:Res:8085.0,312.0')] ).

cnf(8100,plain,
    member(f1(cs,ds),bs),
    inference(res,[status(thm),theory(equality)],[8085,292]),
    [iquote('1:Res:8085.0,292.0')] ).

cnf(8197,plain,
    ( ~ member(f1(cs,ds),as)
    | ~ member(f1(cs,ds),bs) ),
    inference(res,[status(thm),theory(equality)],[2934,8084]),
    [iquote('1:Res:2934.2,8084.0')] ).

cnf(8200,plain,
    $false,
    inference(mrr,[status(thm)],[8197,8099,8100]),
    [iquote('1:MRR:8197.0,8197.1,8099.0,8100.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n028.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 : Mon Jul 11 09:33:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.82/2.01  
% 1.82/2.01  SPASS V 3.9 
% 1.82/2.01  SPASS beiseite: Proof found.
% 1.82/2.01  % SZS status Theorem
% 1.82/2.01  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.82/2.01  SPASS derived 6784 clauses, backtracked 1532 clauses, performed 20 splits and kept 4772 clauses.
% 1.82/2.01  SPASS allocated 81729 KBytes.
% 1.82/2.01  SPASS spent	0:00:01.62 on the problem.
% 1.82/2.01  		0:00:00.04 for the input.
% 1.82/2.01  		0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.01  		0:00:00.08 for inferences.
% 1.82/2.01  		0:00:00.07 for the backtracking.
% 1.82/2.01  		0:00:01.35 for the reduction.
% 1.82/2.01  
% 1.82/2.01  
% 1.82/2.01  Here is a proof with depth 3, length 28 :
% 1.82/2.01  % SZS output start Refutation
% See solution above
% 1.82/2.01  Formulae used in the proof : intersection_of_a_and_b_is_c intersection_of_b_and_a_is_d prove_c_equals_d extensionality2 extensionality3 intersection1 intersection2 intersection3
% 1.82/2.01  
%------------------------------------------------------------------------------