TSTP Solution File: SET047-5 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:23:09 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   27 (  12 unt;   7 nHn;  27 RR)
%            Number of literals    :   50 (   0 equ;  19 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ element(u,v)
    | ~ set_equal(v,w)
    | element(u,w) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ element(u,v)
    | ~ set_equal(w,v)
    | element(u,w) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(3,axiom,
    ( set_equal(u,v)
    | element(f(u,v),v)
    | element(f(u,v),u) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ element(f(u,v),u)
    | ~ element(f(u,v),v)
    | set_equal(u,v) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(5,axiom,
    ( set_equal(b,a)
    | set_equal(a,b) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ set_equal(a,b)
    | ~ set_equal(b,a) ),
    file('SET047-5.p',unknown),
    [] ).

cnf(7,plain,
    set_equal(b,a),
    inference(spt,[spt(split,[position(s1)])],[5]),
    [iquote('1:Spt:5.0')] ).

cnf(8,plain,
    ~ set_equal(a,b),
    inference(mrr,[status(thm)],[6,7]),
    [iquote('1:MRR:6.1,7.0')] ).

cnf(10,plain,
    ( ~ set_equal(u,v)
    | set_equal(w,u)
    | element(f(w,u),w)
    | element(f(w,u),v) ),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.1,1.0')] ).

cnf(26,plain,
    ( set_equal(u,b)
    | element(f(u,b),u)
    | element(f(u,b),a) ),
    inference(res,[status(thm),theory(equality)],[7,10]),
    [iquote('1:Res:7.0,10.0')] ).

cnf(28,plain,
    ( set_equal(a,b)
    | element(f(a,b),a) ),
    inference(fac,[status(thm)],[26]),
    [iquote('1:Fac:26.1,26.2')] ).

cnf(34,plain,
    element(f(a,b),a),
    inference(mrr,[status(thm)],[28,8]),
    [iquote('1:MRR:28.0,8.0')] ).

cnf(37,plain,
    ( ~ set_equal(u,a)
    | element(f(a,b),u) ),
    inference(res,[status(thm),theory(equality)],[34,2]),
    [iquote('1:Res:34.0,2.0')] ).

cnf(38,plain,
    ( ~ element(f(a,b),b)
    | set_equal(a,b) ),
    inference(res,[status(thm),theory(equality)],[34,4]),
    [iquote('1:Res:34.0,4.0')] ).

cnf(39,plain,
    ~ element(f(a,b),b),
    inference(mrr,[status(thm)],[38,8]),
    [iquote('1:MRR:38.1,8.0')] ).

cnf(49,plain,
    ~ set_equal(b,a),
    inference(res,[status(thm),theory(equality)],[37,39]),
    [iquote('1:Res:37.1,39.0')] ).

cnf(50,plain,
    $false,
    inference(mrr,[status(thm)],[49,7]),
    [iquote('1:MRR:49.0,7.0')] ).

cnf(51,plain,
    ~ set_equal(b,a),
    inference(spt,[spt(split,[position(sa)])],[50,7]),
    [iquote('1:Spt:50.0,5.0,7.0')] ).

cnf(52,plain,
    set_equal(a,b),
    inference(spt,[spt(split,[position(s2)])],[5]),
    [iquote('1:Spt:50.0,5.1')] ).

cnf(54,plain,
    ( set_equal(u,a)
    | element(f(u,a),u)
    | element(f(u,a),b) ),
    inference(res,[status(thm),theory(equality)],[52,10]),
    [iquote('1:Res:52.0,10.0')] ).

cnf(64,plain,
    ( set_equal(b,a)
    | element(f(b,a),b) ),
    inference(fac,[status(thm)],[54]),
    [iquote('1:Fac:54.1,54.2')] ).

cnf(70,plain,
    element(f(b,a),b),
    inference(mrr,[status(thm)],[64,51]),
    [iquote('1:MRR:64.0,51.0')] ).

cnf(73,plain,
    ( ~ set_equal(u,b)
    | element(f(b,a),u) ),
    inference(res,[status(thm),theory(equality)],[70,2]),
    [iquote('1:Res:70.0,2.0')] ).

cnf(74,plain,
    ( ~ element(f(b,a),a)
    | set_equal(b,a) ),
    inference(res,[status(thm),theory(equality)],[70,4]),
    [iquote('1:Res:70.0,4.0')] ).

cnf(75,plain,
    ~ element(f(b,a),a),
    inference(mrr,[status(thm)],[74,51]),
    [iquote('1:MRR:74.1,51.0')] ).

cnf(86,plain,
    ~ set_equal(a,b),
    inference(res,[status(thm),theory(equality)],[73,75]),
    [iquote('1:Res:73.1,75.0')] ).

cnf(87,plain,
    $false,
    inference(mrr,[status(thm)],[86,52]),
    [iquote('1:MRR:86.0,52.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 00:54:32 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 68 clauses, backtracked 3 clauses, performed 1 splits and kept 61 clauses.
% 0.19/0.40  SPASS allocated 63147 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 5, length 27 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : element_substitution1 element_substitution2 clause_3 clause_4 prove_symmetry1 prove_symmetry2
% 0.19/0.40  
%------------------------------------------------------------------------------