TSTP Solution File: SET994+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET994+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 05:30:17 EDT 2022

% Result   : Theorem 0.21s 0.48s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   36 (  16 unt;   3 nHn;  36 RR)
%            Number of literals    :   80 (   0 equ;  45 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    empty(empty_set),
    file('SET994+1.p',unknown),
    [] ).

cnf(15,axiom,
    empty(n0),
    file('SET994+1.p',unknown),
    [] ).

cnf(20,axiom,
    relation(skf8(u)),
    file('SET994+1.p',unknown),
    [] ).

cnf(21,axiom,
    function(skf8(u)),
    file('SET994+1.p',unknown),
    [] ).

cnf(22,axiom,
    relation(skf9(u)),
    file('SET994+1.p',unknown),
    [] ).

cnf(23,axiom,
    function(skf9(u)),
    file('SET994+1.p',unknown),
    [] ).

cnf(24,axiom,
    ~ empty(n1),
    file('SET994+1.p',unknown),
    [] ).

cnf(25,axiom,
    ~ equal(skc7,empty_set),
    file('SET994+1.p',unknown),
    [] ).

cnf(26,axiom,
    element(skf5(u),u),
    file('SET994+1.p',unknown),
    [] ).

cnf(32,axiom,
    equal(relation_dom(skf8(u)),u),
    file('SET994+1.p',unknown),
    [] ).

cnf(33,axiom,
    equal(relation_dom(skf9(u)),u),
    file('SET994+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ empty(u)
    | equal(u,empty_set) ),
    file('SET994+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SET994+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ in(u,v)
    | equal(apply(skf8(v),u),n0) ),
    file('SET994+1.p',unknown),
    [] ).

cnf(47,axiom,
    ( ~ in(u,v)
    | equal(apply(skf9(v),u),n1) ),
    file('SET994+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ function(u)
    | ~ relation(u)
    | ~ function(v)
    | ~ relation(v)
    | ~ equal(relation_dom(v),skc7)
    | ~ equal(relation_dom(u),skc7)
    | equal(v,u) ),
    file('SET994+1.p',unknown),
    [] ).

cnf(51,plain,
    ~ empty(skc7),
    inference(res,[status(thm),theory(equality)],[37,25]),
    [iquote('0:Res:37.1,25.0')] ).

cnf(78,plain,
    ( ~ relation(skf9(skc7))
    | ~ function(skf9(skc7))
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(u),skc7)
    | equal(skf9(skc7),u) ),
    inference(res,[status(thm),theory(equality)],[33,50]),
    [iquote('0:Res:33.0,50.5')] ).

cnf(79,plain,
    ( ~ relation(skf8(skc7))
    | ~ function(skf8(skc7))
    | ~ relation(u)
    | ~ function(u)
    | ~ equal(relation_dom(u),skc7)
    | equal(skf8(skc7),u) ),
    inference(res,[status(thm),theory(equality)],[32,50]),
    [iquote('0:Res:32.0,50.5')] ).

cnf(84,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc7)
    | equal(skf8(skc7),u) ),
    inference(mrr,[status(thm)],[79,20,21]),
    [iquote('0:MRR:79.0,79.1,20.0,21.0')] ).

cnf(85,plain,
    ( ~ function(u)
    | ~ relation(u)
    | ~ equal(relation_dom(u),skc7)
    | equal(skf9(skc7),u) ),
    inference(mrr,[status(thm)],[78,22,23]),
    [iquote('0:MRR:78.0,78.1,22.0,23.0')] ).

cnf(97,plain,
    equal(n0,empty_set),
    inference(ems,[status(thm)],[37,15]),
    [iquote('0:EmS:37.0,15.0')] ).

cnf(103,plain,
    ( ~ in(u,v)
    | equal(apply(skf8(v),u),empty_set) ),
    inference(rew,[status(thm),theory(equality)],[97,46]),
    [iquote('0:Rew:97.0,46.1')] ).

cnf(156,plain,
    ( empty(u)
    | in(skf5(u),u) ),
    inference(res,[status(thm),theory(equality)],[26,44]),
    [iquote('0:Res:26.0,44.0')] ).

cnf(387,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ equal(u,skc7)
    | equal(skf9(skc7),skf9(u)) ),
    inference(spl,[status(thm),theory(equality)],[33,85]),
    [iquote('0:SpL:33.0,85.2')] ).

cnf(391,plain,
    ( ~ equal(u,skc7)
    | equal(skf9(skc7),skf9(u)) ),
    inference(ssi,[status(thm)],[387,23,22]),
    [iquote('0:SSi:387.1,387.0,23.0,22.0,23.0,22.0')] ).

cnf(398,plain,
    ( ~ equal(u,skc7)
    | ~ in(v,skc7)
    | equal(apply(skf9(u),v),n1) ),
    inference(spr,[status(thm),theory(equality)],[391,47]),
    [iquote('0:SpR:391.1,47.1')] ).

cnf(436,plain,
    ( ~ function(skf9(u))
    | ~ relation(skf9(u))
    | ~ equal(u,skc7)
    | equal(skf9(u),skf8(skc7)) ),
    inference(spl,[status(thm),theory(equality)],[33,84]),
    [iquote('0:SpL:33.0,84.2')] ).

cnf(440,plain,
    ( ~ equal(u,skc7)
    | equal(skf9(u),skf8(skc7)) ),
    inference(ssi,[status(thm)],[436,23,22]),
    [iquote('0:SSi:436.1,436.0,23.0,22.0,23.0,22.0')] ).

cnf(444,plain,
    ( ~ equal(u,skc7)
    | ~ in(v,skc7)
    | equal(apply(skf8(skc7),v),n1) ),
    inference(rew,[status(thm),theory(equality)],[440,398]),
    [iquote('0:Rew:440.1,398.2')] ).

cnf(455,plain,
    ( ~ in(u,skc7)
    | equal(apply(skf8(skc7),u),n1) ),
    inference(aed,[status(thm),theory(equality)],[25,444]),
    [iquote('0:AED:25.0,444.0')] ).

cnf(456,plain,
    ( ~ in(u,skc7)
    | equal(n1,empty_set) ),
    inference(rew,[status(thm),theory(equality)],[103,455]),
    [iquote('0:Rew:103.1,455.1')] ).

cnf(466,plain,
    ( empty(skc7)
    | equal(n1,empty_set) ),
    inference(res,[status(thm),theory(equality)],[156,456]),
    [iquote('0:Res:156.1,456.0')] ).

cnf(470,plain,
    equal(n1,empty_set),
    inference(mrr,[status(thm)],[466,51]),
    [iquote('0:MRR:466.0,51.0')] ).

cnf(471,plain,
    ~ empty(empty_set),
    inference(rew,[status(thm),theory(equality)],[470,24]),
    [iquote('0:Rew:470.0,24.0')] ).

cnf(473,plain,
    $false,
    inference(mrr,[status(thm)],[471,5]),
    [iquote('0:MRR:471.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SET994+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n005.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 23:27:22 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.48  
% 0.21/0.48  SPASS V 3.9 
% 0.21/0.48  SPASS beiseite: Proof found.
% 0.21/0.48  % SZS status Theorem
% 0.21/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.48  SPASS derived 346 clauses, backtracked 0 clauses, performed 0 splits and kept 190 clauses.
% 0.21/0.48  SPASS allocated 97907 KBytes.
% 0.21/0.48  SPASS spent	0:00:00.11 on the problem.
% 0.21/0.48  		0:00:00.03 for the input.
% 0.21/0.48  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.48  		0:00:00.01 for inferences.
% 0.21/0.48  		0:00:00.00 for the backtracking.
% 0.21/0.48  		0:00:00.02 for the reduction.
% 0.21/0.48  
% 0.21/0.48  
% 0.21/0.48  Here is a proof with depth 4, length 36 :
% 0.21/0.48  % SZS output start Refutation
% See solution above
% 0.21/0.48  Formulae used in the proof : fc4_relat_1 spc0_boole s3_funct_1__e4_14__funct_1 s3_funct_1__e7_14__funct_1 spc1_boole t16_funct_1 existence_m1_subset_1 t6_boole t2_subset
% 0.21/0.48  
%------------------------------------------------------------------------------