TSTP Solution File: SET134-6 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET134-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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  : 300s
% DateTime : Fri May  3 03:00:02 EDT 2024

% Result   : Unsatisfiable 93.08s 13.22s
% Output   : CNFRefutation 93.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   72 (  42 unt;   8 nHn;  41 RR)
%            Number of literals    :  105 (  31 equ;  31 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :   87 (  16 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    union(singleton(X0),X1) = set_builder(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).

cnf(c_50,negated_conjecture,
    member(u,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_1) ).

cnf(c_51,negated_conjecture,
    set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_2) ).

cnf(c_53,plain,
    ( member(not_subclass_element(X0,X1),X0)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(c_54,plain,
    ( ~ member(not_subclass_element(X0,X1),X1)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(c_58,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(X1,X0)
    | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(c_60,plain,
    ( ~ member(X0,universal_class)
    | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(c_63,plain,
    unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(c_72,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(c_73,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(c_75,plain,
    ( ~ member(X0,complement(X1))
    | ~ member(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(c_76,plain,
    ( ~ member(X0,universal_class)
    | member(X0,complement(X1))
    | member(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).

cnf(c_77,plain,
    complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).

cnf(c_78,plain,
    intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',symmetric_difference) ).

cnf(c_79,plain,
    intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).

cnf(c_81,plain,
    ( restrict(X0,singleton(X1),universal_class) != null_class
    | ~ member(X1,domain_of(X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).

cnf(c_117,plain,
    ( X0 = null_class
    | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(c_118,plain,
    ( intersection(X0,regular(X0)) = null_class
    | X0 = null_class ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).

cnf(c_738,plain,
    intersection(complement(intersection(X0,X1)),union(X0,X1)) = symmetric_difference(X0,X1),
    inference(light_normalisation,[status(thm)],[c_78,c_77]) ).

cnf(c_4072,plain,
    ( member(not_subclass_element(intersection(X0,X1),X2),X0)
    | subclass(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_53,c_72]) ).

cnf(c_4080,plain,
    ( member(not_subclass_element(intersection(X0,X1),X2),X1)
    | subclass(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_53,c_73]) ).

cnf(c_5544,plain,
    subclass(intersection(X0,X1),X0),
    inference(superposition,[status(thm)],[c_4072,c_54]) ).

cnf(c_5624,plain,
    subclass(restrict(X0,X1,X2),X0),
    inference(superposition,[status(thm)],[c_79,c_5544]) ).

cnf(c_5626,plain,
    ( X0 = null_class
    | subclass(null_class,X0) ),
    inference(superposition,[status(thm)],[c_118,c_5544]) ).

cnf(c_5662,plain,
    ( ~ subclass(X0,null_class)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_5626,c_58]) ).

cnf(c_5847,plain,
    subclass(intersection(X0,X1),X1),
    inference(superposition,[status(thm)],[c_4080,c_54]) ).

cnf(c_6067,plain,
    intersection(null_class,X0) = null_class,
    inference(superposition,[status(thm)],[c_5544,c_5662]) ).

cnf(c_6068,plain,
    restrict(null_class,X0,X1) = null_class,
    inference(superposition,[status(thm)],[c_5624,c_5662]) ).

cnf(c_6074,plain,
    subclass(null_class,X0),
    inference(superposition,[status(thm)],[c_6067,c_5847]) ).

cnf(c_6077,plain,
    subclass(null_class,null_class),
    inference(superposition,[status(thm)],[c_6067,c_5544]) ).

cnf(c_8229,plain,
    ~ member(X0,domain_of(null_class)),
    inference(superposition,[status(thm)],[c_6068,c_81]) ).

cnf(c_8458,plain,
    domain_of(null_class) = null_class,
    inference(superposition,[status(thm)],[c_117,c_8229]) ).

cnf(c_8472,plain,
    ~ member(X0,null_class),
    inference(superposition,[status(thm)],[c_8458,c_8229]) ).

cnf(c_38651,plain,
    ( ~ subclass(X0,null_class)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_6074,c_58]) ).

cnf(c_47426,plain,
    subclass(intersection(X0,X1),X0),
    inference(superposition,[status(thm)],[c_4072,c_54]) ).

cnf(c_47523,plain,
    subclass(symmetric_difference(X0,X1),complement(intersection(X0,X1))),
    inference(superposition,[status(thm)],[c_738,c_47426]) ).

cnf(c_47827,plain,
    subclass(symmetric_difference(complement(X0),complement(X1)),union(X0,X1)),
    inference(superposition,[status(thm)],[c_77,c_47523]) ).

cnf(c_48084,plain,
    subclass(symmetric_difference(complement(singleton(X0)),complement(X1)),set_builder(X0,X1)),
    inference(superposition,[status(thm)],[c_49,c_47827]) ).

cnf(c_48429,plain,
    subclass(symmetric_difference(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))),null_class),
    inference(superposition,[status(thm)],[c_51,c_48084]) ).

cnf(c_48514,plain,
    symmetric_difference(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))) = null_class,
    inference(superposition,[status(thm)],[c_48429,c_38651]) ).

cnf(c_48520,plain,
    subclass(null_class,complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))))),
    inference(superposition,[status(thm)],[c_48514,c_47523]) ).

cnf(c_48670,plain,
    subclass(intersection(X0,X1),X1),
    inference(superposition,[status(thm)],[c_4080,c_54]) ).

cnf(c_48851,plain,
    ( ~ subclass(complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))),null_class)
    | complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))) = null_class ),
    inference(superposition,[status(thm)],[c_48520,c_58]) ).

cnf(c_48865,plain,
    subclass(symmetric_difference(X0,X1),union(X0,X1)),
    inference(superposition,[status(thm)],[c_738,c_48670]) ).

cnf(c_48881,plain,
    subclass(symmetric_difference(singleton(X0),X1),set_builder(X0,X1)),
    inference(superposition,[status(thm)],[c_49,c_48865]) ).

cnf(c_48888,plain,
    ( ~ subclass(union(X0,X1),symmetric_difference(X0,X1))
    | union(X0,X1) = symmetric_difference(X0,X1) ),
    inference(superposition,[status(thm)],[c_48865,c_58]) ).

cnf(c_48894,plain,
    subclass(symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))),null_class),
    inference(superposition,[status(thm)],[c_51,c_48881]) ).

cnf(c_50267,plain,
    symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))) = null_class,
    inference(superposition,[status(thm)],[c_48894,c_38651]) ).

cnf(c_51899,plain,
    ( ~ subclass(union(singleton(u),set_builder(y,set_builder(z,null_class))),null_class)
    | union(singleton(u),set_builder(y,set_builder(z,null_class))) = symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))) ),
    inference(superposition,[status(thm)],[c_50267,c_48888]) ).

cnf(c_51958,plain,
    ( ~ subclass(set_builder(u,set_builder(y,set_builder(z,null_class))),null_class)
    | union(singleton(u),set_builder(y,set_builder(z,null_class))) = symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))) ),
    inference(superposition,[status(thm)],[c_49,c_51899]) ).

cnf(c_52529,plain,
    ( ~ subclass(union(singleton(u),set_builder(y,set_builder(z,null_class))),null_class)
    | complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))) = null_class ),
    inference(superposition,[status(thm)],[c_77,c_48851]) ).

cnf(c_52532,plain,
    ( ~ subclass(null_class,null_class)
    | union(singleton(u),set_builder(y,set_builder(z,null_class))) = symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))) ),
    inference(superposition,[status(thm)],[c_51,c_51958]) ).

cnf(c_52533,plain,
    union(singleton(u),set_builder(y,set_builder(z,null_class))) = symmetric_difference(singleton(u),set_builder(y,set_builder(z,null_class))),
    inference(global_subsumption_just,[status(thm)],[c_52532,c_6077,c_52532]) ).

cnf(c_52547,plain,
    subclass(union(singleton(u),set_builder(y,set_builder(z,null_class))),null_class),
    inference(superposition,[status(thm)],[c_52533,c_48894]) ).

cnf(c_65027,plain,
    ( ~ member(X0,universal_class)
    | member(X0,singleton(X0)) ),
    inference(superposition,[status(thm)],[c_63,c_60]) ).

cnf(c_65393,plain,
    ( ~ subclass(X0,null_class)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_6074,c_58]) ).

cnf(c_75889,plain,
    subclass(intersection(X0,X1),X0),
    inference(superposition,[status(thm)],[c_4072,c_54]) ).

cnf(c_75967,plain,
    subclass(symmetric_difference(X0,X1),complement(intersection(X0,X1))),
    inference(superposition,[status(thm)],[c_738,c_75889]) ).

cnf(c_76422,plain,
    subclass(symmetric_difference(complement(X0),complement(X1)),union(X0,X1)),
    inference(superposition,[status(thm)],[c_77,c_75967]) ).

cnf(c_77230,plain,
    subclass(symmetric_difference(complement(singleton(X0)),complement(X1)),set_builder(X0,X1)),
    inference(superposition,[status(thm)],[c_49,c_76422]) ).

cnf(c_77682,plain,
    subclass(symmetric_difference(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))),null_class),
    inference(superposition,[status(thm)],[c_51,c_77230]) ).

cnf(c_77968,plain,
    symmetric_difference(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))) = null_class,
    inference(superposition,[status(thm)],[c_77682,c_65393]) ).

cnf(c_77969,plain,
    subclass(null_class,complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))))),
    inference(superposition,[status(thm)],[c_77968,c_75967]) ).

cnf(c_78379,plain,
    ( ~ subclass(complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))),null_class)
    | complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))) = null_class ),
    inference(superposition,[status(thm)],[c_77969,c_58]) ).

cnf(c_79357,plain,
    complement(intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))) = null_class,
    inference(global_subsumption_just,[status(thm)],[c_78379,c_52529,c_52547]) ).

cnf(c_79378,plain,
    ( ~ member(X0,universal_class)
    | member(X0,intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_79357,c_76]) ).

cnf(c_82250,plain,
    ( member(X0,intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class)))))
    | ~ member(X0,universal_class) ),
    inference(global_subsumption_just,[status(thm)],[c_79378,c_8472,c_79378]) ).

cnf(c_82251,plain,
    ( ~ member(X0,universal_class)
    | member(X0,intersection(complement(singleton(u)),complement(set_builder(y,set_builder(z,null_class))))) ),
    inference(renaming,[status(thm)],[c_82250]) ).

cnf(c_82256,plain,
    ( ~ member(X0,universal_class)
    | member(X0,complement(singleton(u))) ),
    inference(superposition,[status(thm)],[c_82251,c_72]) ).

cnf(c_82389,plain,
    ( ~ member(X0,singleton(u))
    | ~ member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_82256,c_75]) ).

cnf(c_82505,plain,
    ~ member(u,universal_class),
    inference(superposition,[status(thm)],[c_65027,c_82389]) ).

cnf(c_82527,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_82505,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET134-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 20:32:59 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 93.08/13.22  % SZS status Started for theBenchmark.p
% 93.08/13.22  % SZS status Unsatisfiable for theBenchmark.p
% 93.08/13.22  
% 93.08/13.22  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 93.08/13.22  
% 93.08/13.22  ------  iProver source info
% 93.08/13.22  
% 93.08/13.22  git: date: 2024-05-02 19:28:25 +0000
% 93.08/13.22  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 93.08/13.22  git: non_committed_changes: false
% 93.08/13.22  
% 93.08/13.22  ------ Parsing...successful
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 93.08/13.22  
% 93.08/13.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 93.08/13.22  
% 93.08/13.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 93.08/13.22  ------ Proving...
% 93.08/13.22  ------ Problem Properties 
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  clauses                                 86
% 93.08/13.22  conjectures                             2
% 93.08/13.22  EPR                                     13
% 93.08/13.22  Horn                                    78
% 93.08/13.22  unary                                   34
% 93.08/13.22  binary                                  32
% 93.08/13.22  lits                                    164
% 93.08/13.22  lits eq                                 38
% 93.08/13.22  fd_pure                                 0
% 93.08/13.22  fd_pseudo                               0
% 93.08/13.22  fd_cond                                 3
% 93.08/13.22  fd_pseudo_cond                          3
% 93.08/13.22  AC symbols                              0
% 93.08/13.22  
% 93.08/13.22  ------ Input Options Time Limit: Unbounded
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  ------ 
% 93.08/13.22  Current options:
% 93.08/13.22  ------ 
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  ------ Proving...
% 93.08/13.22  
% 93.08/13.22  
% 93.08/13.22  % SZS status Unsatisfiable for theBenchmark.p
% 93.08/13.22  
% 93.08/13.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 93.08/13.22  
% 93.08/13.23  
%------------------------------------------------------------------------------