TSTP Solution File: SET468-6 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET468-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 : Mon Jun 24 14:34:38 EDT 2024

% Result   : Unsatisfiable 192.80s 26.33s
% Output   : CNFRefutation 192.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   36 (  16 unt;   7 nHn;  23 RR)
%            Number of literals    :   58 (  14 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   56 (  17 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,negated_conjecture,
    x = null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sets_with_one_member2_1) ).

cnf(c_50,negated_conjecture,
    ~ subclass(cross_product(x,x),identity_relation),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sets_with_one_member2_2) ).

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

cnf(c_73,plain,
    ( member(not_subclass_element(X0,X1),X0)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(c_74,plain,
    ( ~ member(not_subclass_element(X0,X1),X1)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(c_75,plain,
    subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(c_78,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(X1,X0)
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(c_86,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).

cnf(c_88,plain,
    ( ~ member(X0,cross_product(X1,X2))
    | ordered_pair(first(X0),second(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).

cnf(c_92,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(c_95,plain,
    ( ~ member(X0,complement(X1))
    | ~ member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(c_99,plain,
    intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).

cnf(c_101,plain,
    ( restrict(X0,singleton(X1),universal_class) != null_class
    | ~ member(X1,domain_of(X0)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).

cnf(c_137,plain,
    ( X0 = null_class
    | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(c_1053,plain,
    ~ subclass(cross_product(null_class,null_class),identity_relation),
    inference(light_normalisation,[status(thm)],[c_50,c_49]) ).

cnf(c_4082,plain,
    ( ~ member(not_subclass_element(complement(X0),X1),X0)
    | subclass(complement(X0),X1) ),
    inference(superposition,[status(thm)],[c_73,c_95]) ).

cnf(c_4083,plain,
    ( ~ member(regular(complement(X0)),X0)
    | complement(X0) = null_class ),
    inference(superposition,[status(thm)],[c_137,c_95]) ).

cnf(c_4125,plain,
    ( ~ member(X0,X1)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_75,c_72]) ).

cnf(c_4139,plain,
    ( member(not_subclass_element(X0,X1),universal_class)
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_73,c_4125]) ).

cnf(c_4148,plain,
    ( X0 = null_class
    | member(regular(X0),universal_class) ),
    inference(superposition,[status(thm)],[c_137,c_4125]) ).

cnf(c_4701,plain,
    subclass(complement(universal_class),X0),
    inference(superposition,[status(thm)],[c_4139,c_4082]) ).

cnf(c_4916,plain,
    complement(universal_class) = null_class,
    inference(superposition,[status(thm)],[c_4148,c_4083]) ).

cnf(c_4927,plain,
    subclass(null_class,X0),
    inference(demodulation,[status(thm)],[c_4701,c_4916]) ).

cnf(c_7575,plain,
    ( member(not_subclass_element(intersection(X0,X1),X2),X0)
    | subclass(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_73,c_92]) ).

cnf(c_8054,plain,
    ( ~ subclass(X0,null_class)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_4927,c_78]) ).

cnf(c_8591,plain,
    subclass(intersection(X0,X1),X0),
    inference(superposition,[status(thm)],[c_7575,c_74]) ).

cnf(c_8653,plain,
    subclass(restrict(X0,X1,X2),X0),
    inference(superposition,[status(thm)],[c_99,c_8591]) ).

cnf(c_8687,plain,
    restrict(null_class,X0,X1) = null_class,
    inference(superposition,[status(thm)],[c_8653,c_8054]) ).

cnf(c_8741,plain,
    ~ member(X0,domain_of(null_class)),
    inference(superposition,[status(thm)],[c_8687,c_101]) ).

cnf(c_8749,plain,
    domain_of(null_class) = null_class,
    inference(superposition,[status(thm)],[c_137,c_8741]) ).

cnf(c_8755,plain,
    ~ member(X0,null_class),
    inference(demodulation,[status(thm)],[c_8741,c_8749]) ).

cnf(c_58511,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2)
    | subclass(cross_product(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_73,c_88]) ).

cnf(c_84822,plain,
    ordered_pair(first(not_subclass_element(cross_product(null_class,null_class),identity_relation)),second(not_subclass_element(cross_product(null_class,null_class),identity_relation))) = not_subclass_element(cross_product(null_class,null_class),identity_relation),
    inference(superposition,[status(thm)],[c_58511,c_1053]) ).

cnf(c_85164,plain,
    ( ~ member(not_subclass_element(cross_product(null_class,null_class),identity_relation),cross_product(X0,X1))
    | member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),X1) ),
    inference(superposition,[status(thm)],[c_84822,c_86]) ).

cnf(c_87612,plain,
    ( member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),null_class)
    | subclass(cross_product(null_class,null_class),identity_relation) ),
    inference(superposition,[status(thm)],[c_73,c_85164]) ).

cnf(c_87622,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_87612,c_1053,c_8755]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET468-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n026.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  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 15:33:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 192.80/26.33  % SZS status Started for theBenchmark.p
% 192.80/26.33  % SZS status Unsatisfiable for theBenchmark.p
% 192.80/26.33  
% 192.80/26.33  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 192.80/26.33  
% 192.80/26.33  ------  iProver source info
% 192.80/26.33  
% 192.80/26.33  git: date: 2024-06-12 09:56:46 +0000
% 192.80/26.33  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 192.80/26.33  git: non_committed_changes: false
% 192.80/26.33  
% 192.80/26.33  ------ Parsing...successful
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  ------ Preprocessing... sup_sim: 3  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 192.80/26.33  
% 192.80/26.33  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 192.80/26.33  
% 192.80/26.33  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 192.80/26.33  ------ Proving...
% 192.80/26.33  ------ Problem Properties 
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  clauses                                 102
% 192.80/26.33  conjectures                             1
% 192.80/26.33  EPR                                     13
% 192.80/26.33  Horn                                    94
% 192.80/26.33  unary                                   41
% 192.80/26.33  binary                                  40
% 192.80/26.33  lits                                    190
% 192.80/26.33  lits eq                                 45
% 192.80/26.33  fd_pure                                 0
% 192.80/26.33  fd_pseudo                               0
% 192.80/26.33  fd_cond                                 3
% 192.80/26.33  fd_pseudo_cond                          7
% 192.80/26.33  AC symbols                              0
% 192.80/26.33  
% 192.80/26.33  ------ Input Options Time Limit: Unbounded
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  ------ 
% 192.80/26.33  Current options:
% 192.80/26.33  ------ 
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  ------ Proving...
% 192.80/26.33  
% 192.80/26.33  
% 192.80/26.33  % SZS status Unsatisfiable for theBenchmark.p
% 192.80/26.33  
% 192.80/26.33  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 192.80/26.34  
% 192.80/26.34  
%------------------------------------------------------------------------------