TSTP Solution File: SET097-7 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 : Tue May 21 02:53:10 EDT 2024

% Result   : Unsatisfiable 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   59 (  23 unt;  10 nHn;  45 RR)
%            Number of literals    :  108 (  25 equ;  54 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_number_of_elements_in_class_1,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(intersection3,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).

cnf(null_class_is_unique,axiom,
    ( X1 = null_class
    | member(not_subclass_element(X1,null_class),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).

cnf(existence_of_null_class,axiom,
    ~ member(X1,null_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).

cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(only_member_in_singleton,axiom,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).

cnf(complement2,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(prove_number_of_elements_in_class_3,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).

cnf(property_of_singletons2,axiom,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons2) ).

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(subclass_implies_equal,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(prove_number_of_elements_in_class_2,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).

cnf(c_0_16,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_1]) ).

cnf(c_0_17,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    c_0_16 ).

cnf(c_0_18,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_19,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(fof_simplification,[status(thm)],[intersection3]) ).

cnf(c_0_20,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).

cnf(c_0_21,axiom,
    ( X1 = null_class
    | member(not_subclass_element(X1,null_class),X1) ),
    null_class_is_unique ).

cnf(c_0_22,plain,
    ~ member(X1,null_class),
    inference(fof_simplification,[status(thm)],[existence_of_null_class]) ).

cnf(c_0_23,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_24,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).

cnf(c_0_25,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    c_0_19 ).

cnf(c_0_26,negated_conjecture,
    intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    ~ member(X1,null_class),
    c_0_22 ).

cnf(c_0_28,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[complement2]) ).

cnf(c_0_29,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_23 ).

cnf(c_0_30,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_31,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    c_0_24 ).

cnf(c_0_32,negated_conjecture,
    ( ~ member(X1,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
    | ~ member(X1,x) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_33,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    c_0_28 ).

cnf(c_0_34,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | ~ member(X1,unordered_pair(X2,X2)) ),
    inference(rw,[status(thm)],[c_0_31,c_0_18]) ).

cnf(c_0_36,negated_conjecture,
    ( member(X1,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
    | ~ member(X1,x) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    x != null_class,
    inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_3]) ).

cnf(c_0_38,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[property_of_singletons2]) ).

cnf(c_0_39,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).

cnf(c_0_40,negated_conjecture,
    ( X1 = not_subclass_element(x,null_class)
    | ~ member(X1,x) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_42,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_43,negated_conjecture,
    x != null_class,
    c_0_37 ).

cnf(c_0_44,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).

cnf(c_0_45,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    c_0_38 ).

cnf(c_0_46,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_39 ).

cnf(c_0_47,negated_conjecture,
    ( not_subclass_element(x,X1) = not_subclass_element(x,null_class)
    | subclass(x,X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    regular(x) = not_subclass_element(x,null_class),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(fof_simplification,[status(thm)],[prove_number_of_elements_in_class_2]) ).

cnf(c_0_50,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    c_0_44 ).

cnf(c_0_51,plain,
    ( subclass(unordered_pair(X1,X1),X2)
    | ~ member(X1,X2) ),
    inference(rw,[status(thm)],[c_0_45,c_0_18]) ).

cnf(c_0_52,negated_conjecture,
    ( subclass(x,X1)
    | ~ member(not_subclass_element(x,null_class),X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_53,negated_conjecture,
    member(not_subclass_element(x,null_class),x),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_48]),c_0_43]) ).

cnf(c_0_54,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    c_0_49 ).

cnf(c_0_55,plain,
    ( X1 = unordered_pair(X2,X2)
    | ~ member(X2,X1)
    | ~ subclass(X1,unordered_pair(X2,X2)) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_56,negated_conjecture,
    subclass(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_36]),c_0_53])]) ).

cnf(c_0_57,negated_conjecture,
    unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
    inference(rw,[status(thm)],[c_0_54,c_0_18]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53])]),c_0_57]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n010.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    : 300
% 0.13/0.34  % DateTime   : Mon May 20 12:49:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.59  # Version: 3.1.0
% 0.19/0.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.59  # Starting sh5l with 300s (1) cores
% 0.19/0.59  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 7710 completed with status 0
% 0.19/0.59  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.19/0.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.59  # No SInE strategy applied
% 0.19/0.59  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.19/0.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.19/0.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.59  # Starting new_bool_1 with 308s (1) cores
% 0.19/0.59  # Starting sh5l with 304s (1) cores
% 0.19/0.59  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.19/0.59  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 7718 completed with status 0
% 0.19/0.59  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.19/0.59  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.19/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.19/0.59  # No SInE strategy applied
% 0.19/0.59  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.19/0.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.19/0.59  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.19/0.59  # Preprocessing time       : 0.003 s
% 0.19/0.59  # Presaturation interreduction done
% 0.19/0.59  
% 0.19/0.59  # Proof found!
% 0.19/0.59  # SZS status Unsatisfiable
% 0.19/0.59  # SZS output start CNFRefutation
% See solution above
% 0.19/0.59  # Parsed axioms                        : 143
% 0.19/0.59  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.59  # Initial clauses                      : 143
% 0.19/0.59  # Removed in clause preprocessing      : 15
% 0.19/0.59  # Initial clauses in saturation        : 128
% 0.19/0.59  # Processed clauses                    : 818
% 0.19/0.59  # ...of these trivial                  : 20
% 0.19/0.59  # ...subsumed                          : 370
% 0.19/0.59  # ...remaining for further processing  : 428
% 0.19/0.59  # Other redundant clauses eliminated   : 35
% 0.19/0.59  # Clauses deleted for lack of memory   : 0
% 0.19/0.59  # Backward-subsumed                    : 18
% 0.19/0.59  # Backward-rewritten                   : 12
% 0.19/0.59  # Generated clauses                    : 4243
% 0.19/0.59  # ...of the previous two non-redundant : 3404
% 0.19/0.59  # ...aggressively subsumed             : 0
% 0.19/0.59  # Contextual simplify-reflections      : 3
% 0.19/0.59  # Paramodulations                      : 4195
% 0.19/0.59  # Factorizations                       : 9
% 0.19/0.59  # NegExts                              : 0
% 0.19/0.59  # Equation resolutions                 : 39
% 0.19/0.59  # Disequality decompositions           : 0
% 0.19/0.59  # Total rewrite steps                  : 938
% 0.19/0.59  # ...of those cached                   : 838
% 0.19/0.59  # Propositional unsat checks           : 0
% 0.19/0.59  #    Propositional check models        : 0
% 0.19/0.59  #    Propositional check unsatisfiable : 0
% 0.19/0.59  #    Propositional clauses             : 0
% 0.19/0.59  #    Propositional clauses after purity: 0
% 0.19/0.59  #    Propositional unsat core size     : 0
% 0.19/0.59  #    Propositional preprocessing time  : 0.000
% 0.19/0.59  #    Propositional encoding time       : 0.000
% 0.19/0.59  #    Propositional solver time         : 0.000
% 0.19/0.59  #    Success case prop preproc time    : 0.000
% 0.19/0.59  #    Success case prop encoding time   : 0.000
% 0.19/0.59  #    Success case prop solver time     : 0.000
% 0.19/0.59  # Current number of processed clauses  : 274
% 0.19/0.59  #    Positive orientable unit clauses  : 42
% 0.19/0.59  #    Positive unorientable unit clauses: 2
% 0.19/0.59  #    Negative unit clauses             : 12
% 0.19/0.59  #    Non-unit-clauses                  : 218
% 0.19/0.59  # Current number of unprocessed clauses: 2813
% 0.19/0.59  # ...number of literals in the above   : 9068
% 0.19/0.59  # Current number of archived formulas  : 0
% 0.19/0.59  # Current number of archived clauses   : 166
% 0.19/0.59  # Clause-clause subsumption calls (NU) : 13805
% 0.19/0.59  # Rec. Clause-clause subsumption calls : 6302
% 0.19/0.59  # Non-unit clause-clause subsumptions  : 256
% 0.19/0.59  # Unit Clause-clause subsumption calls : 679
% 0.19/0.59  # Rewrite failures with RHS unbound    : 0
% 0.19/0.59  # BW rewrite match attempts            : 62
% 0.19/0.59  # BW rewrite match successes           : 57
% 0.19/0.59  # Condensation attempts                : 0
% 0.19/0.59  # Condensation successes               : 0
% 0.19/0.59  # Termbank termtop insertions          : 139586
% 0.19/0.59  # Search garbage collected termcells   : 230
% 0.19/0.59  
% 0.19/0.59  # -------------------------------------------------
% 0.19/0.59  # User time                : 0.106 s
% 0.19/0.59  # System time              : 0.004 s
% 0.19/0.59  # Total time               : 0.110 s
% 0.19/0.59  # Maximum resident set size: 2104 pages
% 0.19/0.59  
% 0.19/0.59  # -------------------------------------------------
% 0.19/0.59  # User time                : 0.520 s
% 0.19/0.59  # System time              : 0.013 s
% 0.19/0.59  # Total time               : 0.533 s
% 0.19/0.59  # Maximum resident set size: 1816 pages
% 0.19/0.59  % E---3.1 exiting
% 0.19/0.59  % E exiting
%------------------------------------------------------------------------------