TSTP Solution File: SET067-7 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET067-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 02:52:55 EDT 2024

% Result   : Unsatisfiable 0.37s 0.56s
% Output   : CNFRefutation 0.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   43 (  17 unt;  14 nHn;  21 RR)
%            Number of literals    :   77 (  19 equ;  25 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   63 (  13 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pair_member,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

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

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

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

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

cnf(equality1,axiom,
    ( X1 = X2
    | member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).

cnf(prove_singleton_in_unordered_pair1_1,negated_conjecture,
    ~ subclass(singleton(x),unordered_pair(x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair1_1) ).

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

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(null_class_is_subclass,axiom,
    subclass(null_class,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).

cnf(c_0_13,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    c_0_12 ).

cnf(c_0_14,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_15,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,axiom,
    ( X1 = null_class
    | member(not_subclass_element(X1,null_class),X1) ),
    null_class_is_unique ).

cnf(c_0_17,plain,
    ~ member(X1,null_class),
    inference(fof_simplification,[status(thm)],[existence_of_null_class]) ).

cnf(c_0_18,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_19,axiom,
    ( X1 = X2
    | member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2) ),
    equality1 ).

cnf(c_0_20,plain,
    ( not_subclass_element(singleton(X1),null_class) = X1
    | singleton(X1) = null_class ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ~ member(X1,null_class),
    c_0_17 ).

cnf(c_0_22,negated_conjecture,
    ~ subclass(singleton(x),unordered_pair(x,y)),
    inference(fof_simplification,[status(thm)],[prove_singleton_in_unordered_pair1_1]) ).

cnf(c_0_23,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_18 ).

cnf(c_0_24,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_25,plain,
    ( singleton(X1) = null_class
    | member(X1,singleton(X1)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ~ subclass(singleton(x),unordered_pair(x,y)),
    c_0_22 ).

cnf(c_0_27,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,unordered_pair(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_14]) ).

cnf(c_0_29,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).

cnf(c_0_30,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_31,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[unordered_pair2]) ).

cnf(c_0_32,negated_conjecture,
    ~ subclass(unordered_pair(x,x),unordered_pair(x,y)),
    inference(rw,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_33,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,axiom,
    subclass(null_class,X1),
    null_class_is_subclass ).

cnf(c_0_35,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_29 ).

cnf(c_0_36,plain,
    ( not_subclass_element(singleton(X1),X2) = X1
    | subclass(singleton(X1),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_30]) ).

cnf(c_0_37,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    c_0_31 ).

cnf(c_0_38,negated_conjecture,
    member(x,universal_class),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_39,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    member(x,unordered_pair(x,X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    subclass(unordered_pair(x,x),unordered_pair(x,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_14]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_41])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : SET067-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.13/0.15  % Command    : run_E %s %d THM
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon May 20 11:19:38 EDT 2024
% 0.23/0.37  % CPUTime    : 
% 0.23/0.52  Running first-order theorem proving
% 0.23/0.52  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.37/0.56  # Version: 3.1.0
% 0.37/0.56  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.37/0.56  # Starting new_bool_3 with 300s (1) cores
% 0.37/0.56  # Starting new_bool_1 with 300s (1) cores
% 0.37/0.56  # Starting sh5l with 300s (1) cores
% 0.37/0.56  # sh5l with pid 31483 completed with status 0
% 0.37/0.56  # Result found by sh5l
% 0.37/0.56  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.37/0.56  # Starting new_bool_3 with 300s (1) cores
% 0.37/0.56  # Starting new_bool_1 with 300s (1) cores
% 0.37/0.56  # Starting sh5l with 300s (1) cores
% 0.37/0.56  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.37/0.56  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.37/0.56  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 0.37/0.56  # G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with pid 31486 completed with status 0
% 0.37/0.56  # Result found by G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S
% 0.37/0.56  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.37/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.37/0.56  # Starting new_bool_3 with 300s (1) cores
% 0.37/0.56  # Starting new_bool_1 with 300s (1) cores
% 0.37/0.56  # Starting sh5l with 300s (1) cores
% 0.37/0.56  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.37/0.56  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.37/0.56  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 0.37/0.56  # Preprocessing time       : 0.003 s
% 0.37/0.56  # Presaturation interreduction done
% 0.37/0.56  
% 0.37/0.56  # Proof found!
% 0.37/0.56  # SZS status Unsatisfiable
% 0.37/0.56  # SZS output start CNFRefutation
% See solution above
% 0.37/0.56  # Parsed axioms                        : 109
% 0.37/0.56  # Removed by relevancy pruning/SinE    : 9
% 0.37/0.56  # Initial clauses                      : 100
% 0.37/0.56  # Removed in clause preprocessing      : 0
% 0.37/0.56  # Initial clauses in saturation        : 100
% 0.37/0.56  # Processed clauses                    : 322
% 0.37/0.56  # ...of these trivial                  : 9
% 0.37/0.56  # ...subsumed                          : 42
% 0.37/0.56  # ...remaining for further processing  : 271
% 0.37/0.56  # Other redundant clauses eliminated   : 2
% 0.37/0.56  # Clauses deleted for lack of memory   : 0
% 0.37/0.56  # Backward-subsumed                    : 0
% 0.37/0.56  # Backward-rewritten                   : 4
% 0.37/0.56  # Generated clauses                    : 767
% 0.37/0.56  # ...of the previous two non-redundant : 633
% 0.37/0.56  # ...aggressively subsumed             : 0
% 0.37/0.56  # Contextual simplify-reflections      : 0
% 0.37/0.56  # Paramodulations                      : 761
% 0.37/0.56  # Factorizations                       : 2
% 0.37/0.56  # NegExts                              : 0
% 0.37/0.56  # Equation resolutions                 : 4
% 0.37/0.56  # Disequality decompositions           : 0
% 0.37/0.56  # Total rewrite steps                  : 186
% 0.37/0.56  # ...of those cached                   : 88
% 0.37/0.56  # Propositional unsat checks           : 0
% 0.37/0.56  #    Propositional check models        : 0
% 0.37/0.56  #    Propositional check unsatisfiable : 0
% 0.37/0.56  #    Propositional clauses             : 0
% 0.37/0.56  #    Propositional clauses after purity: 0
% 0.37/0.56  #    Propositional unsat core size     : 0
% 0.37/0.56  #    Propositional preprocessing time  : 0.000
% 0.37/0.56  #    Propositional encoding time       : 0.000
% 0.37/0.56  #    Propositional solver time         : 0.000
% 0.37/0.56  #    Success case prop preproc time    : 0.000
% 0.37/0.56  #    Success case prop encoding time   : 0.000
% 0.37/0.56  #    Success case prop solver time     : 0.000
% 0.37/0.56  # Current number of processed clauses  : 168
% 0.37/0.56  #    Positive orientable unit clauses  : 61
% 0.37/0.56  #    Positive unorientable unit clauses: 4
% 0.37/0.56  #    Negative unit clauses             : 1
% 0.37/0.56  #    Non-unit-clauses                  : 102
% 0.37/0.56  # Current number of unprocessed clauses: 505
% 0.37/0.56  # ...number of literals in the above   : 1054
% 0.37/0.56  # Current number of archived formulas  : 0
% 0.37/0.56  # Current number of archived clauses   : 101
% 0.37/0.56  # Clause-clause subsumption calls (NU) : 2276
% 0.37/0.56  # Rec. Clause-clause subsumption calls : 2022
% 0.37/0.56  # Non-unit clause-clause subsumptions  : 21
% 0.37/0.56  # Unit Clause-clause subsumption calls : 282
% 0.37/0.56  # Rewrite failures with RHS unbound    : 0
% 0.37/0.56  # BW rewrite match attempts            : 22
% 0.37/0.56  # BW rewrite match successes           : 16
% 0.37/0.56  # Condensation attempts                : 0
% 0.37/0.56  # Condensation successes               : 0
% 0.37/0.56  # Termbank termtop insertions          : 11974
% 0.37/0.56  # Search garbage collected termcells   : 214
% 0.37/0.56  
% 0.37/0.56  # -------------------------------------------------
% 0.37/0.56  # User time                : 0.027 s
% 0.37/0.56  # System time              : 0.002 s
% 0.37/0.56  # Total time               : 0.030 s
% 0.37/0.56  # Maximum resident set size: 1876 pages
% 0.37/0.56  
% 0.37/0.56  # -------------------------------------------------
% 0.37/0.56  # User time                : 0.030 s
% 0.37/0.56  # System time              : 0.005 s
% 0.37/0.56  # Total time               : 0.035 s
% 0.37/0.56  # Maximum resident set size: 1792 pages
% 0.37/0.56  % E---3.1 exiting
% 0.37/0.56  % E exiting
%------------------------------------------------------------------------------