TSTP Solution File: SET205-6 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET205-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 02:53:39 EDT 2024

% Result   : Unsatisfiable 34.01s 4.77s
% Output   : CNFRefutation 34.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   47 (  17 unt;   7 nHn;  31 RR)
%            Number of literals    :   81 (  32 equ;  38 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    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :   94 (  24 sgn)

% Comments : 
%------------------------------------------------------------------------------
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(intersection2,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

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

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

cnf(domain1,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).

cnf(restriction1,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).

cnf(restriction2,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).

cnf(cartesian_product4,axiom,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).

cnf(cartesian_product2,axiom,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).

cnf(prove_cross_product_with_null_class1_1,negated_conjecture,
    cross_product(x,null_class) != null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_with_null_class1_1) ).

cnf(c_0_11,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_12,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[intersection2]) ).

cnf(c_0_13,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[complement1]) ).

cnf(c_0_14,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_11 ).

cnf(c_0_15,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_16,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_12 ).

cnf(c_0_17,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_18,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    c_0_13 ).

cnf(c_0_19,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    inference(fof_simplification,[status(thm)],[domain1]) ).

cnf(c_0_21,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_23,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_19,c_0_17]) ).

cnf(c_0_24,plain,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    c_0_20 ).

cnf(c_0_25,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    restriction1 ).

cnf(c_0_26,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    restriction2 ).

cnf(c_0_27,plain,
    ( intersection(X1,complement(X2)) = null_class
    | ~ member(regular(intersection(X1,complement(X2))),X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_21]) ).

cnf(c_0_28,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,plain,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[cartesian_product4]) ).

cnf(c_0_30,plain,
    ( intersection(X1,cross_product(singleton(X2),universal_class)) != null_class
    | ~ member(X2,domain_of(X1)) ),
    inference(rw,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    intersection(X1,cross_product(X2,X3)) = intersection(cross_product(X2,X3),X1),
    inference(rw,[status(thm)],[c_0_26,c_0_25]) ).

cnf(c_0_32,plain,
    intersection(X1,null_class) = null_class,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_28]) ).

cnf(c_0_33,plain,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[cartesian_product2]) ).

cnf(c_0_34,plain,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    c_0_29 ).

cnf(c_0_35,plain,
    ( domain_of(X1) = null_class
    | intersection(X1,cross_product(singleton(regular(domain_of(X1))),universal_class)) != null_class ),
    inference(spm,[status(thm)],[c_0_30,c_0_17]) ).

cnf(c_0_36,plain,
    intersection(null_class,cross_product(X1,X2)) = null_class,
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,plain,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    c_0_33 ).

cnf(c_0_38,plain,
    ( ordered_pair(first(regular(cross_product(X1,X2))),second(regular(cross_product(X1,X2)))) = regular(cross_product(X1,X2))
    | cross_product(X1,X2) = null_class ),
    inference(spm,[status(thm)],[c_0_34,c_0_17]) ).

cnf(c_0_39,plain,
    domain_of(null_class) = null_class,
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,plain,
    ( cross_product(X1,X2) = null_class
    | member(second(regular(cross_product(X1,X2))),X3)
    | ~ member(regular(cross_product(X1,X2)),cross_product(X4,X3)) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    cross_product(x,null_class) != null_class,
    inference(fof_simplification,[status(thm)],[prove_cross_product_with_null_class1_1]) ).

cnf(c_0_42,plain,
    ~ member(X1,null_class),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_36])]) ).

cnf(c_0_43,plain,
    ( cross_product(X1,X2) = null_class
    | member(second(regular(cross_product(X1,X2))),X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_17]) ).

cnf(c_0_44,negated_conjecture,
    cross_product(x,null_class) != null_class,
    c_0_41 ).

cnf(c_0_45,plain,
    cross_product(X1,null_class) = null_class,
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SET205-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.10/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n009.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 11:50:52 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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
% 34.01/4.77  # Version: 3.1.0
% 34.01/4.77  # Preprocessing class: FSLSSMSMSSSNFFN.
% 34.01/4.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.01/4.77  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 34.01/4.77  # Starting new_bool_3 with 300s (1) cores
% 34.01/4.77  # Starting new_bool_1 with 300s (1) cores
% 34.01/4.77  # Starting sh5l with 300s (1) cores
% 34.01/4.77  # sh5l with pid 19296 completed with status 0
% 34.01/4.77  # Result found by sh5l
% 34.01/4.77  # Preprocessing class: FSLSSMSMSSSNFFN.
% 34.01/4.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.01/4.77  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 34.01/4.77  # Starting new_bool_3 with 300s (1) cores
% 34.01/4.77  # Starting new_bool_1 with 300s (1) cores
% 34.01/4.77  # Starting sh5l with 300s (1) cores
% 34.01/4.77  # SinE strategy is gf500_gu_R04_F100_L20000
% 34.01/4.77  # Search class: FGHSM-FFMM31-MFFFFFNN
% 34.01/4.77  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 34.01/4.77  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 34.01/4.77  # G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with pid 19299 completed with status 0
% 34.01/4.77  # Result found by G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S
% 34.01/4.77  # Preprocessing class: FSLSSMSMSSSNFFN.
% 34.01/4.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 34.01/4.77  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 34.01/4.77  # Starting new_bool_3 with 300s (1) cores
% 34.01/4.77  # Starting new_bool_1 with 300s (1) cores
% 34.01/4.77  # Starting sh5l with 300s (1) cores
% 34.01/4.77  # SinE strategy is gf500_gu_R04_F100_L20000
% 34.01/4.77  # Search class: FGHSM-FFMM31-MFFFFFNN
% 34.01/4.77  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 34.01/4.77  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 34.01/4.77  # Preprocessing time       : 0.003 s
% 34.01/4.77  # Presaturation interreduction done
% 34.01/4.77  
% 34.01/4.77  # Proof found!
% 34.01/4.77  # SZS status Unsatisfiable
% 34.01/4.77  # SZS output start CNFRefutation
% See solution above
% 34.01/4.77  # Parsed axioms                        : 113
% 34.01/4.77  # Removed by relevancy pruning/SinE    : 14
% 34.01/4.77  # Initial clauses                      : 99
% 34.01/4.77  # Removed in clause preprocessing      : 0
% 34.01/4.77  # Initial clauses in saturation        : 99
% 34.01/4.77  # Processed clauses                    : 12788
% 34.01/4.77  # ...of these trivial                  : 741
% 34.01/4.77  # ...subsumed                          : 7558
% 34.01/4.77  # ...remaining for further processing  : 4489
% 34.01/4.77  # Other redundant clauses eliminated   : 16
% 34.01/4.77  # Clauses deleted for lack of memory   : 0
% 34.01/4.77  # Backward-subsumed                    : 188
% 34.01/4.77  # Backward-rewritten                   : 718
% 34.01/4.77  # Generated clauses                    : 404550
% 34.01/4.77  # ...of the previous two non-redundant : 330672
% 34.01/4.77  # ...aggressively subsumed             : 0
% 34.01/4.77  # Contextual simplify-reflections      : 7
% 34.01/4.77  # Paramodulations                      : 404503
% 34.01/4.77  # Factorizations                       : 22
% 34.01/4.77  # NegExts                              : 0
% 34.01/4.77  # Equation resolutions                 : 25
% 34.01/4.77  # Disequality decompositions           : 0
% 34.01/4.77  # Total rewrite steps                  : 163939
% 34.01/4.77  # ...of those cached                   : 156465
% 34.01/4.77  # Propositional unsat checks           : 0
% 34.01/4.77  #    Propositional check models        : 0
% 34.01/4.77  #    Propositional check unsatisfiable : 0
% 34.01/4.77  #    Propositional clauses             : 0
% 34.01/4.77  #    Propositional clauses after purity: 0
% 34.01/4.77  #    Propositional unsat core size     : 0
% 34.01/4.77  #    Propositional preprocessing time  : 0.000
% 34.01/4.77  #    Propositional encoding time       : 0.000
% 34.01/4.77  #    Propositional solver time         : 0.000
% 34.01/4.77  #    Success case prop preproc time    : 0.000
% 34.01/4.77  #    Success case prop encoding time   : 0.000
% 34.01/4.77  #    Success case prop solver time     : 0.000
% 34.01/4.77  # Current number of processed clauses  : 3483
% 34.01/4.77  #    Positive orientable unit clauses  : 1460
% 34.01/4.77  #    Positive unorientable unit clauses: 11
% 34.01/4.77  #    Negative unit clauses             : 13
% 34.01/4.77  #    Non-unit-clauses                  : 1999
% 34.01/4.77  # Current number of unprocessed clauses: 316518
% 34.01/4.77  # ...number of literals in the above   : 626651
% 34.01/4.77  # Current number of archived formulas  : 0
% 34.01/4.77  # Current number of archived clauses   : 1004
% 34.01/4.77  # Clause-clause subsumption calls (NU) : 710336
% 34.01/4.77  # Rec. Clause-clause subsumption calls : 477778
% 34.01/4.77  # Non-unit clause-clause subsumptions  : 5560
% 34.01/4.77  # Unit Clause-clause subsumption calls : 189843
% 34.01/4.77  # Rewrite failures with RHS unbound    : 145
% 34.01/4.77  # BW rewrite match attempts            : 6506
% 34.01/4.77  # BW rewrite match successes           : 207
% 34.01/4.77  # Condensation attempts                : 0
% 34.01/4.77  # Condensation successes               : 0
% 34.01/4.77  # Termbank termtop insertions          : 6799073
% 34.01/4.77  # Search garbage collected termcells   : 229
% 34.01/4.77  
% 34.01/4.77  # -------------------------------------------------
% 34.01/4.77  # User time                : 3.970 s
% 34.01/4.77  # System time              : 0.193 s
% 34.01/4.77  # Total time               : 4.163 s
% 34.01/4.77  # Maximum resident set size: 1892 pages
% 34.01/4.77  
% 34.01/4.77  # -------------------------------------------------
% 34.01/4.77  # User time                : 3.973 s
% 34.01/4.77  # System time              : 0.195 s
% 34.01/4.77  # Total time               : 4.169 s
% 34.01/4.77  # Maximum resident set size: 1800 pages
% 34.01/4.77  % E---3.1 exiting
% 34.01/4.77  % E exiting
%------------------------------------------------------------------------------