TSTP Solution File: SET068-7 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SET068-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 02:57:21 EDT 2024

% Result   : Unsatisfiable 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   46 (  20 unt;  14 nHn;  22 RR)
%            Number of literals    :   80 (  21 equ;  26 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   :   67 (  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(prove_singleton_in_unordered_pair2_1,negated_conjecture,
    ~ subclass(singleton(y),unordered_pair(x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair2_1) ).

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

cnf(commutativity_of_unordered_pair,axiom,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).

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_13,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).

cnf(c_0_14,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    c_0_13 ).

cnf(c_0_15,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_16,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,axiom,
    ( X1 = null_class
    | member(not_subclass_element(X1,null_class),X1) ),
    null_class_is_unique ).

cnf(c_0_18,plain,
    ~ member(X1,null_class),
    inference(fof_simplification,[status(thm)],[existence_of_null_class]) ).

cnf(c_0_19,negated_conjecture,
    ~ subclass(singleton(y),unordered_pair(x,y)),
    inference(fof_simplification,[status(thm)],[prove_singleton_in_unordered_pair2_1]) ).

cnf(c_0_20,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_21,axiom,
    ( X1 = X2
    | member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2) ),
    equality1 ).

cnf(c_0_22,plain,
    ( not_subclass_element(singleton(X1),null_class) = X1
    | singleton(X1) = null_class ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,plain,
    ~ member(X1,null_class),
    c_0_18 ).

cnf(c_0_24,negated_conjecture,
    ~ subclass(singleton(y),unordered_pair(x,y)),
    c_0_19 ).

cnf(c_0_25,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_20 ).

cnf(c_0_26,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_27,plain,
    ( singleton(X1) = null_class
    | member(X1,singleton(X1)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ~ subclass(unordered_pair(y,y),unordered_pair(x,y)),
    inference(rw,[status(thm)],[c_0_24,c_0_15]) ).

cnf(c_0_29,axiom,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    commutativity_of_unordered_pair ).

cnf(c_0_30,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,unordered_pair(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_15]) ).

cnf(c_0_32,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).

cnf(c_0_33,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_34,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[unordered_pair2]) ).

cnf(c_0_35,negated_conjecture,
    ~ subclass(unordered_pair(y,y),unordered_pair(y,x)),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,axiom,
    subclass(null_class,X1),
    null_class_is_subclass ).

cnf(c_0_38,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_32 ).

cnf(c_0_39,plain,
    ( not_subclass_element(singleton(X1),X2) = X1
    | subclass(singleton(X1),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_33]) ).

cnf(c_0_40,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    c_0_34 ).

cnf(c_0_41,negated_conjecture,
    member(y,universal_class),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

cnf(c_0_42,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    member(y,unordered_pair(y,X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    subclass(unordered_pair(y,y),unordered_pair(y,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_15]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET068-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 12:16:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order model finding
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.53  # Version: 3.1.0
% 0.21/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # sh5l with pid 10270 completed with status 0
% 0.21/0.53  # Result found by sh5l
% 0.21/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.21/0.53  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 0.21/0.53  # G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with pid 10273 completed with status 0
% 0.21/0.53  # Result found by G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S
% 0.21/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.21/0.53  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 0.21/0.53  # Preprocessing time       : 0.003 s
% 0.21/0.53  # Presaturation interreduction done
% 0.21/0.53  
% 0.21/0.53  # Proof found!
% 0.21/0.53  # SZS status Unsatisfiable
% 0.21/0.53  # SZS output start CNFRefutation
% See solution above
% 0.21/0.53  # Parsed axioms                        : 109
% 0.21/0.53  # Removed by relevancy pruning/SinE    : 9
% 0.21/0.53  # Initial clauses                      : 100
% 0.21/0.53  # Removed in clause preprocessing      : 0
% 0.21/0.53  # Initial clauses in saturation        : 100
% 0.21/0.53  # Processed clauses                    : 322
% 0.21/0.53  # ...of these trivial                  : 9
% 0.21/0.53  # ...subsumed                          : 42
% 0.21/0.53  # ...remaining for further processing  : 271
% 0.21/0.53  # Other redundant clauses eliminated   : 2
% 0.21/0.53  # Clauses deleted for lack of memory   : 0
% 0.21/0.53  # Backward-subsumed                    : 0
% 0.21/0.53  # Backward-rewritten                   : 5
% 0.21/0.53  # Generated clauses                    : 762
% 0.21/0.53  # ...of the previous two non-redundant : 629
% 0.21/0.53  # ...aggressively subsumed             : 0
% 0.21/0.53  # Contextual simplify-reflections      : 0
% 0.21/0.53  # Paramodulations                      : 756
% 0.21/0.53  # Factorizations                       : 2
% 0.21/0.53  # NegExts                              : 0
% 0.21/0.53  # Equation resolutions                 : 4
% 0.21/0.53  # Disequality decompositions           : 0
% 0.21/0.53  # Total rewrite steps                  : 187
% 0.21/0.53  # ...of those cached                   : 87
% 0.21/0.53  # Propositional unsat checks           : 0
% 0.21/0.53  #    Propositional check models        : 0
% 0.21/0.53  #    Propositional check unsatisfiable : 0
% 0.21/0.53  #    Propositional clauses             : 0
% 0.21/0.53  #    Propositional clauses after purity: 0
% 0.21/0.53  #    Propositional unsat core size     : 0
% 0.21/0.53  #    Propositional preprocessing time  : 0.000
% 0.21/0.53  #    Propositional encoding time       : 0.000
% 0.21/0.53  #    Propositional solver time         : 0.000
% 0.21/0.53  #    Success case prop preproc time    : 0.000
% 0.21/0.53  #    Success case prop encoding time   : 0.000
% 0.21/0.53  #    Success case prop solver time     : 0.000
% 0.21/0.53  # Current number of processed clauses  : 167
% 0.21/0.53  #    Positive orientable unit clauses  : 61
% 0.21/0.53  #    Positive unorientable unit clauses: 4
% 0.21/0.53  #    Negative unit clauses             : 1
% 0.21/0.53  #    Non-unit-clauses                  : 101
% 0.21/0.53  # Current number of unprocessed clauses: 501
% 0.21/0.53  # ...number of literals in the above   : 1046
% 0.21/0.53  # Current number of archived formulas  : 0
% 0.21/0.53  # Current number of archived clauses   : 102
% 0.21/0.53  # Clause-clause subsumption calls (NU) : 2221
% 0.21/0.53  # Rec. Clause-clause subsumption calls : 1965
% 0.21/0.53  # Non-unit clause-clause subsumptions  : 21
% 0.21/0.53  # Unit Clause-clause subsumption calls : 280
% 0.21/0.53  # Rewrite failures with RHS unbound    : 0
% 0.21/0.53  # BW rewrite match attempts            : 22
% 0.21/0.53  # BW rewrite match successes           : 16
% 0.21/0.53  # Condensation attempts                : 0
% 0.21/0.53  # Condensation successes               : 0
% 0.21/0.53  # Termbank termtop insertions          : 11900
% 0.21/0.53  # Search garbage collected termcells   : 214
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.027 s
% 0.21/0.53  # System time              : 0.004 s
% 0.21/0.53  # Total time               : 0.031 s
% 0.21/0.53  # Maximum resident set size: 1868 pages
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.032 s
% 0.21/0.53  # System time              : 0.005 s
% 0.21/0.53  # Total time               : 0.037 s
% 0.21/0.53  # Maximum resident set size: 1788 pages
% 0.21/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------