TSTP Solution File: SET103-6 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET103-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 02:53:13 EDT 2024

% Result   : Unsatisfiable 0.72s 0.53s
% Output   : CNFRefutation 0.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   29 (  16 unt;  10 nHn;  16 RR)
%            Number of literals    :   50 (  26 equ;  17 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (   2 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(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(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

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

cnf(prove_property_1_of_ordered_pair_1,negated_conjecture,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_1) ).

cnf(ordered_pair,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

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

cnf(prove_property_1_of_ordered_pair_2,negated_conjecture,
    ~ member(y,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_2) ).

cnf(c_0_8,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_9,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).

cnf(c_0_10,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_8 ).

cnf(c_0_11,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_12,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    c_0_9 ).

cnf(c_0_13,plain,
    ( X1 = null_class
    | member(regular(X1),X2)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_15,plain,
    ( regular(unordered_pair(X1,X2)) = X1
    | regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class ),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    inference(fof_simplification,[status(thm)],[prove_property_1_of_ordered_pair_1]) ).

cnf(c_0_17,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

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

cnf(c_0_19,negated_conjecture,
    ~ member(y,universal_class),
    inference(fof_simplification,[status(thm)],[prove_property_1_of_ordered_pair_2]) ).

cnf(c_0_20,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_21,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_15])]) ).

cnf(c_0_22,negated_conjecture,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    c_0_16 ).

cnf(c_0_23,plain,
    unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ~ member(y,universal_class),
    c_0_19 ).

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

cnf(c_0_26,negated_conjecture,
    unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_18]),c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    unordered_pair(y,y) = null_class,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_26,c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem    : SET103-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.05/0.12  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n016.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon May 20 11:49:52 EDT 2024
% 0.15/0.31  % CPUTime    : 
% 0.15/0.45  Running first-order theorem proving
% 0.15/0.45  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
% 0.72/0.53  # Version: 3.1.0
% 0.72/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.72/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.72/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.72/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.72/0.53  # Starting sh5l with 300s (1) cores
% 0.72/0.53  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 13601 completed with status 0
% 0.72/0.53  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.72/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.72/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.72/0.53  # No SInE strategy applied
% 0.72/0.53  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.72/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.72/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.72/0.53  # Starting new_bool_1 with 308s (1) cores
% 0.72/0.53  # Starting sh5l with 304s (1) cores
% 0.72/0.53  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.72/0.53  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 13612 completed with status 0
% 0.72/0.53  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.72/0.53  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.72/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.72/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.72/0.53  # No SInE strategy applied
% 0.72/0.53  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.72/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.72/0.53  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.72/0.53  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.72/0.53  # Starting new_bool_1 with 308s (1) cores
% 0.72/0.53  # Starting sh5l with 304s (1) cores
% 0.72/0.53  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.72/0.53  # Preprocessing time       : 0.003 s
% 0.72/0.53  # Presaturation interreduction done
% 0.72/0.53  
% 0.72/0.53  # Proof found!
% 0.72/0.53  # SZS status Unsatisfiable
% 0.72/0.53  # SZS output start CNFRefutation
% See solution above
% 0.72/0.53  # Parsed axioms                        : 93
% 0.72/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.72/0.53  # Initial clauses                      : 93
% 0.72/0.53  # Removed in clause preprocessing      : 15
% 0.72/0.53  # Initial clauses in saturation        : 78
% 0.72/0.53  # Processed clauses                    : 510
% 0.72/0.53  # ...of these trivial                  : 1
% 0.72/0.53  # ...subsumed                          : 129
% 0.72/0.53  # ...remaining for further processing  : 380
% 0.72/0.53  # Other redundant clauses eliminated   : 5
% 0.72/0.53  # Clauses deleted for lack of memory   : 0
% 0.72/0.53  # Backward-subsumed                    : 40
% 0.72/0.53  # Backward-rewritten                   : 17
% 0.72/0.53  # Generated clauses                    : 992
% 0.72/0.53  # ...of the previous two non-redundant : 843
% 0.72/0.53  # ...aggressively subsumed             : 0
% 0.72/0.53  # Contextual simplify-reflections      : 2
% 0.72/0.53  # Paramodulations                      : 976
% 0.72/0.53  # Factorizations                       : 6
% 0.72/0.53  # NegExts                              : 0
% 0.72/0.53  # Equation resolutions                 : 5
% 0.72/0.53  # Disequality decompositions           : 0
% 0.72/0.53  # Total rewrite steps                  : 244
% 0.72/0.53  # ...of those cached                   : 196
% 0.72/0.53  # Propositional unsat checks           : 0
% 0.72/0.53  #    Propositional check models        : 0
% 0.72/0.53  #    Propositional check unsatisfiable : 0
% 0.72/0.53  #    Propositional clauses             : 0
% 0.72/0.53  #    Propositional clauses after purity: 0
% 0.72/0.53  #    Propositional unsat core size     : 0
% 0.72/0.53  #    Propositional preprocessing time  : 0.000
% 0.72/0.53  #    Propositional encoding time       : 0.000
% 0.72/0.53  #    Propositional solver time         : 0.000
% 0.72/0.53  #    Success case prop preproc time    : 0.000
% 0.72/0.53  #    Success case prop encoding time   : 0.000
% 0.72/0.53  #    Success case prop solver time     : 0.000
% 0.72/0.53  # Current number of processed clauses  : 238
% 0.72/0.53  #    Positive orientable unit clauses  : 36
% 0.72/0.53  #    Positive unorientable unit clauses: 1
% 0.72/0.53  #    Negative unit clauses             : 4
% 0.72/0.53  #    Non-unit-clauses                  : 197
% 0.72/0.53  # Current number of unprocessed clauses: 387
% 0.72/0.53  # ...number of literals in the above   : 1223
% 0.72/0.53  # Current number of archived formulas  : 0
% 0.72/0.53  # Current number of archived clauses   : 154
% 0.72/0.53  # Clause-clause subsumption calls (NU) : 15214
% 0.72/0.53  # Rec. Clause-clause subsumption calls : 7616
% 0.72/0.53  # Non-unit clause-clause subsumptions  : 130
% 0.72/0.53  # Unit Clause-clause subsumption calls : 1070
% 0.72/0.53  # Rewrite failures with RHS unbound    : 0
% 0.72/0.53  # BW rewrite match attempts            : 26
% 0.72/0.53  # BW rewrite match successes           : 14
% 0.72/0.53  # Condensation attempts                : 0
% 0.72/0.53  # Condensation successes               : 0
% 0.72/0.53  # Termbank termtop insertions          : 36500
% 0.72/0.53  # Search garbage collected termcells   : 158
% 0.72/0.53  
% 0.72/0.53  # -------------------------------------------------
% 0.72/0.53  # User time                : 0.051 s
% 0.72/0.53  # System time              : 0.003 s
% 0.72/0.53  # Total time               : 0.054 s
% 0.72/0.53  # Maximum resident set size: 1928 pages
% 0.72/0.53  
% 0.72/0.53  # -------------------------------------------------
% 0.72/0.53  # User time                : 0.250 s
% 0.72/0.53  # System time              : 0.016 s
% 0.72/0.53  # Total time               : 0.266 s
% 0.72/0.53  # Maximum resident set size: 1776 pages
% 0.72/0.53  % E---3.1 exiting
% 0.72/0.53  % E exiting
%------------------------------------------------------------------------------