TSTP Solution File: SET075-6 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET075-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 02:52:59 EDT 2024

% Result   : Unsatisfiable 0.14s 0.42s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   35 (  16 unt;   3 nHn;  22 RR)
%            Number of literals    :   57 (  12 equ;  23 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    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   53 (  13 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(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(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(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(unordered_pair3,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).

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

cnf(prove_corollary_to_unordered_pair_axiom3_1,negated_conjecture,
    member(ordered_pair(x,y),cross_product(u,v)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).

cnf(prove_corollary_to_unordered_pair_axiom3_2,negated_conjecture,
    unordered_pair(x,y) = null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).

cnf(c_0_10,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_11,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[complement1]) ).

cnf(c_0_12,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_10 ).

cnf(c_0_13,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_14,plain,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(fof_simplification,[status(thm)],[cartesian_product2]) ).

cnf(c_0_15,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

cnf(c_0_16,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_17,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[unordered_pair3]) ).

cnf(c_0_18,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    c_0_11 ).

cnf(c_0_19,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_20,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_21,plain,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    c_0_14 ).

cnf(c_0_22,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_15,c_0_16]),c_0_16]) ).

cnf(c_0_23,negated_conjecture,
    member(ordered_pair(x,y),cross_product(u,v)),
    prove_corollary_to_unordered_pair_axiom3_1 ).

cnf(c_0_24,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    c_0_17 ).

cnf(c_0_25,negated_conjecture,
    unordered_pair(x,y) = null_class,
    prove_corollary_to_unordered_pair_axiom3_2 ).

cnf(c_0_26,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_27,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_20,c_0_19]) ).

cnf(c_0_28,plain,
    ( member(X2,X4)
    | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
    inference(rw,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_30,negated_conjecture,
    ( member(y,null_class)
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    null_class = complement(universal_class),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    member(y,v),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ~ member(y,universal_class),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_18]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SET075-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.05/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n014.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon May 20 12:28:07 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  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
% 0.14/0.42  # Version: 3.1.0
% 0.14/0.42  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.42  # Starting new_bool_3 with 300s (1) cores
% 0.14/0.42  # Starting new_bool_1 with 300s (1) cores
% 0.14/0.42  # Starting sh5l with 300s (1) cores
% 0.14/0.42  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 7708 completed with status 0
% 0.14/0.42  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.42  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.42  # No SInE strategy applied
% 0.14/0.42  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.42  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.14/0.42  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.42  # Starting new_bool_1 with 308s (1) cores
% 0.14/0.42  # Starting sh5l with 304s (1) cores
% 0.14/0.42  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.42  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 7716 completed with status 0
% 0.14/0.42  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.42  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.42  # No SInE strategy applied
% 0.14/0.42  # Search class: FGHSM-FFLM31-DFFFFFNN
% 0.14/0.42  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 0.14/0.42  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.42  # Preprocessing time       : 0.002 s
% 0.14/0.42  # Presaturation interreduction done
% 0.14/0.42  
% 0.14/0.42  # Proof found!
% 0.14/0.42  # SZS status Unsatisfiable
% 0.14/0.42  # SZS output start CNFRefutation
% See solution above
% 0.14/0.42  # Parsed axioms                        : 93
% 0.14/0.42  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.42  # Initial clauses                      : 93
% 0.14/0.42  # Removed in clause preprocessing      : 15
% 0.14/0.42  # Initial clauses in saturation        : 78
% 0.14/0.42  # Processed clauses                    : 156
% 0.14/0.42  # ...of these trivial                  : 0
% 0.14/0.42  # ...subsumed                          : 1
% 0.14/0.42  # ...remaining for further processing  : 155
% 0.14/0.42  # Other redundant clauses eliminated   : 3
% 0.14/0.42  # Clauses deleted for lack of memory   : 0
% 0.14/0.42  # Backward-subsumed                    : 0
% 0.14/0.42  # Backward-rewritten                   : 19
% 0.14/0.42  # Generated clauses                    : 109
% 0.14/0.42  # ...of the previous two non-redundant : 108
% 0.14/0.42  # ...aggressively subsumed             : 0
% 0.14/0.42  # Contextual simplify-reflections      : 2
% 0.14/0.42  # Paramodulations                      : 106
% 0.14/0.42  # Factorizations                       : 0
% 0.14/0.42  # NegExts                              : 0
% 0.14/0.42  # Equation resolutions                 : 3
% 0.14/0.42  # Disequality decompositions           : 0
% 0.14/0.42  # Total rewrite steps                  : 36
% 0.14/0.42  # ...of those cached                   : 29
% 0.14/0.42  # Propositional unsat checks           : 0
% 0.14/0.42  #    Propositional check models        : 0
% 0.14/0.42  #    Propositional check unsatisfiable : 0
% 0.14/0.42  #    Propositional clauses             : 0
% 0.14/0.42  #    Propositional clauses after purity: 0
% 0.14/0.42  #    Propositional unsat core size     : 0
% 0.14/0.42  #    Propositional preprocessing time  : 0.000
% 0.14/0.42  #    Propositional encoding time       : 0.000
% 0.14/0.42  #    Propositional solver time         : 0.000
% 0.14/0.42  #    Success case prop preproc time    : 0.000
% 0.14/0.42  #    Success case prop encoding time   : 0.000
% 0.14/0.42  #    Success case prop solver time     : 0.000
% 0.14/0.42  # Current number of processed clauses  : 56
% 0.14/0.42  #    Positive orientable unit clauses  : 19
% 0.14/0.42  #    Positive unorientable unit clauses: 1
% 0.14/0.42  #    Negative unit clauses             : 2
% 0.14/0.42  #    Non-unit-clauses                  : 34
% 0.14/0.42  # Current number of unprocessed clauses: 107
% 0.14/0.42  # ...number of literals in the above   : 262
% 0.14/0.42  # Current number of archived formulas  : 0
% 0.14/0.42  # Current number of archived clauses   : 111
% 0.14/0.42  # Clause-clause subsumption calls (NU) : 1217
% 0.14/0.42  # Rec. Clause-clause subsumption calls : 726
% 0.14/0.42  # Non-unit clause-clause subsumptions  : 3
% 0.14/0.42  # Unit Clause-clause subsumption calls : 56
% 0.14/0.42  # Rewrite failures with RHS unbound    : 0
% 0.14/0.42  # BW rewrite match attempts            : 4
% 0.14/0.42  # BW rewrite match successes           : 3
% 0.14/0.42  # Condensation attempts                : 0
% 0.14/0.42  # Condensation successes               : 0
% 0.14/0.42  # Termbank termtop insertions          : 7282
% 0.14/0.42  # Search garbage collected termcells   : 154
% 0.14/0.42  
% 0.14/0.42  # -------------------------------------------------
% 0.14/0.42  # User time                : 0.015 s
% 0.14/0.42  # System time              : 0.002 s
% 0.14/0.42  # Total time               : 0.017 s
% 0.14/0.42  # Maximum resident set size: 1932 pages
% 0.14/0.42  
% 0.14/0.42  # -------------------------------------------------
% 0.14/0.42  # User time                : 0.063 s
% 0.14/0.42  # System time              : 0.009 s
% 0.14/0.42  # Total time               : 0.072 s
% 0.14/0.42  # Maximum resident set size: 1780 pages
% 0.14/0.42  % E---3.1 exiting
% 0.14/0.42  % E exiting
%------------------------------------------------------------------------------