TSTP Solution File: SEU327+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU327+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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  : 600s
% DateTime : Tue Jul 19 09:19:01 EDT 2022

% Result   : Theorem 0.26s 1.42s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  13 unt;   0 def)
%            Number of atoms       :   58 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   50 (  22   ~;  16   |;   3   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   42 (   0 sgn  26   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t47_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t47_setfam_1) ).

fof(d4_subset_1,axiom,
    ! [X1] : cast_to_subset(X1) = X1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d4_subset_1) ).

fof(dt_k2_subset_1,axiom,
    ! [X1] : element(cast_to_subset(X1),powerset(X1)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_subset_1) ).

fof(t11_tops_2,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t11_tops_2) ).

fof(redefinition_k6_subset_1,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_k6_subset_1) ).

fof(dt_k5_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(union_of_subsets(X1,X2),powerset(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k5_setfam_1) ).

fof(d5_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_subset_1) ).

fof(c_0_7,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | X4 = empty_set
      | subset_difference(X3,cast_to_subset(X3),union_of_subsets(X3,X4)) = meet_of_subsets(X3,complements_of_subsets(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).

fof(c_0_8,plain,
    ! [X2] : cast_to_subset(X2) = X2,
    inference(variable_rename,[status(thm)],[d4_subset_1]) ).

fof(c_0_9,plain,
    ! [X2] : element(cast_to_subset(X2),powerset(X2)),
    inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(powerset(X1)))
       => ( X2 != empty_set
         => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    inference(assume_negation,[status(cth)],[t11_tops_2]) ).

cnf(c_0_11,plain,
    ( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | X2 = empty_set
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    cast_to_subset(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X4,X5,X6] :
      ( ~ element(X5,powerset(X4))
      | ~ element(X6,powerset(X4))
      | subset_difference(X4,X5,X6) = set_difference(X5,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).

cnf(c_0_14,plain,
    element(cast_to_subset(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_15,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(powerset(X3)))
      | element(union_of_subsets(X3,X4),powerset(X3)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).

fof(c_0_16,negated_conjecture,
    ( element(esk2_0,powerset(powerset(esk1_0)))
    & esk2_0 != empty_set
    & meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union_of_subsets(esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

cnf(c_0_17,plain,
    ( X2 = empty_set
    | subset_difference(X1,X1,union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_18,plain,
    ( subset_difference(X1,X2,X3) = set_difference(X2,X3)
    | ~ element(X3,powerset(X1))
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    element(X1,powerset(X1)),
    inference(rw,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_20,plain,
    ( element(union_of_subsets(X1,X2),powerset(X1))
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union_of_subsets(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( meet_of_subsets(X1,complements_of_subsets(X1,X2)) = set_difference(X1,union_of_subsets(X1,X2))
    | X2 = empty_set
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    element(esk2_0,powerset(powerset(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    esk2_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_25,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,X4) = set_difference(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).

cnf(c_0_26,negated_conjecture,
    subset_complement(esk1_0,union_of_subsets(esk1_0,esk2_0)) != set_difference(esk1_0,union_of_subsets(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).

cnf(c_0_27,plain,
    ( subset_complement(X1,X2) = set_difference(X1,X2)
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    ~ element(union_of_subsets(esk1_0,esk2_0),powerset(esk1_0)),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU327+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n023.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  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 11:06:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.26/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.42  # Preprocessing time       : 0.030 s
% 0.26/1.42  
% 0.26/1.42  # Proof found!
% 0.26/1.42  # SZS status Theorem
% 0.26/1.42  # SZS output start CNFRefutation
% See solution above
% 0.26/1.42  # Proof object total steps             : 30
% 0.26/1.42  # Proof object clause steps            : 15
% 0.26/1.42  # Proof object formula steps           : 15
% 0.26/1.42  # Proof object conjectures             : 9
% 0.26/1.42  # Proof object clause conjectures      : 6
% 0.26/1.42  # Proof object formula conjectures     : 3
% 0.26/1.42  # Proof object initial clauses used    : 9
% 0.26/1.42  # Proof object initial formulas used   : 7
% 0.26/1.42  # Proof object generating inferences   : 4
% 0.26/1.42  # Proof object simplifying inferences  : 10
% 0.26/1.42  # Training examples: 0 positive, 0 negative
% 0.26/1.42  # Parsed axioms                        : 59
% 0.26/1.42  # Removed by relevancy pruning/SinE    : 21
% 0.26/1.42  # Initial clauses                      : 76
% 0.26/1.42  # Removed in clause preprocessing      : 1
% 0.26/1.42  # Initial clauses in saturation        : 75
% 0.26/1.42  # Processed clauses                    : 611
% 0.26/1.42  # ...of these trivial                  : 12
% 0.26/1.42  # ...subsumed                          : 203
% 0.26/1.42  # ...remaining for further processing  : 396
% 0.26/1.42  # Other redundant clauses eliminated   : 0
% 0.26/1.42  # Clauses deleted for lack of memory   : 0
% 0.26/1.42  # Backward-subsumed                    : 2
% 0.26/1.42  # Backward-rewritten                   : 7
% 0.26/1.42  # Generated clauses                    : 1870
% 0.26/1.42  # ...of the previous two non-trivial   : 1384
% 0.26/1.42  # Contextual simplify-reflections      : 31
% 0.26/1.42  # Paramodulations                      : 1870
% 0.26/1.42  # Factorizations                       : 0
% 0.26/1.42  # Equation resolutions                 : 0
% 0.26/1.42  # Current number of processed clauses  : 387
% 0.26/1.42  #    Positive orientable unit clauses  : 63
% 0.26/1.42  #    Positive unorientable unit clauses: 0
% 0.26/1.42  #    Negative unit clauses             : 6
% 0.26/1.42  #    Non-unit-clauses                  : 318
% 0.26/1.42  # Current number of unprocessed clauses: 799
% 0.26/1.42  # ...number of literals in the above   : 2435
% 0.26/1.42  # Current number of archived formulas  : 0
% 0.26/1.42  # Current number of archived clauses   : 10
% 0.26/1.42  # Clause-clause subsumption calls (NU) : 13118
% 0.26/1.42  # Rec. Clause-clause subsumption calls : 12258
% 0.26/1.42  # Non-unit clause-clause subsumptions  : 234
% 0.26/1.42  # Unit Clause-clause subsumption calls : 183
% 0.26/1.42  # Rewrite failures with RHS unbound    : 0
% 0.26/1.42  # BW rewrite match attempts            : 76
% 0.26/1.42  # BW rewrite match successes           : 5
% 0.26/1.42  # Condensation attempts                : 0
% 0.26/1.42  # Condensation successes               : 0
% 0.26/1.42  # Termbank termtop insertions          : 25612
% 0.26/1.42  
% 0.26/1.42  # -------------------------------------------------
% 0.26/1.42  # User time                : 0.094 s
% 0.26/1.42  # System time              : 0.006 s
% 0.26/1.42  # Total time               : 0.100 s
% 0.26/1.42  # Maximum resident set size: 4408 pages
% 0.26/23.43  eprover: CPU time limit exceeded, terminating
% 0.26/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.48  eprover: No such file or directory
% 0.26/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.48  eprover: No such file or directory
% 0.26/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.49  eprover: No such file or directory
% 0.26/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.49  eprover: No such file or directory
% 0.26/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.50  eprover: No such file or directory
% 0.26/23.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.50  eprover: No such file or directory
% 0.26/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.51  eprover: No such file or directory
% 0.26/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.51  eprover: No such file or directory
% 0.26/23.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.51  eprover: No such file or directory
% 0.26/23.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.52  eprover: No such file or directory
% 0.26/23.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.52  eprover: No such file or directory
%------------------------------------------------------------------------------