TSTP Solution File: SEU394+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n024.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 09:19:38 EDT 2022

% Result   : Theorem 0.23s 1.40s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (  13 unt;   0 def)
%            Number of atoms       :  140 (  17 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  168 (  68   ~;  58   |;  31   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   48 (   3 sgn  28   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).

fof(rc1_relat_1,axiom,
    ? [X1] :
      ( empty(X1)
      & relation(X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_relat_1) ).

fof(t14_yellow19,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
         => set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t14_yellow19) ).

fof(t2_yellow19,axiom,
    ! [X1] :
      ( ~ empty(X1)
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(X1))
            & upper_relstr_subset(X2,boole_POSet(X1))
            & proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
            & element(X2,powerset(the_carrier(boole_POSet(X1)))) )
         => ! [X3] :
              ~ ( in(X3,X2)
                & empty(X3) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_yellow19) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).

fof(t15_yellow19,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty(X2)
            & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
            & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
            & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
         => X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t15_yellow19) ).

fof(t65_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t65_zfmisc_1) ).

fof(fc2_pre_topc,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(cast_as_carrier_subset(X1)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc2_pre_topc) ).

fof(c_0_8,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_9,plain,
    ( empty(esk28_0)
    & relation(esk28_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).

fof(c_0_10,plain,
    ! [X3,X4] :
      ( empty_carrier(X3)
      | ~ one_sorted_str(X3)
      | empty(X4)
      | ~ filtered_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
      | ~ upper_relstr_subset(X4,boole_POSet(cast_as_carrier_subset(X3)))
      | ~ element(X4,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X3)))))
      | set_difference(X4,singleton(empty_set)) = filter_of_net_str(X3,net_of_bool_filter(X3,cast_as_carrier_subset(X3),X4)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t14_yellow19])])])])])]) ).

cnf(c_0_11,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    empty(esk28_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_13,plain,
    ! [X4,X5,X6] :
      ( empty(X4)
      | empty(X5)
      | ~ filtered_subset(X5,boole_POSet(X4))
      | ~ upper_relstr_subset(X5,boole_POSet(X4))
      | ~ proper_element(X5,powerset(the_carrier(boole_POSet(X4))))
      | ~ element(X5,powerset(the_carrier(boole_POSet(X4))))
      | ~ in(X6,X5)
      | ~ empty(X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t2_yellow19])])])])])]) ).

fof(c_0_14,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ empty(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( ( ~ empty(X2)
              & filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
              & proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
              & element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
           => X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
    inference(assume_negation,[status(cth)],[t15_yellow19]) ).

fof(c_0_16,plain,
    ! [X3,X4,X3,X4] :
      ( ( set_difference(X3,singleton(X4)) != X3
        | ~ in(X4,X3) )
      & ( in(X4,X3)
        | set_difference(X3,singleton(X4)) = X3 ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t65_zfmisc_1])])])])]) ).

cnf(c_0_17,plain,
    ( set_difference(X1,singleton(empty_set)) = filter_of_net_str(X2,net_of_bool_filter(X2,cast_as_carrier_subset(X2),X1))
    | empty(X1)
    | empty_carrier(X2)
    | ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X2)))))
    | ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X2)))
    | ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X2)))
    | ~ one_sorted_str(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    empty_set = esk28_0,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_19,plain,
    ( empty(X2)
    | empty(X3)
    | ~ empty(X1)
    | ~ in(X1,X2)
    | ~ element(X2,powerset(the_carrier(boole_POSet(X3))))
    | ~ proper_element(X2,powerset(the_carrier(boole_POSet(X3))))
    | ~ upper_relstr_subset(X2,boole_POSet(X3))
    | ~ filtered_subset(X2,boole_POSet(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( ~ empty(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_21,negated_conjecture,
    ( ~ empty_carrier(esk1_0)
    & one_sorted_str(esk1_0)
    & ~ empty(esk2_0)
    & filtered_subset(esk2_0,boole_POSet(cast_as_carrier_subset(esk1_0)))
    & upper_relstr_subset(esk2_0,boole_POSet(cast_as_carrier_subset(esk1_0)))
    & proper_element(esk2_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk1_0)))))
    & element(esk2_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk1_0)))))
    & esk2_0 != filter_of_net_str(esk1_0,net_of_bool_filter(esk1_0,cast_as_carrier_subset(esk1_0),esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15])])])])])]) ).

cnf(c_0_22,plain,
    ( set_difference(X1,singleton(X2)) = X1
    | in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( set_difference(X1,singleton(esk28_0)) = filter_of_net_str(X2,net_of_bool_filter(X2,cast_as_carrier_subset(X2),X1))
    | empty(X1)
    | empty_carrier(X2)
    | ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X2)))
    | ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X2)))
    | ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X2)))))
    | ~ one_sorted_str(X2) ),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,plain,
    ( empty(X1)
    | ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ upper_relstr_subset(X2,boole_POSet(X1))
    | ~ filtered_subset(X2,boole_POSet(X1))
    | ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
    | ~ empty(X3)
    | ~ in(X3,X2) ),
    inference(csr,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    proper_element(esk2_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk1_0))))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    upper_relstr_subset(esk2_0,boole_POSet(cast_as_carrier_subset(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    filtered_subset(esk2_0,boole_POSet(cast_as_carrier_subset(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    element(esk2_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk1_0))))),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,negated_conjecture,
    esk2_0 != filter_of_net_str(esk1_0,net_of_bool_filter(esk1_0,cast_as_carrier_subset(esk1_0),esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    ( filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) = X2
    | empty(X2)
    | empty_carrier(X1)
    | in(esk28_0,X2)
    | ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
    | ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
    | ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
    | ~ one_sorted_str(X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_31,negated_conjecture,
    one_sorted_str(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_32,negated_conjecture,
    ~ empty(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_33,negated_conjecture,
    ~ empty_carrier(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_34,plain,
    ! [X2] :
      ( empty_carrier(X2)
      | ~ one_sorted_str(X2)
      | ~ empty(cast_as_carrier_subset(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_pre_topc])])]) ).

cnf(c_0_35,negated_conjecture,
    ( empty(cast_as_carrier_subset(esk1_0))
    | ~ empty(X1)
    | ~ in(X1,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).

cnf(c_0_36,negated_conjecture,
    in(esk28_0,esk2_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26]),c_0_27]),c_0_28]),c_0_31])]),c_0_32]),c_0_33]) ).

cnf(c_0_37,plain,
    ( empty_carrier(X1)
    | ~ empty(cast_as_carrier_subset(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    empty(cast_as_carrier_subset(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_12])]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU394+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : run_ET %s %d
% 0.12/0.32  % Computer : n024.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Sun Jun 19 18:48:02 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.23/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40  # Preprocessing time       : 0.027 s
% 0.23/1.40  
% 0.23/1.40  # Proof found!
% 0.23/1.40  # SZS status Theorem
% 0.23/1.40  # SZS output start CNFRefutation
% See solution above
% 0.23/1.40  # Proof object total steps             : 40
% 0.23/1.40  # Proof object clause steps            : 23
% 0.23/1.40  # Proof object formula steps           : 17
% 0.23/1.40  # Proof object conjectures             : 15
% 0.23/1.40  # Proof object clause conjectures      : 12
% 0.23/1.40  # Proof object formula conjectures     : 3
% 0.23/1.40  # Proof object initial clauses used    : 15
% 0.23/1.40  # Proof object initial formulas used   : 8
% 0.23/1.40  # Proof object generating inferences   : 6
% 0.23/1.40  # Proof object simplifying inferences  : 18
% 0.23/1.40  # Training examples: 0 positive, 0 negative
% 0.23/1.40  # Parsed axioms                        : 127
% 0.23/1.40  # Removed by relevancy pruning/SinE    : 37
% 0.23/1.40  # Initial clauses                      : 311
% 0.23/1.40  # Removed in clause preprocessing      : 23
% 0.23/1.40  # Initial clauses in saturation        : 288
% 0.23/1.40  # Processed clauses                    : 2139
% 0.23/1.40  # ...of these trivial                  : 48
% 0.23/1.40  # ...subsumed                          : 1176
% 0.23/1.40  # ...remaining for further processing  : 915
% 0.23/1.40  # Other redundant clauses eliminated   : 0
% 0.23/1.40  # Clauses deleted for lack of memory   : 0
% 0.23/1.40  # Backward-subsumed                    : 57
% 0.23/1.40  # Backward-rewritten                   : 68
% 0.23/1.40  # Generated clauses                    : 8861
% 0.23/1.40  # ...of the previous two non-trivial   : 8476
% 0.23/1.40  # Contextual simplify-reflections      : 1066
% 0.23/1.40  # Paramodulations                      : 8825
% 0.23/1.40  # Factorizations                       : 32
% 0.23/1.40  # Equation resolutions                 : 4
% 0.23/1.40  # Current number of processed clauses  : 790
% 0.23/1.40  #    Positive orientable unit clauses  : 129
% 0.23/1.40  #    Positive unorientable unit clauses: 0
% 0.23/1.40  #    Negative unit clauses             : 39
% 0.23/1.40  #    Non-unit-clauses                  : 622
% 0.23/1.40  # Current number of unprocessed clauses: 5889
% 0.23/1.40  # ...number of literals in the above   : 32514
% 0.23/1.40  # Current number of archived formulas  : 0
% 0.23/1.40  # Current number of archived clauses   : 125
% 0.23/1.40  # Clause-clause subsumption calls (NU) : 314214
% 0.23/1.40  # Rec. Clause-clause subsumption calls : 135829
% 0.23/1.40  # Non-unit clause-clause subsumptions  : 2018
% 0.23/1.40  # Unit Clause-clause subsumption calls : 2038
% 0.23/1.40  # Rewrite failures with RHS unbound    : 0
% 0.23/1.40  # BW rewrite match attempts            : 5
% 0.23/1.40  # BW rewrite match successes           : 5
% 0.23/1.40  # Condensation attempts                : 0
% 0.23/1.40  # Condensation successes               : 0
% 0.23/1.40  # Termbank termtop insertions          : 174296
% 0.23/1.40  
% 0.23/1.40  # -------------------------------------------------
% 0.23/1.40  # User time                : 0.328 s
% 0.23/1.40  # System time              : 0.007 s
% 0.23/1.40  # Total time               : 0.335 s
% 0.23/1.40  # Maximum resident set size: 11536 pages
%------------------------------------------------------------------------------