TSTP Solution File: SET814+4 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:20:56 EDT 2023

% Result   : Theorem 0.16s 0.45s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   4 unt;   0 def)
%            Number of atoms       :   92 (   0 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  104 (  41   ~;  42   |;  13   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (   0 sgn;  28   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thI3,axiom,
    ! [X1,X2,X9] :
      ( ( subset(X1,X2)
        & subset(X2,X9) )
     => subset(X1,X9) ),
    file('/export/starexec/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p',thI3) ).

fof(ordinal_number,axiom,
    ! [X1] :
      ( member(X1,on)
    <=> ( set(X1)
        & strict_well_order(member_predicate,X1)
        & ! [X3] :
            ( member(X3,X1)
           => subset(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p',ordinal_number) ).

fof(thV14,conjecture,
    ! [X1] :
      ( member(X1,on)
     => subset(sum(X1),X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p',thV14) ).

fof(sum,axiom,
    ! [X3,X1] :
      ( member(X3,sum(X1))
    <=> ? [X5] :
          ( member(X5,X1)
          & member(X3,X5) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p',sum) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p',subset) ).

fof(c_0_5,plain,
    ! [X17,X18,X19] :
      ( ~ subset(X17,X18)
      | ~ subset(X18,X19)
      | subset(X17,X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thI3])]) ).

fof(c_0_6,plain,
    ! [X26,X27,X28] :
      ( ( set(X26)
        | ~ member(X26,on) )
      & ( strict_well_order(member_predicate,X26)
        | ~ member(X26,on) )
      & ( ~ member(X27,X26)
        | subset(X27,X26)
        | ~ member(X26,on) )
      & ( member(esk4_1(X28),X28)
        | ~ set(X28)
        | ~ strict_well_order(member_predicate,X28)
        | member(X28,on) )
      & ( ~ subset(esk4_1(X28),X28)
        | ~ set(X28)
        | ~ strict_well_order(member_predicate,X28)
        | member(X28,on) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ordinal_number])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => subset(sum(X1),X1) ),
    inference(assume_negation,[status(cth)],[thV14]) ).

cnf(c_0_8,plain,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ member(X1,X2)
    | ~ member(X2,on) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,negated_conjecture,
    ( member(esk1_0,on)
    & ~ subset(sum(esk1_0),esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | ~ member(X2,on)
    | ~ member(X3,X2)
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    member(esk1_0,on),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,plain,
    ! [X20,X21,X23,X24,X25] :
      ( ( member(esk3_2(X20,X21),X21)
        | ~ member(X20,sum(X21)) )
      & ( member(X20,esk3_2(X20,X21))
        | ~ member(X20,sum(X21)) )
      & ( ~ member(X25,X24)
        | ~ member(X23,X25)
        | member(X23,sum(X24)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sum])])])])])]) ).

fof(c_0_14,plain,
    ! [X11,X12,X13,X14,X15] :
      ( ( ~ subset(X11,X12)
        | ~ member(X13,X11)
        | member(X13,X12) )
      & ( member(esk2_2(X14,X15),X14)
        | subset(X14,X15) )
      & ( ~ member(esk2_2(X14,X15),X15)
        | subset(X14,X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).

cnf(c_0_15,negated_conjecture,
    ( subset(X1,esk1_0)
    | ~ member(X2,esk1_0)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,plain,
    ( member(esk3_2(X1,X2),X2)
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( member(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( member(X1,esk3_2(X1,X2))
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(X1,esk1_0)
    | ~ member(X2,sum(esk1_0))
    | ~ subset(X1,esk3_2(X2,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,plain,
    subset(X1,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( member(X1,X2)
    | ~ member(X1,sum(X3))
    | ~ subset(esk3_2(X1,X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    ( subset(esk3_2(X1,esk1_0),esk1_0)
    | ~ member(X1,sum(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( member(X1,esk1_0)
    | ~ member(X1,sum(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_26,negated_conjecture,
    ( member(esk2_2(sum(esk1_0),X1),esk1_0)
    | subset(sum(esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_27,negated_conjecture,
    ~ subset(sum(esk1_0),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SET814+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n004.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 2400
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Oct  2 17:04:15 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.jnMHgHTG0W/E---3.1_18871.p
% 0.16/0.45  # Version: 3.1pre001
% 0.16/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.45  # Starting new_bool_1 with 300s (1) cores
% 0.16/0.45  # Starting sh5l with 300s (1) cores
% 0.16/0.45  # new_bool_3 with pid 18955 completed with status 0
% 0.16/0.45  # Result found by new_bool_3
% 0.16/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.45  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.45  # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.16/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.16/0.45  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 18964 completed with status 0
% 0.16/0.45  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.45  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.45  # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.16/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.16/0.45  # Preprocessing time       : 0.001 s
% 0.16/0.45  # Presaturation interreduction done
% 0.16/0.45  
% 0.16/0.45  # Proof found!
% 0.16/0.45  # SZS status Theorem
% 0.16/0.45  # SZS output start CNFRefutation
% See solution above
% 0.16/0.45  # Parsed axioms                        : 21
% 0.16/0.45  # Removed by relevancy pruning/SinE    : 11
% 0.16/0.45  # Initial clauses                      : 53
% 0.16/0.45  # Removed in clause preprocessing      : 0
% 0.16/0.45  # Initial clauses in saturation        : 53
% 0.16/0.45  # Processed clauses                    : 168
% 0.16/0.45  # ...of these trivial                  : 0
% 0.16/0.45  # ...subsumed                          : 9
% 0.16/0.45  # ...remaining for further processing  : 159
% 0.16/0.45  # Other redundant clauses eliminated   : 0
% 0.16/0.45  # Clauses deleted for lack of memory   : 0
% 0.16/0.45  # Backward-subsumed                    : 4
% 0.16/0.45  # Backward-rewritten                   : 0
% 0.16/0.45  # Generated clauses                    : 247
% 0.16/0.45  # ...of the previous two non-redundant : 237
% 0.16/0.45  # ...aggressively subsumed             : 0
% 0.16/0.45  # Contextual simplify-reflections      : 0
% 0.16/0.45  # Paramodulations                      : 247
% 0.16/0.45  # Factorizations                       : 0
% 0.16/0.45  # NegExts                              : 0
% 0.16/0.45  # Equation resolutions                 : 0
% 0.16/0.45  # Total rewrite steps                  : 3
% 0.16/0.45  # Propositional unsat checks           : 0
% 0.16/0.45  #    Propositional check models        : 0
% 0.16/0.45  #    Propositional check unsatisfiable : 0
% 0.16/0.45  #    Propositional clauses             : 0
% 0.16/0.45  #    Propositional clauses after purity: 0
% 0.16/0.45  #    Propositional unsat core size     : 0
% 0.16/0.45  #    Propositional preprocessing time  : 0.000
% 0.16/0.45  #    Propositional encoding time       : 0.000
% 0.16/0.45  #    Propositional solver time         : 0.000
% 0.16/0.45  #    Success case prop preproc time    : 0.000
% 0.16/0.45  #    Success case prop encoding time   : 0.000
% 0.16/0.45  #    Success case prop solver time     : 0.000
% 0.16/0.45  # Current number of processed clauses  : 102
% 0.16/0.45  #    Positive orientable unit clauses  : 2
% 0.16/0.45  #    Positive unorientable unit clauses: 0
% 0.16/0.45  #    Negative unit clauses             : 2
% 0.16/0.45  #    Non-unit-clauses                  : 98
% 0.16/0.45  # Current number of unprocessed clauses: 170
% 0.16/0.45  # ...number of literals in the above   : 707
% 0.16/0.45  # Current number of archived formulas  : 0
% 0.16/0.45  # Current number of archived clauses   : 57
% 0.16/0.45  # Clause-clause subsumption calls (NU) : 1424
% 0.16/0.45  # Rec. Clause-clause subsumption calls : 982
% 0.16/0.45  # Non-unit clause-clause subsumptions  : 13
% 0.16/0.45  # Unit Clause-clause subsumption calls : 3
% 0.16/0.45  # Rewrite failures with RHS unbound    : 0
% 0.16/0.45  # BW rewrite match attempts            : 2
% 0.16/0.45  # BW rewrite match successes           : 0
% 0.16/0.45  # Condensation attempts                : 0
% 0.16/0.45  # Condensation successes               : 0
% 0.16/0.45  # Termbank termtop insertions          : 7616
% 0.16/0.45  
% 0.16/0.45  # -------------------------------------------------
% 0.16/0.45  # User time                : 0.014 s
% 0.16/0.45  # System time              : 0.003 s
% 0.16/0.45  # Total time               : 0.016 s
% 0.16/0.45  # Maximum resident set size: 1868 pages
% 0.16/0.45  
% 0.16/0.45  # -------------------------------------------------
% 0.16/0.45  # User time                : 0.015 s
% 0.16/0.45  # System time              : 0.004 s
% 0.16/0.45  # Total time               : 0.019 s
% 0.16/0.45  # Maximum resident set size: 1708 pages
% 0.16/0.45  % E---3.1 exiting
% 0.16/0.45  % E---3.1 exiting
%------------------------------------------------------------------------------