TSTP Solution File: SET931+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SET931+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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  : 300s
% DateTime : Tue May 21 03:00:28 EDT 2024

% Result   : Theorem 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  10 unt;   0 def)
%            Number of atoms       :   94 (  72 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  118 (  55   ~;  37   |;  21   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (   5 sgn  22   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t75_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( set_difference(X1,unordered_pair(X2,X3)) = empty_set
    <=> ~ ( X1 != empty_set
          & X1 != singleton(X2)
          & X1 != singleton(X3)
          & X1 != unordered_pair(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).

fof(l46_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( subset(X1,unordered_pair(X2,X3))
    <=> ~ ( X1 != empty_set
          & X1 != singleton(X2)
          & X1 != singleton(X3)
          & X1 != unordered_pair(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).

fof(t37_xboole_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_difference(X1,unordered_pair(X2,X3)) = empty_set
      <=> ~ ( X1 != empty_set
            & X1 != singleton(X2)
            & X1 != singleton(X3)
            & X1 != unordered_pair(X2,X3) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t75_zfmisc_1])]) ).

fof(c_0_5,plain,
    ! [X1,X2,X3] :
      ( subset(X1,unordered_pair(X2,X3))
    <=> ~ ( X1 != empty_set
          & X1 != singleton(X2)
          & X1 != singleton(X3)
          & X1 != unordered_pair(X2,X3) ) ),
    inference(fof_simplification,[status(thm)],[l46_zfmisc_1]) ).

fof(c_0_6,negated_conjecture,
    ( ( esk3_0 != empty_set
      | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
    & ( esk3_0 != singleton(esk4_0)
      | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
    & ( esk3_0 != singleton(esk5_0)
      | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
    & ( esk3_0 != unordered_pair(esk4_0,esk5_0)
      | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set )
    & ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set
      | esk3_0 = empty_set
      | esk3_0 = singleton(esk4_0)
      | esk3_0 = singleton(esk5_0)
      | esk3_0 = unordered_pair(esk4_0,esk5_0) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).

fof(c_0_7,plain,
    ! [X12,X13] :
      ( ( set_difference(X12,X13) != empty_set
        | subset(X12,X13) )
      & ( ~ subset(X12,X13)
        | set_difference(X12,X13) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])]) ).

fof(c_0_8,plain,
    ! [X6,X7,X8] :
      ( ( ~ subset(X6,unordered_pair(X7,X8))
        | X6 = empty_set
        | X6 = singleton(X7)
        | X6 = singleton(X8)
        | X6 = unordered_pair(X7,X8) )
      & ( X6 != empty_set
        | subset(X6,unordered_pair(X7,X8)) )
      & ( X6 != singleton(X7)
        | subset(X6,unordered_pair(X7,X8)) )
      & ( X6 != singleton(X8)
        | subset(X6,unordered_pair(X7,X8)) )
      & ( X6 != unordered_pair(X7,X8)
        | subset(X6,unordered_pair(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

cnf(c_0_9,negated_conjecture,
    ( esk3_0 != empty_set
    | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( subset(X1,unordered_pair(X2,X3))
    | X1 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( esk3_0 != singleton(esk5_0)
    | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,plain,
    ( subset(X1,unordered_pair(X3,X2))
    | X1 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( esk3_0 != singleton(esk4_0)
    | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,plain,
    ( subset(X1,unordered_pair(X2,X3))
    | X1 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set
    | esk3_0 = empty_set
    | esk3_0 = singleton(esk4_0)
    | esk3_0 = singleton(esk5_0)
    | esk3_0 = unordered_pair(esk4_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,negated_conjecture,
    empty_set != esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    singleton(esk5_0) != esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    singleton(esk4_0) != esk3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_15]) ).

cnf(c_0_20,plain,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_21,negated_conjecture,
    ( set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) = empty_set
    | unordered_pair(esk4_0,esk5_0) = esk3_0 ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).

cnf(c_0_22,plain,
    ( subset(X1,unordered_pair(X2,X3))
    | X1 != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_23,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | X1 = singleton(X3)
    | X1 = unordered_pair(X2,X3)
    | ~ subset(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    subset(esk3_0,unordered_pair(esk4_0,esk5_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( esk3_0 != unordered_pair(esk4_0,esk5_0)
    | set_difference(esk3_0,unordered_pair(esk4_0,esk5_0)) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_26,negated_conjecture,
    unordered_pair(esk4_0,esk5_0) = esk3_0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_18]),c_0_17]) ).

fof(c_0_27,plain,
    ! [X11] : subset(X11,X11),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

cnf(c_0_28,negated_conjecture,
    set_difference(esk3_0,esk3_0) != empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26])]) ).

cnf(c_0_29,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_10]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET931+1 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 12:49:23 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.20/0.46  Running first-order model finding
% 0.20/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48  # Version: 3.1.0
% 0.20/0.48  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.48  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.48  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.48  # Starting sh5l with 300s (1) cores
% 0.20/0.48  # G-E--_302_C18_F1_URBAN_RG_S04BN with pid 30736 completed with status 0
% 0.20/0.48  # Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.20/0.48  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.20/0.48  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.20/0.48  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.20/0.48  # Starting new_bool_3 with 136s (1) cores
% 0.20/0.48  # Starting new_bool_1 with 136s (1) cores
% 0.20/0.48  # Starting sh5l with 136s (1) cores
% 0.20/0.48  # G-E--_302_C18_F1_URBAN_RG_S04BN with pid 30741 completed with status 0
% 0.20/0.48  # Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.20/0.48  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.20/0.48  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.20/0.48  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.20/0.48  # Preprocessing time       : 0.002 s
% 0.20/0.48  
% 0.20/0.48  # Proof found!
% 0.20/0.48  # SZS status Theorem
% 0.20/0.48  # SZS output start CNFRefutation
% See solution above
% 0.20/0.48  # Parsed axioms                        : 8
% 0.20/0.48  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.48  # Initial clauses                      : 17
% 0.20/0.48  # Removed in clause preprocessing      : 0
% 0.20/0.48  # Initial clauses in saturation        : 17
% 0.20/0.48  # Processed clauses                    : 29
% 0.20/0.48  # ...of these trivial                  : 0
% 0.20/0.48  # ...subsumed                          : 2
% 0.20/0.48  # ...remaining for further processing  : 27
% 0.20/0.48  # Other redundant clauses eliminated   : 0
% 0.20/0.48  # Clauses deleted for lack of memory   : 0
% 0.20/0.48  # Backward-subsumed                    : 3
% 0.20/0.48  # Backward-rewritten                   : 4
% 0.20/0.48  # Generated clauses                    : 102
% 0.20/0.48  # ...of the previous two non-redundant : 58
% 0.20/0.48  # ...aggressively subsumed             : 0
% 0.20/0.48  # Contextual simplify-reflections      : 4
% 0.20/0.48  # Paramodulations                      : 51
% 0.20/0.48  # Factorizations                       : 50
% 0.20/0.48  # NegExts                              : 0
% 0.20/0.48  # Equation resolutions                 : 0
% 0.20/0.48  # Disequality decompositions           : 0
% 0.20/0.48  # Total rewrite steps                  : 13
% 0.20/0.48  # ...of those cached                   : 6
% 0.20/0.48  # Propositional unsat checks           : 0
% 0.20/0.48  #    Propositional check models        : 0
% 0.20/0.48  #    Propositional check unsatisfiable : 0
% 0.20/0.48  #    Propositional clauses             : 0
% 0.20/0.48  #    Propositional clauses after purity: 0
% 0.20/0.48  #    Propositional unsat core size     : 0
% 0.20/0.48  #    Propositional preprocessing time  : 0.000
% 0.20/0.48  #    Propositional encoding time       : 0.000
% 0.20/0.48  #    Propositional solver time         : 0.000
% 0.20/0.48  #    Success case prop preproc time    : 0.000
% 0.20/0.48  #    Success case prop encoding time   : 0.000
% 0.20/0.48  #    Success case prop solver time     : 0.000
% 0.20/0.48  # Current number of processed clauses  : 19
% 0.20/0.48  #    Positive orientable unit clauses  : 4
% 0.20/0.48  #    Positive unorientable unit clauses: 1
% 0.20/0.48  #    Negative unit clauses             : 5
% 0.20/0.48  #    Non-unit-clauses                  : 9
% 0.20/0.48  # Current number of unprocessed clauses: 43
% 0.20/0.48  # ...number of literals in the above   : 176
% 0.20/0.48  # Current number of archived formulas  : 0
% 0.20/0.48  # Current number of archived clauses   : 8
% 0.20/0.48  # Clause-clause subsumption calls (NU) : 35
% 0.20/0.48  # Rec. Clause-clause subsumption calls : 17
% 0.20/0.48  # Non-unit clause-clause subsumptions  : 5
% 0.20/0.48  # Unit Clause-clause subsumption calls : 11
% 0.20/0.48  # Rewrite failures with RHS unbound    : 0
% 0.20/0.48  # BW rewrite match attempts            : 3
% 0.20/0.48  # BW rewrite match successes           : 3
% 0.20/0.48  # Condensation attempts                : 0
% 0.20/0.48  # Condensation successes               : 0
% 0.20/0.48  # Termbank termtop insertions          : 1722
% 0.20/0.48  # Search garbage collected termcells   : 206
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.006 s
% 0.20/0.48  # System time              : 0.003 s
% 0.20/0.48  # Total time               : 0.009 s
% 0.20/0.48  # Maximum resident set size: 1752 pages
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.021 s
% 0.20/0.48  # System time              : 0.007 s
% 0.20/0.48  # Total time               : 0.028 s
% 0.20/0.48  # Maximum resident set size: 1692 pages
% 0.20/0.48  % E---3.1 exiting
%------------------------------------------------------------------------------