TSTP Solution File: SET955+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 02:56:39 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   4 unt;   0 def)
%            Number of atoms       :   87 (  28 equ)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives :   99 (  34   ~;  45   |;  12   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-4 aty)
%            Number of variables   :   64 (   8 sgn  35   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t108_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ! [X5,X6] :
          ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
        <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
     => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).

fof(d2_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( X3 = cartesian_product2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ? [X5,X6] :
              ( in(X5,X1)
              & in(X6,X2)
              & X4 = ordered_pair(X5,X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ! [X5,X6] :
            ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
          <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
       => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    inference(assume_negation,[status(cth)],[t108_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X13,X14,X15,X16,X19,X20,X21,X22,X23,X24,X26,X27] :
      ( ( in(esk5_4(X13,X14,X15,X16),X13)
        | ~ in(X16,X15)
        | X15 != cartesian_product2(X13,X14) )
      & ( in(esk6_4(X13,X14,X15,X16),X14)
        | ~ in(X16,X15)
        | X15 != cartesian_product2(X13,X14) )
      & ( X16 = ordered_pair(esk5_4(X13,X14,X15,X16),esk6_4(X13,X14,X15,X16))
        | ~ in(X16,X15)
        | X15 != cartesian_product2(X13,X14) )
      & ( ~ in(X20,X13)
        | ~ in(X21,X14)
        | X19 != ordered_pair(X20,X21)
        | in(X19,X15)
        | X15 != cartesian_product2(X13,X14) )
      & ( ~ in(esk7_3(X22,X23,X24),X24)
        | ~ in(X26,X22)
        | ~ in(X27,X23)
        | esk7_3(X22,X23,X24) != ordered_pair(X26,X27)
        | X24 = cartesian_product2(X22,X23) )
      & ( in(esk8_3(X22,X23,X24),X22)
        | in(esk7_3(X22,X23,X24),X24)
        | X24 = cartesian_product2(X22,X23) )
      & ( in(esk9_3(X22,X23,X24),X23)
        | in(esk7_3(X22,X23,X24),X24)
        | X24 = cartesian_product2(X22,X23) )
      & ( esk7_3(X22,X23,X24) = ordered_pair(esk8_3(X22,X23,X24),esk9_3(X22,X23,X24))
        | in(esk7_3(X22,X23,X24),X24)
        | X24 = cartesian_product2(X22,X23) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d2_zfmisc_1])])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ! [X11,X12] :
      ( ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0)) )
      & ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0)) )
      & cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).

cnf(c_0_6,plain,
    ( X1 = ordered_pair(esk5_4(X2,X3,X4,X1),esk6_4(X2,X3,X4,X1))
    | ~ in(X1,X4)
    | X4 != cartesian_product2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( ordered_pair(esk5_4(X1,X2,cartesian_product2(X1,X2),X3),esk6_4(X1,X2,cartesian_product2(X1,X2),X3)) = X3
    | ~ in(X3,cartesian_product2(X1,X2)) ),
    inference(er,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X32,X33] :
      ( ( ~ in(esk10_2(X32,X33),X32)
        | ~ in(esk10_2(X32,X33),X33)
        | X32 = X33 )
      & ( in(esk10_2(X32,X33),X32)
        | in(esk10_2(X32,X33),X33)
        | X32 = X33 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).

cnf(c_0_10,negated_conjecture,
    ( in(X1,cartesian_product2(esk1_0,esk2_0))
    | ~ in(X1,cartesian_product2(esk3_0,esk4_0))
    | ~ in(X1,cartesian_product2(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( in(esk10_2(X1,X2),X1)
    | in(esk10_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ( X1 = cartesian_product2(esk3_0,esk4_0)
    | in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk1_0,esk2_0))
    | in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),X1)
    | ~ in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),cartesian_product2(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    ( X1 = cartesian_product2(esk3_0,esk4_0)
    | in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk1_0,esk2_0))
    | in(esk10_2(X1,cartesian_product2(esk3_0,esk4_0)),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    ( in(X1,cartesian_product2(esk3_0,esk4_0))
    | ~ in(X1,cartesian_product2(esk1_0,esk2_0))
    | ~ in(X1,cartesian_product2(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_14]),c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk3_0,esk4_0))
    | ~ in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ in(esk10_2(X1,X2),X1)
    | ~ in(esk10_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_20,negated_conjecture,
    in(esk10_2(cartesian_product2(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)),cartesian_product2(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n006.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    : 300
% 0.13/0.34  % DateTime   : Mon May 20 12:50:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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
% 0.19/0.49  # Version: 3.1.0
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.49  # Starting sh5l with 300s (1) cores
% 0.19/0.49  # new_bool_3 with pid 3019 completed with status 0
% 0.19/0.49  # Result found by new_bool_3
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.49  # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.19/0.49  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.19/0.49  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3027 completed with status 0
% 0.19/0.49  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.49  # Search class: FGHSF-FFMF32-SFFFFFNN
% 0.19/0.49  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.19/0.49  # Preprocessing time       : 0.001 s
% 0.19/0.49  # Presaturation interreduction done
% 0.19/0.49  
% 0.19/0.49  # Proof found!
% 0.19/0.49  # SZS status Theorem
% 0.19/0.49  # SZS output start CNFRefutation
% See solution above
% 0.19/0.49  # Parsed axioms                        : 9
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 2
% 0.19/0.49  # Initial clauses                      : 17
% 0.19/0.49  # Removed in clause preprocessing      : 0
% 0.19/0.49  # Initial clauses in saturation        : 17
% 0.19/0.49  # Processed clauses                    : 80
% 0.19/0.49  # ...of these trivial                  : 1
% 0.19/0.49  # ...subsumed                          : 8
% 0.19/0.49  # ...remaining for further processing  : 71
% 0.19/0.49  # Other redundant clauses eliminated   : 5
% 0.19/0.49  # Clauses deleted for lack of memory   : 0
% 0.19/0.49  # Backward-subsumed                    : 2
% 0.19/0.49  # Backward-rewritten                   : 1
% 0.19/0.49  # Generated clauses                    : 117
% 0.19/0.49  # ...of the previous two non-redundant : 109
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 0
% 0.19/0.49  # Paramodulations                      : 109
% 0.19/0.49  # Factorizations                       : 4
% 0.19/0.49  # NegExts                              : 0
% 0.19/0.49  # Equation resolutions                 : 5
% 0.19/0.49  # Disequality decompositions           : 0
% 0.19/0.49  # Total rewrite steps                  : 5
% 0.19/0.49  # ...of those cached                   : 3
% 0.19/0.49  # Propositional unsat checks           : 0
% 0.19/0.49  #    Propositional check models        : 0
% 0.19/0.49  #    Propositional check unsatisfiable : 0
% 0.19/0.49  #    Propositional clauses             : 0
% 0.19/0.49  #    Propositional clauses after purity: 0
% 0.19/0.49  #    Propositional unsat core size     : 0
% 0.19/0.49  #    Propositional preprocessing time  : 0.000
% 0.19/0.49  #    Propositional encoding time       : 0.000
% 0.19/0.49  #    Propositional solver time         : 0.000
% 0.19/0.49  #    Success case prop preproc time    : 0.000
% 0.19/0.49  #    Success case prop encoding time   : 0.000
% 0.19/0.49  #    Success case prop solver time     : 0.000
% 0.19/0.49  # Current number of processed clauses  : 47
% 0.19/0.49  #    Positive orientable unit clauses  : 3
% 0.19/0.49  #    Positive unorientable unit clauses: 0
% 0.19/0.49  #    Negative unit clauses             : 5
% 0.19/0.49  #    Non-unit-clauses                  : 39
% 0.19/0.49  # Current number of unprocessed clauses: 60
% 0.19/0.49  # ...number of literals in the above   : 269
% 0.19/0.49  # Current number of archived formulas  : 0
% 0.19/0.49  # Current number of archived clauses   : 20
% 0.19/0.49  # Clause-clause subsumption calls (NU) : 338
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 221
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 7
% 0.19/0.49  # Unit Clause-clause subsumption calls : 2
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 1
% 0.19/0.49  # BW rewrite match successes           : 1
% 0.19/0.49  # Condensation attempts                : 0
% 0.19/0.49  # Condensation successes               : 0
% 0.19/0.49  # Termbank termtop insertions          : 3735
% 0.19/0.49  # Search garbage collected termcells   : 415
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.010 s
% 0.19/0.49  # System time              : 0.002 s
% 0.19/0.49  # Total time               : 0.012 s
% 0.19/0.49  # Maximum resident set size: 1724 pages
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.012 s
% 0.19/0.49  # System time              : 0.003 s
% 0.19/0.49  # Total time               : 0.015 s
% 0.19/0.49  # Maximum resident set size: 1692 pages
% 0.19/0.49  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------