TSTP Solution File: ALG227+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 : Mon May 20 18:05:45 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  16 unt;   0 def)
%            Number of atoms       :  117 (  37 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  128 (  48   ~;  43   |;  18   &)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   49 (   0 sgn  27   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
    ! [X1] :
      ( v1_xboole_0(X1)
     => X1 = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(rc2_funct_1,axiom,
    ? [X1] :
      ( v1_relat_1(X1)
      & v1_xboole_0(X1)
      & v1_funct_1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(fraenkel_a_2_0_closure3,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_pboole(X3,X2) )
     => ( r2_hidden(X1,a_2_0_closure3(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,X2)
            & X1 = X4
            & k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).

fof(d3_closure3,axiom,
    ! [X1] :
      ( ~ v1_xboole_0(X1)
     => ! [X2] :
          ( m1_pboole(X2,X1)
         => ! [X3] :
              ( X3 = k1_closure3(X1,X2)
            <=> X3 = a_2_0_closure3(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : v1_xboole_0(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(t8_closure3,conjecture,
    ! [X1] :
      ( ~ v1_xboole_0(X1)
     => ! [X2] :
          ( m1_pboole(X2,X1)
         => ! [X3] :
              ( m1_subset_1(X3,X1)
             => ( ~ r2_hidden(X3,k1_closure3(X1,X2))
               => k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).

fof(c_0_6,plain,
    ! [X8] :
      ( ~ v1_xboole_0(X8)
      | X8 = k1_xboole_0 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).

fof(c_0_7,plain,
    ( v1_relat_1(esk11_0)
    & v1_xboole_0(esk11_0)
    & v1_funct_1(esk11_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).

fof(c_0_8,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_pboole(X3,X2) )
     => ( r2_hidden(X1,a_2_0_closure3(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,X2)
            & X1 = X4
            & k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
    inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_closure3]) ).

cnf(c_0_9,plain,
    ( X1 = k1_xboole_0
    | ~ v1_xboole_0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    v1_xboole_0(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X1] :
      ( ~ v1_xboole_0(X1)
     => ! [X2] :
          ( m1_pboole(X2,X1)
         => ! [X3] :
              ( X3 = k1_closure3(X1,X2)
            <=> X3 = a_2_0_closure3(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d3_closure3]) ).

fof(c_0_12,plain,
    ! [X9,X10,X11,X13] :
      ( ( m1_subset_1(esk4_3(X9,X10,X11),X10)
        | ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
        | v1_xboole_0(X10)
        | ~ m1_pboole(X11,X10) )
      & ( X9 = esk4_3(X9,X10,X11)
        | ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
        | v1_xboole_0(X10)
        | ~ m1_pboole(X11,X10) )
      & ( k1_funct_1(X11,esk4_3(X9,X10,X11)) != k1_xboole_0
        | ~ r2_hidden(X9,a_2_0_closure3(X10,X11))
        | v1_xboole_0(X10)
        | ~ m1_pboole(X11,X10) )
      & ( ~ m1_subset_1(X13,X10)
        | X9 != X13
        | k1_funct_1(X11,X13) = k1_xboole_0
        | r2_hidden(X9,a_2_0_closure3(X10,X11))
        | v1_xboole_0(X10)
        | ~ m1_pboole(X11,X10) ) ),
    inference(distribute,[status(thm)],[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_8])])])])])]) ).

cnf(c_0_13,plain,
    k1_xboole_0 = esk11_0,
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_14,plain,
    v1_xboole_0(esk8_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ~ v1_xboole_0(X1)
       => ! [X2] :
            ( m1_pboole(X2,X1)
           => ! [X3] :
                ( m1_subset_1(X3,X1)
               => ( ~ r2_hidden(X3,k1_closure3(X1,X2))
                 => k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t8_closure3])]) ).

fof(c_0_16,plain,
    ! [X25,X26,X27] :
      ( ( X27 != k1_closure3(X25,X26)
        | X27 = a_2_0_closure3(X25,X26)
        | ~ m1_pboole(X26,X25)
        | v1_xboole_0(X25) )
      & ( X27 != a_2_0_closure3(X25,X26)
        | X27 = k1_closure3(X25,X26)
        | ~ m1_pboole(X26,X25)
        | v1_xboole_0(X25) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).

cnf(c_0_17,plain,
    ( k1_funct_1(X4,X1) = k1_xboole_0
    | r2_hidden(X3,a_2_0_closure3(X2,X4))
    | v1_xboole_0(X2)
    | ~ m1_subset_1(X1,X2)
    | X3 != X1
    | ~ m1_pboole(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( X1 = esk11_0
    | ~ v1_xboole_0(X1) ),
    inference(rw,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_19,plain,
    v1_xboole_0(esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_20,negated_conjecture,
    ( ~ v1_xboole_0(esk1_0)
    & m1_pboole(esk2_0,esk1_0)
    & m1_subset_1(esk3_0,esk1_0)
    & ~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0))
    & k1_funct_1(esk2_0,esk3_0) != k1_xboole_0 ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

cnf(c_0_21,plain,
    ( X1 = k1_closure3(X2,X3)
    | v1_xboole_0(X2)
    | X1 != a_2_0_closure3(X2,X3)
    | ~ m1_pboole(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( k1_funct_1(X1,X2) = k1_xboole_0
    | r2_hidden(X2,a_2_0_closure3(X3,X1))
    | v1_xboole_0(X3)
    | ~ m1_subset_1(X2,X3)
    | ~ m1_pboole(X1,X3) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    esk11_0 = esk8_0,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    k1_funct_1(esk2_0,esk3_0) != k1_xboole_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    ( k1_closure3(X1,X2) = a_2_0_closure3(X1,X2)
    | v1_xboole_0(X1)
    | ~ m1_pboole(X2,X1) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    m1_pboole(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,negated_conjecture,
    ~ v1_xboole_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( k1_funct_1(X1,X2) = esk8_0
    | r2_hidden(X2,a_2_0_closure3(X3,X1))
    | v1_xboole_0(X3)
    | ~ m1_subset_1(X2,X3)
    | ~ m1_pboole(X1,X3) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_13]),c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    m1_subset_1(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,negated_conjecture,
    k1_funct_1(esk2_0,esk3_0) != esk11_0,
    inference(rw,[status(thm)],[c_0_24,c_0_13]) ).

cnf(c_0_31,negated_conjecture,
    ~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_32,negated_conjecture,
    k1_closure3(esk1_0,esk2_0) = a_2_0_closure3(esk1_0,esk2_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    ( k1_funct_1(X1,esk3_0) = esk8_0
    | r2_hidden(esk3_0,a_2_0_closure3(esk1_0,X1))
    | ~ m1_pboole(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    k1_funct_1(esk2_0,esk3_0) != esk8_0,
    inference(rw,[status(thm)],[c_0_30,c_0_23]) ).

cnf(c_0_35,negated_conjecture,
    ~ r2_hidden(esk3_0,a_2_0_closure3(esk1_0,esk2_0)),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 23:00:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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/benchmark/theBenchmark.p
% 0.20/0.50  # Version: 3.1.0
% 0.20/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.50  # Starting sh5l with 300s (1) cores
% 0.20/0.50  # new_bool_3 with pid 25461 completed with status 0
% 0.20/0.50  # Result found by new_bool_3
% 0.20/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.50  # Search class: FGHSS-FFMM31-SFFFFFNN
% 0.20/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting U----_206d_00_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.20/0.50  # U----_206d_00_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 25464 completed with status 0
% 0.20/0.50  # Result found by U----_206d_00_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.50  # Search class: FGHSS-FFMM31-SFFFFFNN
% 0.20/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting U----_206d_00_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.20/0.50  # Preprocessing time       : 0.001 s
% 0.20/0.50  # Presaturation interreduction done
% 0.20/0.50  
% 0.20/0.50  # Proof found!
% 0.20/0.50  # SZS status Theorem
% 0.20/0.50  # SZS output start CNFRefutation
% See solution above
% 0.20/0.50  # Parsed axioms                        : 29
% 0.20/0.50  # Removed by relevancy pruning/SinE    : 10
% 0.20/0.50  # Initial clauses                      : 32
% 0.20/0.50  # Removed in clause preprocessing      : 0
% 0.20/0.50  # Initial clauses in saturation        : 32
% 0.20/0.50  # Processed clauses                    : 107
% 0.20/0.50  # ...of these trivial                  : 0
% 0.20/0.50  # ...subsumed                          : 6
% 0.20/0.50  # ...remaining for further processing  : 101
% 0.20/0.50  # Other redundant clauses eliminated   : 3
% 0.20/0.50  # Clauses deleted for lack of memory   : 0
% 0.20/0.50  # Backward-subsumed                    : 0
% 0.20/0.50  # Backward-rewritten                   : 9
% 0.20/0.50  # Generated clauses                    : 58
% 0.20/0.50  # ...of the previous two non-redundant : 59
% 0.20/0.50  # ...aggressively subsumed             : 0
% 0.20/0.50  # Contextual simplify-reflections      : 2
% 0.20/0.50  # Paramodulations                      : 53
% 0.20/0.50  # Factorizations                       : 2
% 0.20/0.50  # NegExts                              : 0
% 0.20/0.50  # Equation resolutions                 : 3
% 0.20/0.50  # Disequality decompositions           : 0
% 0.20/0.50  # Total rewrite steps                  : 19
% 0.20/0.50  # ...of those cached                   : 12
% 0.20/0.50  # Propositional unsat checks           : 0
% 0.20/0.50  #    Propositional check models        : 0
% 0.20/0.50  #    Propositional check unsatisfiable : 0
% 0.20/0.50  #    Propositional clauses             : 0
% 0.20/0.50  #    Propositional clauses after purity: 0
% 0.20/0.50  #    Propositional unsat core size     : 0
% 0.20/0.50  #    Propositional preprocessing time  : 0.000
% 0.20/0.50  #    Propositional encoding time       : 0.000
% 0.20/0.50  #    Propositional solver time         : 0.000
% 0.20/0.50  #    Success case prop preproc time    : 0.000
% 0.20/0.50  #    Success case prop encoding time   : 0.000
% 0.20/0.50  #    Success case prop solver time     : 0.000
% 0.20/0.50  # Current number of processed clauses  : 58
% 0.20/0.50  #    Positive orientable unit clauses  : 17
% 0.20/0.50  #    Positive unorientable unit clauses: 0
% 0.20/0.50  #    Negative unit clauses             : 5
% 0.20/0.50  #    Non-unit-clauses                  : 36
% 0.20/0.50  # Current number of unprocessed clauses: 12
% 0.20/0.50  # ...number of literals in the above   : 52
% 0.20/0.50  # Current number of archived formulas  : 0
% 0.20/0.50  # Current number of archived clauses   : 40
% 0.20/0.50  # Clause-clause subsumption calls (NU) : 245
% 0.20/0.50  # Rec. Clause-clause subsumption calls : 170
% 0.20/0.50  # Non-unit clause-clause subsumptions  : 7
% 0.20/0.50  # Unit Clause-clause subsumption calls : 20
% 0.20/0.50  # Rewrite failures with RHS unbound    : 0
% 0.20/0.50  # BW rewrite match attempts            : 3
% 0.20/0.50  # BW rewrite match successes           : 3
% 0.20/0.50  # Condensation attempts                : 0
% 0.20/0.50  # Condensation successes               : 0
% 0.20/0.50  # Termbank termtop insertions          : 2737
% 0.20/0.50  # Search garbage collected termcells   : 424
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.009 s
% 0.20/0.50  # System time              : 0.003 s
% 0.20/0.50  # Total time               : 0.012 s
% 0.20/0.50  # Maximum resident set size: 1848 pages
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.011 s
% 0.20/0.50  # System time              : 0.005 s
% 0.20/0.50  # Total time               : 0.015 s
% 0.20/0.50  # Maximum resident set size: 1712 pages
% 0.20/0.50  % E---3.1 exiting
% 0.20/0.51  % E exiting
%------------------------------------------------------------------------------