TSTP Solution File: NUN086+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUN086+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.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 : Mon Jul 18 16:26:07 EDT 2022

% Result   : Theorem 0.24s 1.43s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   67 (  35 unt;   0 def)
%            Number of atoms       :  174 (  58 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  170 (  63   ~;  51   |;  56   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   1 con; 0-2 aty)
%            Number of variables   :  144 (  12 sgn  35   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_4,axiom,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4) ).

fof(axiom_2a,axiom,
    ! [X20,X21] :
    ? [X22] :
      ( ? [X23] :
          ( ? [X24] :
              ( r2(X21,X24)
              & r4(X20,X24,X23) )
          & X23 = X22 )
      & ? [X25] :
          ( r3(X25,X20,X22)
          & r4(X20,X21,X25) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).

fof(axiom_5a,axiom,
    ! [X33] :
    ? [X34] :
      ( ? [X35] :
          ( r1(X35)
          & r4(X33,X35,X34) )
      & ? [X36] :
          ( r1(X36)
          & X34 = X36 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).

fof(zerotimesoneeqzero,conjecture,
    ? [X39] :
      ( ? [X22] :
          ( ? [X23] :
              ( r1(X23)
              & r2(X23,X22) )
          & ? [X16] :
              ( r1(X16)
              & r4(X16,X22,X39) ) )
      & ? [X17] :
          ( r1(X17)
          & X39 = X17 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',zerotimesoneeqzero) ).

fof(axiom_3,axiom,
    ! [X6,X7] :
    ? [X8] :
    ! [X9] :
      ( ( ~ r3(X6,X7,X9)
        & X9 != X8 )
      | ( r3(X6,X7,X9)
        & X9 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).

fof(axiom_1a,axiom,
    ! [X14,X15] :
    ? [X16] :
      ( ? [X17] :
          ( ? [X18] :
              ( r2(X15,X18)
              & r3(X14,X18,X17) )
          & X17 = X16 )
      & ? [X19] :
          ( r2(X19,X16)
          & r3(X14,X15,X19) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).

fof(axiom_4a,axiom,
    ! [X30] :
    ? [X31] :
      ( ? [X32] :
          ( r1(X32)
          & r3(X30,X32,X31) )
      & X31 = X30 ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).

fof(c_0_9,plain,
    ! [X14,X15,X17] :
      ( ( r4(X14,X15,X17)
        | ~ r4(X14,X15,X17) )
      & ( X17 = esk5_2(X14,X15)
        | ~ r4(X14,X15,X17) )
      & ( r4(X14,X15,X17)
        | X17 != esk5_2(X14,X15) )
      & ( X17 = esk5_2(X14,X15)
        | X17 != esk5_2(X14,X15) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_4])])])]) ).

fof(c_0_10,plain,
    ! [X26,X27] :
      ( r2(X27,esk8_2(X26,X27))
      & r4(X26,esk8_2(X26,X27),esk7_2(X26,X27))
      & esk7_2(X26,X27) = esk6_2(X26,X27)
      & r3(esk9_2(X26,X27),X26,esk6_2(X26,X27))
      & r4(X26,X27,esk9_2(X26,X27)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_2a])])])]) ).

fof(c_0_11,plain,
    ! [X6,X8] :
      ( ( r2(X6,X8)
        | ~ r2(X6,X8) )
      & ( X8 = esk13_1(X6)
        | ~ r2(X6,X8) )
      & ( r2(X6,X8)
        | X8 != esk13_1(X6) )
      & ( X8 = esk13_1(X6)
        | X8 != esk13_1(X6) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_2])])])]) ).

cnf(c_0_12,plain,
    ( X3 = esk5_2(X1,X2)
    | ~ r4(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    r4(X1,X2,esk9_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    r4(X1,esk8_2(X1,X2),esk7_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    esk7_2(X1,X2) = esk6_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( X2 = esk13_1(X1)
    | ~ r2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    r2(X1,esk8_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_18,plain,
    ! [X37] :
      ( r1(esk11_1(X37))
      & r4(X37,esk11_1(X37),esk10_1(X37))
      & r1(esk12_1(X37))
      & esk10_1(X37) = esk12_1(X37) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_5a])])])]) ).

fof(c_0_19,negated_conjecture,
    ~ ? [X39] :
        ( ? [X22] :
            ( ? [X23] :
                ( r1(X23)
                & r2(X23,X22) )
            & ? [X16] :
                ( r1(X16)
                & r4(X16,X22,X39) ) )
        & ? [X17] :
            ( r1(X17)
            & X39 = X17 ) ),
    inference(assume_negation,[status(cth)],[zerotimesoneeqzero]) ).

fof(c_0_20,plain,
    ! [X10,X11,X13] :
      ( ( r3(X10,X11,X13)
        | ~ r3(X10,X11,X13) )
      & ( X13 = esk14_2(X10,X11)
        | ~ r3(X10,X11,X13) )
      & ( r3(X10,X11,X13)
        | X13 != esk14_2(X10,X11) )
      & ( X13 = esk14_2(X10,X11)
        | X13 != esk14_2(X10,X11) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_3])])])]) ).

fof(c_0_21,plain,
    ! [X20,X21] :
      ( r2(X21,esk17_2(X20,X21))
      & r3(X20,esk17_2(X20,X21),esk16_2(X20,X21))
      & esk16_2(X20,X21) = esk15_2(X20,X21)
      & r2(esk18_2(X20,X21),esk15_2(X20,X21))
      & r3(X20,X21,esk18_2(X20,X21)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_1a])])])]) ).

cnf(c_0_22,plain,
    esk5_2(X1,X2) = esk9_2(X1,X2),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_23,plain,
    r4(X1,esk8_2(X1,X2),esk6_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_24,plain,
    esk8_2(X1,X2) = esk13_1(X2),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_25,plain,
    ! [X4] :
      ( ( r1(X4)
        | ~ r1(X4) )
      & ( X4 = esk1_0
        | ~ r1(X4) )
      & ( r1(X4)
        | X4 != esk1_0 )
      & ( X4 = esk1_0
        | X4 != esk1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_1])])])]) ).

cnf(c_0_26,plain,
    r1(esk12_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,plain,
    esk10_1(X1) = esk12_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_28,negated_conjecture,
    ! [X40,X41,X42,X43,X44] :
      ( ~ r1(X42)
      | ~ r2(X42,X41)
      | ~ r1(X43)
      | ~ r4(X43,X41,X40)
      | ~ r1(X44)
      | X40 != X44 ),
    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)],[c_0_19])])])])]) ).

cnf(c_0_29,plain,
    ( X3 = esk14_2(X1,X2)
    | ~ r3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    r3(X1,X2,esk18_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    ( X1 = esk9_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_12,c_0_22]) ).

cnf(c_0_32,plain,
    r4(X1,esk13_1(X2),esk6_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_33,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,plain,
    r1(esk10_1(X1)),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,plain,
    r1(esk11_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_36,negated_conjecture,
    ( X1 != X2
    | ~ r1(X2)
    | ~ r4(X3,X4,X1)
    | ~ r1(X3)
    | ~ r2(X5,X4)
    | ~ r1(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,plain,
    esk14_2(X1,X2) = esk18_2(X1,X2),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,plain,
    r3(esk9_2(X1,X2),X1,esk6_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_39,plain,
    esk6_2(X1,X2) = esk9_2(X1,esk13_1(X2)),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,plain,
    r4(X1,esk11_1(X1),esk10_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_41,plain,
    esk10_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_42,plain,
    esk11_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_33,c_0_35]) ).

fof(c_0_43,plain,
    ! [X33] :
      ( r1(esk20_1(X33))
      & r3(X33,esk20_1(X33),esk19_1(X33))
      & esk19_1(X33) = X33 ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_4a])])])]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ r4(X1,X2,X3)
    | ~ r2(X4,X2)
    | ~ r1(X4)
    | ~ r1(X1)
    | ~ r1(X3) ),
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_45,plain,
    ( X1 = esk18_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_29,c_0_37]) ).

cnf(c_0_46,plain,
    r3(esk9_2(X1,X2),X1,esk9_2(X1,esk13_1(X2))),
    inference(rw,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_47,plain,
    r4(X1,esk1_0,esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_48,plain,
    r3(X1,esk20_1(X1),esk19_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_49,plain,
    esk19_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_50,plain,
    r1(esk20_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_51,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r1(esk9_2(X3,X2))
    | ~ r1(X1)
    | ~ r1(X3) ),
    inference(spm,[status(thm)],[c_0_44,c_0_13]) ).

cnf(c_0_52,plain,
    esk9_2(X1,esk13_1(X2)) = esk18_2(esk9_2(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_53,plain,
    esk5_2(X1,esk1_0) = esk1_0,
    inference(spm,[status(thm)],[c_0_12,c_0_47]) ).

cnf(c_0_54,plain,
    r3(X1,esk20_1(X1),X1),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_55,plain,
    esk20_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_33,c_0_50]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ r2(X1,esk13_1(X2))
    | ~ r1(esk18_2(esk9_2(X3,X2),X3))
    | ~ r1(X1)
    | ~ r1(X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_57,plain,
    esk9_2(X1,esk1_0) = esk1_0,
    inference(rw,[status(thm)],[c_0_53,c_0_22]) ).

cnf(c_0_58,plain,
    ( r2(X2,X1)
    | X1 != esk13_1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_59,plain,
    r3(X1,esk1_0,X1),
    inference(rw,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_60,negated_conjecture,
    ( ~ r2(X1,esk13_1(esk1_0))
    | ~ r1(esk18_2(esk1_0,X2))
    | ~ r1(X1)
    | ~ r1(X2) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_61,plain,
    r2(X1,esk13_1(X1)),
    inference(er,[status(thm)],[c_0_58]) ).

cnf(c_0_62,plain,
    r1(esk1_0),
    inference(rw,[status(thm)],[c_0_34,c_0_41]) ).

cnf(c_0_63,plain,
    esk14_2(X1,esk1_0) = X1,
    inference(spm,[status(thm)],[c_0_29,c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    ( ~ r1(esk18_2(esk1_0,X1))
    | ~ r1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).

cnf(c_0_65,plain,
    esk18_2(X1,esk1_0) = X1,
    inference(rw,[status(thm)],[c_0_63,c_0_37]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_62])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : NUN086+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.14  % Command  : run_ET %s %d
% 0.14/0.35  % Computer : n021.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  : 600
% 0.14/0.35  % DateTime : Thu Jun  2 06:19:16 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.24/1.43  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43  # Preprocessing time       : 0.016 s
% 0.24/1.43  
% 0.24/1.43  # Proof found!
% 0.24/1.43  # SZS status Theorem
% 0.24/1.43  # SZS output start CNFRefutation
% See solution above
% 0.24/1.43  # Proof object total steps             : 67
% 0.24/1.43  # Proof object clause steps            : 48
% 0.24/1.43  # Proof object formula steps           : 19
% 0.24/1.43  # Proof object conjectures             : 10
% 0.24/1.43  # Proof object clause conjectures      : 7
% 0.24/1.43  # Proof object formula conjectures     : 3
% 0.24/1.43  # Proof object initial clauses used    : 19
% 0.24/1.43  # Proof object initial formulas used   : 9
% 0.24/1.43  # Proof object generating inferences   : 16
% 0.24/1.43  # Proof object simplifying inferences  : 18
% 0.24/1.43  # Training examples: 0 positive, 0 negative
% 0.24/1.43  # Parsed axioms                        : 12
% 0.24/1.43  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.43  # Initial clauses                      : 40
% 0.24/1.43  # Removed in clause preprocessing      : 12
% 0.24/1.43  # Initial clauses in saturation        : 28
% 0.24/1.43  # Processed clauses                    : 164
% 0.24/1.43  # ...of these trivial                  : 2
% 0.24/1.43  # ...subsumed                          : 52
% 0.24/1.43  # ...remaining for further processing  : 110
% 0.24/1.43  # Other redundant clauses eliminated   : 13
% 0.24/1.43  # Clauses deleted for lack of memory   : 0
% 0.24/1.43  # Backward-subsumed                    : 2
% 0.24/1.43  # Backward-rewritten                   : 25
% 0.24/1.43  # Generated clauses                    : 289
% 0.24/1.43  # ...of the previous two non-trivial   : 264
% 0.24/1.43  # Contextual simplify-reflections      : 16
% 0.24/1.43  # Paramodulations                      : 268
% 0.24/1.43  # Factorizations                       : 0
% 0.24/1.43  # Equation resolutions                 : 21
% 0.24/1.43  # Current number of processed clauses  : 80
% 0.24/1.43  #    Positive orientable unit clauses  : 22
% 0.24/1.43  #    Positive unorientable unit clauses: 0
% 0.24/1.43  #    Negative unit clauses             : 2
% 0.24/1.43  #    Non-unit-clauses                  : 56
% 0.24/1.43  # Current number of unprocessed clauses: 91
% 0.24/1.43  # ...number of literals in the above   : 274
% 0.24/1.43  # Current number of archived formulas  : 0
% 0.24/1.43  # Current number of archived clauses   : 31
% 0.24/1.43  # Clause-clause subsumption calls (NU) : 1335
% 0.24/1.43  # Rec. Clause-clause subsumption calls : 999
% 0.24/1.43  # Non-unit clause-clause subsumptions  : 68
% 0.24/1.43  # Unit Clause-clause subsumption calls : 44
% 0.24/1.43  # Rewrite failures with RHS unbound    : 0
% 0.24/1.43  # BW rewrite match attempts            : 26
% 0.24/1.43  # BW rewrite match successes           : 18
% 0.24/1.43  # Condensation attempts                : 0
% 0.24/1.43  # Condensation successes               : 0
% 0.24/1.43  # Termbank termtop insertions          : 4155
% 0.24/1.43  
% 0.24/1.43  # -------------------------------------------------
% 0.24/1.43  # User time                : 0.024 s
% 0.24/1.43  # System time              : 0.002 s
% 0.24/1.43  # Total time               : 0.026 s
% 0.24/1.43  # Maximum resident set size: 3000 pages
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