TSTP Solution File: NUN085+2 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n020.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 0.23s 1.40s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   65 (  38 unt;   0 def)
%            Number of atoms       :  139 (  58 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  129 (  55   ~;  42   |;  32   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   93 (   6 sgn  34   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(zeroplusoneidzero,conjecture,
    ! [X39] :
      ( ! [X22] :
          ( ! [X23] :
              ( ~ r1(X23)
              | ~ r3(X23,X22,X39) )
          | ! [X16] :
              ( ~ r1(X16)
              | ~ r2(X16,X22) ) )
      | ! [X17] :
          ( X39 != X17
          | ~ r1(X17) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',zeroplusoneidzero) ).

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_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_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_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(axiom_7a,axiom,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X39] :
        ( ! [X22] :
            ( ! [X23] :
                ( ~ r1(X23)
                | ~ r3(X23,X22,X39) )
            | ! [X16] :
                ( ~ r1(X16)
                | ~ r2(X16,X22) ) )
        | ! [X17] :
            ( X39 != X17
            | ~ r1(X17) ) ),
    inference(assume_negation,[status(cth)],[zeroplusoneidzero]) ).

fof(c_0_8,plain,
    ! [X4] :
      ( ( r1(X4)
        | ~ r1(X4) )
      & ( X4 = esk6_0
        | ~ r1(X4) )
      & ( r1(X4)
        | X4 != esk6_0 )
      & ( X4 = esk6_0
        | X4 != esk6_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_1])])])]) ).

fof(c_0_9,negated_conjecture,
    ( r1(esk3_0)
    & r3(esk3_0,esk2_0,esk1_0)
    & r1(esk4_0)
    & r2(esk4_0,esk2_0)
    & esk1_0 = esk5_0
    & r1(esk5_0) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])])]) ).

cnf(c_0_10,plain,
    ( X1 = esk6_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    r1(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    esk6_0 = esk4_0,
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,plain,
    ( X1 = esk4_0
    | ~ r1(X1) ),
    inference(rw,[status(thm)],[c_0_10,c_0_12]) ).

cnf(c_0_14,negated_conjecture,
    r1(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    esk4_0 = esk3_0,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    r1(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,negated_conjecture,
    esk1_0 = esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,plain,
    ( X1 = esk3_0
    | ~ r1(X1) ),
    inference(rw,[status(thm)],[c_0_13,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    r1(esk1_0),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_20,plain,
    ! [X10,X11,X13] :
      ( ( r3(X10,X11,X13)
        | ~ r3(X10,X11,X13) )
      & ( X13 = esk17_2(X10,X11)
        | ~ r3(X10,X11,X13) )
      & ( r3(X10,X11,X13)
        | X13 != esk17_2(X10,X11) )
      & ( X13 = esk17_2(X10,X11)
        | X13 != esk17_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,esk15_2(X20,X21))
      & r3(X20,esk15_2(X20,X21),esk14_2(X20,X21))
      & esk14_2(X20,X21) = esk13_2(X20,X21)
      & r2(esk16_2(X20,X21),esk13_2(X20,X21))
      & r3(X20,X21,esk16_2(X20,X21)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_1a])])])]) ).

fof(c_0_22,plain,
    ! [X6,X8] :
      ( ( r2(X6,X8)
        | ~ r2(X6,X8) )
      & ( X8 = esk12_1(X6)
        | ~ r2(X6,X8) )
      & ( r2(X6,X8)
        | X8 != esk12_1(X6) )
      & ( X8 = esk12_1(X6)
        | X8 != esk12_1(X6) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_2])])])]) ).

fof(c_0_23,plain,
    ! [X33] :
      ( r1(esk8_1(X33))
      & r3(X33,esk8_1(X33),esk7_1(X33))
      & esk7_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_24,negated_conjecture,
    esk3_0 = esk1_0,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_25,plain,
    ! [X44,X45,X46] :
      ( ~ r1(X46)
      | X46 != X45
      | ~ r2(X44,X45) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_7a])])])])]) ).

cnf(c_0_26,plain,
    ( X3 = esk17_2(X1,X2)
    | ~ r3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,plain,
    r3(X1,X2,esk16_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    r3(X1,esk15_2(X1,X2),esk14_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,plain,
    esk14_2(X1,X2) = esk13_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    ( X2 = esk12_1(X1)
    | ~ r2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_31,plain,
    r2(X1,esk15_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_32,plain,
    r2(esk16_2(X1,X2),esk13_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_33,negated_conjecture,
    r2(esk4_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_34,plain,
    r3(X1,esk8_1(X1),esk7_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_35,plain,
    esk7_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_36,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(rw,[status(thm)],[c_0_18,c_0_24]) ).

cnf(c_0_37,plain,
    r1(esk8_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_38,plain,
    ( ~ r2(X1,X2)
    | X3 != X2
    | ~ r1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_39,plain,
    ( r1(X1)
    | X1 != esk6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_40,plain,
    esk17_2(X1,X2) = esk16_2(X1,X2),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_41,plain,
    r3(X1,esk15_2(X1,X2),esk13_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_42,plain,
    esk15_2(X1,X2) = esk12_1(X2),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_43,plain,
    esk13_2(X1,X2) = esk12_1(esk16_2(X1,X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_32]) ).

cnf(c_0_44,negated_conjecture,
    esk12_1(esk4_0) = esk2_0,
    inference(spm,[status(thm)],[c_0_30,c_0_33]) ).

cnf(c_0_45,plain,
    r3(X1,esk8_1(X1),X1),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_46,plain,
    esk8_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_47,plain,
    ( ~ r2(X1,X2)
    | ~ r1(X2) ),
    inference(er,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    ( r1(X1)
    | X1 != esk4_0 ),
    inference(rw,[status(thm)],[c_0_39,c_0_12]) ).

cnf(c_0_49,negated_conjecture,
    r3(esk3_0,esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_50,plain,
    ( X1 = esk16_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_26,c_0_40]) ).

cnf(c_0_51,plain,
    r3(X1,esk12_1(X2),esk12_1(esk16_2(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_52,negated_conjecture,
    esk12_1(esk3_0) = esk2_0,
    inference(rw,[status(thm)],[c_0_44,c_0_15]) ).

cnf(c_0_53,plain,
    r3(X1,esk1_0,X1),
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ~ r1(esk2_0),
    inference(spm,[status(thm)],[c_0_47,c_0_33]) ).

cnf(c_0_55,plain,
    ( r1(X1)
    | X1 != esk3_0 ),
    inference(rw,[status(thm)],[c_0_48,c_0_15]) ).

cnf(c_0_56,negated_conjecture,
    esk17_2(esk3_0,esk2_0) = esk1_0,
    inference(spm,[status(thm)],[c_0_26,c_0_49]) ).

cnf(c_0_57,plain,
    esk16_2(X1,esk12_1(X2)) = esk12_1(esk16_2(X1,X2)),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_58,negated_conjecture,
    esk12_1(esk1_0) = esk2_0,
    inference(rw,[status(thm)],[c_0_52,c_0_24]) ).

cnf(c_0_59,plain,
    esk16_2(X1,esk1_0) = X1,
    inference(spm,[status(thm)],[c_0_50,c_0_53]) ).

cnf(c_0_60,negated_conjecture,
    esk2_0 != esk3_0,
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_61,negated_conjecture,
    esk16_2(esk1_0,esk2_0) = esk1_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_24]),c_0_40]) ).

cnf(c_0_62,negated_conjecture,
    esk16_2(X1,esk2_0) = esk12_1(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_63,negated_conjecture,
    esk2_0 != esk1_0,
    inference(rw,[status(thm)],[c_0_60,c_0_24]) ).

cnf(c_0_64,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_58]),c_0_63]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun  2 07:20:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.23/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40  # Preprocessing time       : 0.016 s
% 0.23/1.40  
% 0.23/1.40  # Proof found!
% 0.23/1.40  # SZS status Theorem
% 0.23/1.40  # SZS output start CNFRefutation
% See solution above
% 0.23/1.40  # Proof object total steps             : 65
% 0.23/1.40  # Proof object clause steps            : 50
% 0.23/1.40  # Proof object formula steps           : 15
% 0.23/1.40  # Proof object conjectures             : 23
% 0.23/1.40  # Proof object clause conjectures      : 20
% 0.23/1.40  # Proof object formula conjectures     : 3
% 0.23/1.40  # Proof object initial clauses used    : 19
% 0.23/1.40  # Proof object initial formulas used   : 7
% 0.23/1.40  # Proof object generating inferences   : 14
% 0.23/1.40  # Proof object simplifying inferences  : 22
% 0.23/1.40  # Training examples: 0 positive, 0 negative
% 0.23/1.40  # Parsed axioms                        : 12
% 0.23/1.40  # Removed by relevancy pruning/SinE    : 3
% 0.23/1.40  # Initial clauses                      : 32
% 0.23/1.40  # Removed in clause preprocessing      : 8
% 0.23/1.40  # Initial clauses in saturation        : 24
% 0.23/1.40  # Processed clauses                    : 137
% 0.23/1.40  # ...of these trivial                  : 2
% 0.23/1.40  # ...subsumed                          : 37
% 0.23/1.40  # ...remaining for further processing  : 98
% 0.23/1.40  # Other redundant clauses eliminated   : 4
% 0.23/1.40  # Clauses deleted for lack of memory   : 0
% 0.23/1.40  # Backward-subsumed                    : 0
% 0.23/1.40  # Backward-rewritten                   : 28
% 0.23/1.40  # Generated clauses                    : 227
% 0.23/1.40  # ...of the previous two non-trivial   : 213
% 0.23/1.40  # Contextual simplify-reflections      : 9
% 0.23/1.40  # Paramodulations                      : 219
% 0.23/1.40  # Factorizations                       : 0
% 0.23/1.40  # Equation resolutions                 : 8
% 0.23/1.40  # Current number of processed clauses  : 68
% 0.23/1.40  #    Positive orientable unit clauses  : 21
% 0.23/1.40  #    Positive unorientable unit clauses: 0
% 0.23/1.40  #    Negative unit clauses             : 4
% 0.23/1.40  #    Non-unit-clauses                  : 43
% 0.23/1.40  # Current number of unprocessed clauses: 80
% 0.23/1.40  # ...number of literals in the above   : 225
% 0.23/1.40  # Current number of archived formulas  : 0
% 0.23/1.40  # Current number of archived clauses   : 30
% 0.23/1.40  # Clause-clause subsumption calls (NU) : 388
% 0.23/1.40  # Rec. Clause-clause subsumption calls : 342
% 0.23/1.40  # Non-unit clause-clause subsumptions  : 36
% 0.23/1.40  # Unit Clause-clause subsumption calls : 43
% 0.23/1.40  # Rewrite failures with RHS unbound    : 0
% 0.23/1.40  # BW rewrite match attempts            : 13
% 0.23/1.40  # BW rewrite match successes           : 11
% 0.23/1.40  # Condensation attempts                : 0
% 0.23/1.40  # Condensation successes               : 0
% 0.23/1.40  # Termbank termtop insertions          : 2914
% 0.23/1.40  
% 0.23/1.40  # -------------------------------------------------
% 0.23/1.40  # User time                : 0.022 s
% 0.23/1.40  # System time              : 0.000 s
% 0.23/1.40  # Total time               : 0.022 s
% 0.23/1.40  # Maximum resident set size: 2968 pages
%------------------------------------------------------------------------------