TSTP Solution File: RNG122+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n017.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 20:27:00 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  13 unt;   0 def)
%            Number of atoms       :  129 (  28 equ)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives :  142 (  54   ~;  51   |;  25   &)
%                                         (   1 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-2 aty)
%            Number of variables   :   44 (   1 sgn  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddAsso) ).

fof(mAddInvr,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddInvr) ).

fof(mSortsU,axiom,
    ! [X1] :
      ( aElement0(X1)
     => aElement0(smndt0(X1)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsU) ).

fof(m__,conjecture,
    xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).

fof(m__2666,hypothesis,
    ( aElement0(xq)
    & aElement0(xr)
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & ( xr = sz00
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2666) ).

fof(mDefIdeal,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefIdeal) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddZero) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mEOfElem) ).

fof(m__2273,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2273) ).

fof(m__2174,hypothesis,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2174) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).

fof(c_0_11,plain,
    ! [X4,X5,X6] :
      ( ~ aElement0(X4)
      | ~ aElement0(X5)
      | ~ aElement0(X6)
      | sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

fof(c_0_12,plain,
    ! [X2] :
      ( ( sdtpldt0(X2,smndt0(X2)) = sz00
        | ~ aElement0(X2) )
      & ( sz00 = sdtpldt0(smndt0(X2),X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).

fof(c_0_13,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | aElement0(smndt0(X2)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).

fof(c_0_14,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_15,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( aElement0(smndt0(X1))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_20,hypothesis,
    xb = sdtpldt0(sdtasdt0(xq,xu),xr),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

cnf(c_0_21,hypothesis,
    aElement0(xr),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

fof(c_0_22,plain,
    ! [X4,X5,X6,X7,X4] :
      ( ( aSet0(X4)
        | ~ aIdeal0(X4) )
      & ( ~ aElementOf0(X6,X4)
        | aElementOf0(sdtpldt0(X5,X6),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( ~ aElement0(X7)
        | aElementOf0(sdtasdt0(X7,X5),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( aElementOf0(esk13_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk15_1(X4))
        | aElementOf0(esk14_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk15_1(X4),esk13_1(X4)),X4)
        | aElementOf0(esk14_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk15_1(X4))
        | ~ aElementOf0(sdtpldt0(esk13_1(X4),esk14_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk15_1(X4),esk13_1(X4)),X4)
        | ~ aElementOf0(sdtpldt0(esk13_1(X4),esk14_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefIdeal])])])])])])]) ).

cnf(c_0_23,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,hypothesis,
    ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sdtpldt0(sz00,xr)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

fof(c_0_25,plain,
    ! [X2] :
      ( ( sdtpldt0(X2,sz00) = X2
        | ~ aElement0(X2) )
      & ( X2 = sdtpldt0(sz00,X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).

fof(c_0_26,plain,
    ! [X3,X4] :
      ( ~ aSet0(X3)
      | ~ aElementOf0(X4,X3)
      | aElement0(X4) ),
    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)],[mEOfElem])])])])]) ).

fof(c_0_27,hypothesis,
    ! [X2] :
      ( aElementOf0(xu,xI)
      & xu != sz00
      & ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
    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)],[inference(fof_simplification,[status(thm)],[m__2273])])])])])]) ).

cnf(c_0_28,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__2174]) ).

cnf(c_0_30,negated_conjecture,
    ( sdtpldt0(sz00,xr) != xr
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_32,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | aElement0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_33,plain,
    ( aElement0(X1)
    | ~ aElementOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_34,hypothesis,
    aElementOf0(xu,xI),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,negated_conjecture,
    ~ aElement0(sdtasdt0(xq,xu)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21])]) ).

cnf(c_0_37,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_38,hypothesis,
    aElement0(xu),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).

cnf(c_0_39,hypothesis,
    aElement0(xq),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

cnf(c_0_40,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon May 30 21:15:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.020 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 41
% 0.23/1.41  # Proof object clause steps            : 20
% 0.23/1.41  # Proof object formula steps           : 21
% 0.23/1.41  # Proof object conjectures             : 7
% 0.23/1.41  # Proof object clause conjectures      : 4
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 13
% 0.23/1.41  # Proof object initial formulas used   : 11
% 0.23/1.41  # Proof object generating inferences   : 7
% 0.23/1.41  # Proof object simplifying inferences  : 10
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 54
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 5
% 0.23/1.41  # Initial clauses                      : 104
% 0.23/1.41  # Removed in clause preprocessing      : 4
% 0.23/1.41  # Initial clauses in saturation        : 100
% 0.23/1.41  # Processed clauses                    : 403
% 0.23/1.41  # ...of these trivial                  : 15
% 0.23/1.41  # ...subsumed                          : 141
% 0.23/1.41  # ...remaining for further processing  : 247
% 0.23/1.41  # Other redundant clauses eliminated   : 16
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 15
% 0.23/1.41  # Backward-rewritten                   : 5
% 0.23/1.41  # Generated clauses                    : 1447
% 0.23/1.41  # ...of the previous two non-trivial   : 1263
% 0.23/1.41  # Contextual simplify-reflections      : 43
% 0.23/1.41  # Paramodulations                      : 1416
% 0.23/1.41  # Factorizations                       : 0
% 0.23/1.41  # Equation resolutions                 : 31
% 0.23/1.41  # Current number of processed clauses  : 227
% 0.23/1.41  #    Positive orientable unit clauses  : 40
% 0.23/1.41  #    Positive unorientable unit clauses: 0
% 0.23/1.41  #    Negative unit clauses             : 11
% 0.23/1.41  #    Non-unit-clauses                  : 176
% 0.23/1.41  # Current number of unprocessed clauses: 900
% 0.23/1.41  # ...number of literals in the above   : 3897
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 20
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 7036
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 4679
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 198
% 0.23/1.41  # Unit Clause-clause subsumption calls : 225
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 5
% 0.23/1.41  # BW rewrite match successes           : 5
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 29343
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.060 s
% 0.23/1.41  # System time              : 0.001 s
% 0.23/1.41  # Total time               : 0.061 s
% 0.23/1.41  # Maximum resident set size: 4548 pages
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49  eprover: No such file or directory
%------------------------------------------------------------------------------