TSTP Solution File: SYN390^4 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYN390^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 07:44:35 EDT 2024

% Result   : Theorem 0.16s 0.42s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   52 (  28 unt;  15 typ;   0 def)
%            Number of atoms       :  127 (  24 equ;   0 cnn)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  257 (  34   ~;  35   |;  15   &; 155   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   84 (  84   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   82 (  56   ^  26   !;   0   ?;  82   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    irel: $i > $i > $o ).

thf(decl_23,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(decl_24,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_25,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_26,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_27,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(decl_28,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(decl_32,type,
    iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_34,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_36,type,
    iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_38,type,
    ivalid: ( $i > $o ) > $o ).

thf(decl_42,type,
    p: $i > $o ).

thf(decl_43,type,
    esk1_0: $i ).

thf(decl_44,type,
    esk2_0: $i ).

thf(decl_45,type,
    esk3_0: $i ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X4: $i > $o,X5: $i] :
          ~ ( X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
          ( ( X6 @ X5 )
          | ( X7 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).

thf(iand,axiom,
    ( iand
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand) ).

thf(mand,axiom,
    ( mand
    = ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
          ( ( X8 @ X5 )
          & ( X9 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).

thf(iimplies,axiom,
    ( iimplies
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X12: $i > $o,X1: $i] :
        ! [X2: $i] :
          ( ( irel @ X1 @ X2 )
         => ( X12 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).

thf(iequiv,axiom,
    ( iequiv
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( iand @ ( iimplies @ X12 @ X14 ) @ ( iimplies @ X14 @ X12 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iequiv) ).

thf(iatom,axiom,
    ( iatom
    = ( ^ [X12: $i > $o] : X12 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).

thf(ivalid,axiom,
    ( ivalid
    = ( ^ [X15: $i > $o] :
        ! [X13: $i] : ( X15 @ X13 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).

thf(pel11,conjecture,
    ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel11) ).

thf(c_0_11,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

thf(c_0_12,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_13,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_14,plain,
    ( iand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[iand]) ).

thf(c_0_15,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mand]) ).

thf(c_0_16,plain,
    ( iimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ! [X24: $i] :
                ( ( irel @ Z2 @ X24 )
               => ( Z0 @ X24 ) )
          | ! [X25: $i] :
              ( ( irel @ Z2 @ X25 )
             => ( Z1 @ X25 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iimplies]) ).

thf(c_0_17,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

thf(c_0_18,plain,
    ( mbox_s4
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X2: $i] :
          ( ( irel @ Z1 @ X2 )
         => ( Z0 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_s4]) ).

thf(c_0_19,plain,
    ( iequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( ~ ! [X28: $i] :
                  ( ( irel @ Z2 @ X28 )
                 => ( Z0 @ X28 ) )
            | ! [X29: $i] :
                ( ( irel @ Z2 @ X29 )
               => ( Z1 @ X29 ) ) )
          & ( ~ ! [X30: $i] :
                  ( ( irel @ Z2 @ X30 )
                 => ( Z1 @ X30 ) )
            | ! [X31: $i] :
                ( ( irel @ Z2 @ X31 )
               => ( Z0 @ X31 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iequiv]) ).

thf(c_0_20,plain,
    ( iand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          & ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_21,plain,
    ( iimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ! [X24: $i] :
                ( ( irel @ Z2 @ X24 )
               => ( Z0 @ X24 ) )
          | ! [X25: $i] :
              ( ( irel @ Z2 @ X25 )
             => ( Z1 @ X25 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

thf(c_0_22,plain,
    ( iatom
    = ( ^ [Z0: $i > $o] : Z0 ) ),
    inference(fof_simplification,[status(thm)],[iatom]) ).

thf(c_0_23,plain,
    ( iequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( ~ ! [X28: $i] :
                  ( ( irel @ Z2 @ X28 )
                 => ( Z0 @ X28 ) )
            | ! [X29: $i] :
                ( ( irel @ Z2 @ X29 )
               => ( Z1 @ X29 ) ) )
          & ( ~ ! [X30: $i] :
                  ( ( irel @ Z2 @ X30 )
                 => ( Z1 @ X30 ) )
            | ! [X31: $i] :
                ( ( irel @ Z2 @ X31 )
               => ( Z0 @ X31 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

thf(c_0_24,plain,
    ( ivalid
    = ( ^ [Z0: $i > $o] :
        ! [X13: $i] : ( Z0 @ X13 ) ) ),
    inference(fof_simplification,[status(thm)],[ivalid]) ).

thf(c_0_25,negated_conjecture,
    ~ ! [X41: $i] :
        ( ( ~ ! [X37: $i] :
                ( ( irel @ X41 @ X37 )
               => ( p @ X37 ) )
          | ! [X38: $i] :
              ( ( irel @ X41 @ X38 )
             => ( p @ X38 ) ) )
        & ( ~ ! [X39: $i] :
                ( ( irel @ X41 @ X39 )
               => ( p @ X39 ) )
          | ! [X40: $i] :
              ( ( irel @ X41 @ X40 )
             => ( p @ X40 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[pel11]),c_0_22]),c_0_23]),c_0_24]) ).

thf(c_0_26,negated_conjecture,
    ! [X47: $i,X49: $i] :
      ( ( ~ ( irel @ esk1_0 @ X49 )
        | ( p @ X49 )
        | ~ ( irel @ esk1_0 @ X47 )
        | ( p @ X47 ) )
      & ( ( irel @ esk1_0 @ esk3_0 )
        | ~ ( irel @ esk1_0 @ X47 )
        | ( p @ X47 ) )
      & ( ~ ( p @ esk3_0 )
        | ~ ( irel @ esk1_0 @ X47 )
        | ( p @ X47 ) )
      & ( ~ ( irel @ esk1_0 @ X49 )
        | ( p @ X49 )
        | ( irel @ esk1_0 @ esk2_0 ) )
      & ( ( irel @ esk1_0 @ esk3_0 )
        | ( irel @ esk1_0 @ esk2_0 ) )
      & ( ~ ( p @ esk3_0 )
        | ( irel @ esk1_0 @ esk2_0 ) )
      & ( ~ ( irel @ esk1_0 @ X49 )
        | ( p @ X49 )
        | ~ ( p @ esk2_0 ) )
      & ( ( irel @ esk1_0 @ esk3_0 )
        | ~ ( p @ esk2_0 ) )
      & ( ~ ( p @ esk3_0 )
        | ~ ( p @ esk2_0 ) ) ),
    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_25])])])])])]) ).

thf(c_0_27,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( p @ X1 )
      | ( p @ X2 )
      | ~ ( irel @ esk1_0 @ X1 )
      | ~ ( irel @ esk1_0 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_28,negated_conjecture,
    ! [X1: $i] :
      ( ( p @ X1 )
      | ~ ( irel @ esk1_0 @ X1 ) ),
    inference(condense,[status(thm)],[c_0_27]) ).

thf(c_0_29,negated_conjecture,
    ( ( irel @ esk1_0 @ esk2_0 )
    | ~ ( p @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_30,negated_conjecture,
    ( ~ ( p @ esk3_0 )
    | ~ ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_31,negated_conjecture,
    ( ( irel @ esk1_0 @ esk3_0 )
    | ( irel @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_32,negated_conjecture,
    ~ ( p @ esk3_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

thf(c_0_33,negated_conjecture,
    ( ( irel @ esk1_0 @ esk3_0 )
    | ~ ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_34,negated_conjecture,
    irel @ esk1_0 @ esk2_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_32]) ).

thf(c_0_35,negated_conjecture,
    ~ ( p @ esk2_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_33]),c_0_32]) ).

thf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SYN390^4 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.11  % Command    : run_E %s %d THM
% 0.11/0.30  % Computer : n003.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Mon May 20 15:52:23 EDT 2024
% 0.11/0.30  % CPUTime    : 
% 0.16/0.41  Running higher-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox/solver/bin/eprover-ho --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
% 0.16/0.42  # Version: 3.1.0-ho
% 0.16/0.42  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.42  # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.42  # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.42  # Starting sh1l with 300s (1) cores
% 0.16/0.42  # Starting post_as_ho10 with 300s (1) cores
% 0.16/0.42  # sh1l with pid 14211 completed with status 0
% 0.16/0.42  # Result found by sh1l
% 0.16/0.42  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.42  # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.42  # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.42  # Starting sh1l with 300s (1) cores
% 0.16/0.42  # No SInE strategy applied
% 0.16/0.42  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.16/0.42  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.42  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.42  # new_ho_10 with pid 14213 completed with status 0
% 0.16/0.42  # Result found by new_ho_10
% 0.16/0.42  # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.16/0.42  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.42  # Starting new_ho_9 with 1500s (5) cores
% 0.16/0.42  # Starting post_as_ho1 with 300s (1) cores
% 0.16/0.42  # Starting sh1l with 300s (1) cores
% 0.16/0.42  # No SInE strategy applied
% 0.16/0.42  # Search class: HGHNF-FFSF00-SHSSMFNN
% 0.16/0.42  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.42  # Starting new_ho_10 with 163s (1) cores
% 0.16/0.42  # Preprocessing time       : 0.001 s
% 0.16/0.42  # Presaturation interreduction done
% 0.16/0.42  
% 0.16/0.42  # Proof found!
% 0.16/0.42  # SZS status Theorem
% 0.16/0.42  # SZS output start CNFRefutation
% See solution above
% 0.16/0.42  # Parsed axioms                        : 43
% 0.16/0.42  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.42  # Initial clauses                      : 32
% 0.16/0.42  # Removed in clause preprocessing      : 21
% 0.16/0.42  # Initial clauses in saturation        : 11
% 0.16/0.42  # Processed clauses                    : 22
% 0.16/0.42  # ...of these trivial                  : 0
% 0.16/0.42  # ...subsumed                          : 0
% 0.16/0.42  # ...remaining for further processing  : 22
% 0.16/0.42  # Other redundant clauses eliminated   : 0
% 0.16/0.42  # Clauses deleted for lack of memory   : 0
% 0.16/0.42  # Backward-subsumed                    : 7
% 0.16/0.42  # Backward-rewritten                   : 1
% 0.16/0.42  # Generated clauses                    : 10
% 0.16/0.42  # ...of the previous two non-redundant : 8
% 0.16/0.42  # ...aggressively subsumed             : 0
% 0.16/0.42  # Contextual simplify-reflections      : 1
% 0.16/0.42  # Paramodulations                      : 10
% 0.16/0.42  # Factorizations                       : 0
% 0.16/0.42  # NegExts                              : 0
% 0.16/0.42  # Equation resolutions                 : 0
% 0.16/0.42  # Disequality decompositions           : 0
% 0.16/0.42  # Total rewrite steps                  : 1
% 0.16/0.42  # ...of those cached                   : 0
% 0.16/0.42  # Propositional unsat checks           : 0
% 0.16/0.42  #    Propositional check models        : 0
% 0.16/0.42  #    Propositional check unsatisfiable : 0
% 0.16/0.42  #    Propositional clauses             : 0
% 0.16/0.42  #    Propositional clauses after purity: 0
% 0.16/0.42  #    Propositional unsat core size     : 0
% 0.16/0.42  #    Propositional preprocessing time  : 0.000
% 0.16/0.42  #    Propositional encoding time       : 0.000
% 0.16/0.42  #    Propositional solver time         : 0.000
% 0.16/0.42  #    Success case prop preproc time    : 0.000
% 0.16/0.42  #    Success case prop encoding time   : 0.000
% 0.16/0.42  #    Success case prop solver time     : 0.000
% 0.16/0.42  # Current number of processed clauses  : 7
% 0.16/0.42  #    Positive orientable unit clauses  : 3
% 0.16/0.42  #    Positive unorientable unit clauses: 0
% 0.16/0.42  #    Negative unit clauses             : 2
% 0.16/0.42  #    Non-unit-clauses                  : 2
% 0.16/0.42  # Current number of unprocessed clauses: 3
% 0.16/0.42  # ...number of literals in the above   : 9
% 0.16/0.42  # Current number of archived formulas  : 0
% 0.16/0.42  # Current number of archived clauses   : 15
% 0.16/0.42  # Clause-clause subsumption calls (NU) : 8
% 0.16/0.42  # Rec. Clause-clause subsumption calls : 8
% 0.16/0.42  # Non-unit clause-clause subsumptions  : 6
% 0.16/0.42  # Unit Clause-clause subsumption calls : 11
% 0.16/0.42  # Rewrite failures with RHS unbound    : 0
% 0.16/0.42  # BW rewrite match attempts            : 7
% 0.16/0.42  # BW rewrite match successes           : 1
% 0.16/0.42  # Condensation attempts                : 22
% 0.16/0.42  # Condensation successes               : 1
% 0.16/0.42  # Termbank termtop insertions          : 1958
% 0.16/0.42  # Search garbage collected termcells   : 525
% 0.16/0.42  
% 0.16/0.42  # -------------------------------------------------
% 0.16/0.42  # User time                : 0.004 s
% 0.16/0.42  # System time              : 0.002 s
% 0.16/0.42  # Total time               : 0.006 s
% 0.16/0.42  # Maximum resident set size: 1868 pages
% 0.16/0.42  
% 0.16/0.42  # -------------------------------------------------
% 0.16/0.42  # User time                : 0.005 s
% 0.16/0.42  # System time              : 0.004 s
% 0.16/0.42  # Total time               : 0.010 s
% 0.16/0.42  # Maximum resident set size: 1756 pages
% 0.16/0.42  % E---3.1 exiting
% 0.16/0.42  % E exiting
%------------------------------------------------------------------------------