TSTP Solution File: SYO064^4.001 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO064^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 08:44:28 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   53 (  27 unt;  14 typ;   0 def)
%            Number of atoms       :  117 (  16 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  206 (  22   ~;  28   |;   8   &; 136   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   59 (  59   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   4 con; 0-3 aty)
%            Number of variables   :   74 (  36   ^  38   !;   0   ?;  74   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    irel: $i > $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_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_33,type,
    ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

thf(decl_43,type,
    b: $i > $o ).

thf(decl_44,type,
    c: $i > $o ).

thf(decl_45,type,
    esk1_0: $i ).

thf(decl_46,type,
    esk2_0: $i ).

thf(decl_47,type,
    esk3_0: $i ).

thf(ior,axiom,
    ( ior
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ior) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
          ( ( X6 @ X5 )
          | ( X7 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).

thf(mbox_s4,axiom,
    ( mbox_s4
    = ( ^ [X12: $i > $o,X1: $i] :
        ! [X2: $i] :
          ( ( irel @ X1 @ X2 )
         => ( X12 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).

thf(iand,axiom,
    ( iand
    = ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',mand) ).

thf(iatom,axiom,
    ( iatom
    = ( ^ [X12: $i > $o] : X12 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).

thf(ivalid,axiom,
    ( ivalid
    = ( ^ [X15: $i > $o] :
        ! [X13: $i] : ( X15 @ X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).

thf(axiom2,axiom,
    ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).

thf(con,conjecture,
    ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(axiom1,axiom,
    ivalid @ ( iatom @ c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

thf(refl_axiom,axiom,
    ! [X1: $i] : ( irel @ X1 @ X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).

thf(c_0_11,plain,
    ( ior
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ! [X22: $i] :
              ( ( irel @ Z2 @ X22 )
             => ( Z0 @ X22 ) )
          | ! [X23: $i] :
              ( ( irel @ Z2 @ X23 )
             => ( Z1 @ X23 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ior]) ).

thf(c_0_12,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_13,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_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,
    ( iatom
    = ( ^ [Z0: $i > $o] : Z0 ) ),
    inference(fof_simplification,[status(thm)],[iatom]) ).

thf(c_0_17,plain,
    ( ior
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ! [X22: $i] :
              ( ( irel @ Z2 @ X22 )
             => ( Z0 @ X22 ) )
          | ! [X23: $i] :
              ( ( irel @ Z2 @ X23 )
             => ( Z1 @ X23 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

thf(c_0_18,plain,
    ( ivalid
    = ( ^ [Z0: $i > $o] :
        ! [X13: $i] : ( Z0 @ X13 ) ) ),
    inference(fof_simplification,[status(thm)],[ivalid]) ).

thf(c_0_19,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_20,plain,
    ! [X42: $i] :
      ( ! [X40: $i] :
          ( ( irel @ X42 @ X40 )
         => ( ! [X38: $i] :
                ( ( irel @ X40 @ X38 )
               => ( b @ X38 ) )
            | ! [X39: $i] :
                ( ( irel @ X40 @ X39 )
               => ( a @ X39 ) ) ) )
      | ! [X41: $i] :
          ( ( irel @ X42 @ X41 )
         => ( b @ X41 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_16]),c_0_17]),c_0_18]) ).

thf(c_0_21,negated_conjecture,
    ~ ! [X45: $i] :
        ( ! [X43: $i] :
            ( ( irel @ X45 @ X43 )
           => ( a @ X43 ) )
        | ! [X44: $i] :
            ( ( irel @ X45 @ X44 )
           => ( ( b @ X44 )
              & ( c @ X44 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[con]),c_0_16]),c_0_19]),c_0_17]),c_0_18]) ).

thf(c_0_22,plain,
    ! [X37: $i] : ( c @ X37 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_16]),c_0_18]) ).

thf(c_0_23,plain,
    ! [X51: $i,X52: $i,X53: $i,X54: $i,X55: $i] :
      ( ~ ( irel @ X51 @ X52 )
      | ~ ( irel @ X52 @ X53 )
      | ( b @ X53 )
      | ~ ( irel @ X52 @ X54 )
      | ( a @ X54 )
      | ~ ( irel @ X51 @ X55 )
      | ( b @ X55 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).

thf(c_0_24,negated_conjecture,
    ( ( irel @ esk1_0 @ esk2_0 )
    & ~ ( a @ esk2_0 )
    & ( irel @ esk1_0 @ esk3_0 )
    & ( ~ ( b @ esk3_0 )
      | ~ ( c @ esk3_0 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).

thf(c_0_25,plain,
    ! [X50: $i] : ( c @ X50 ),
    inference(variable_rename,[status(thm)],[c_0_22]) ).

thf(c_0_26,plain,
    ! [X2: $i,X1: $i,X5: $i,X3: $i,X13: $i] :
      ( ( b @ X3 )
      | ( a @ X5 )
      | ( b @ X13 )
      | ~ ( irel @ X1 @ X2 )
      | ~ ( irel @ X2 @ X3 )
      | ~ ( irel @ X2 @ X5 )
      | ~ ( irel @ X1 @ X13 ) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_27,negated_conjecture,
    irel @ esk1_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_28,negated_conjecture,
    ~ ( a @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_29,negated_conjecture,
    ( ~ ( b @ esk3_0 )
    | ~ ( c @ esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_30,plain,
    ! [X1: $i] : ( c @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i,X3: $i,X2: $i] :
      ( ( b @ X1 )
      | ( b @ X2 )
      | ~ ( irel @ esk1_0 @ X1 )
      | ~ ( irel @ X3 @ esk1_0 )
      | ~ ( irel @ X3 @ X2 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

thf(c_0_32,negated_conjecture,
    irel @ esk1_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_33,negated_conjecture,
    ~ ( b @ esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

thf(c_0_34,plain,
    ! [X46: $i] : ( irel @ X46 @ X46 ),
    inference(variable_rename,[status(thm)],[refl_axiom]) ).

thf(c_0_35,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( b @ X1 )
      | ~ ( irel @ X2 @ esk1_0 )
      | ~ ( irel @ X2 @ X1 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

thf(c_0_36,plain,
    ! [X1: $i] : ( irel @ X1 @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i] :
      ( ( b @ X1 )
      | ~ ( irel @ esk1_0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

thf(c_0_38,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYO064^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 09:46:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50  # Version: 3.1.0-ho
% 0.20/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.20/0.50  # Starting full_lambda_8 with 300s (1) cores
% 0.20/0.50  # post_as_ho11 with pid 30307 completed with status 0
% 0.20/0.50  # Result found by post_as_ho11
% 0.20/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.20/0.50  # No SInE strategy applied
% 0.20/0.50  # Search class: HGHNS-FFSF00-SHSSMFNN
% 0.20/0.50  # partial match(1): HGHNF-FFSF00-SHSSMFNN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # new_ho_10 with pid 30310 completed with status 0
% 0.20/0.50  # Result found by new_ho_10
% 0.20/0.50  # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.20/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.50  # Starting post_as_ho11 with 300s (1) cores
% 0.20/0.50  # No SInE strategy applied
% 0.20/0.50  # Search class: HGHNS-FFSF00-SHSSMFNN
% 0.20/0.50  # partial match(1): HGHNF-FFSF00-SHSSMFNN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (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                        : 47
% 0.20/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.50  # Initial clauses                      : 31
% 0.20/0.50  # Removed in clause preprocessing      : 23
% 0.20/0.50  # Initial clauses in saturation        : 8
% 0.20/0.50  # Processed clauses                    : 23
% 0.20/0.50  # ...of these trivial                  : 0
% 0.20/0.50  # ...subsumed                          : 1
% 0.20/0.50  # ...remaining for further processing  : 22
% 0.20/0.50  # Other redundant clauses eliminated   : 0
% 0.20/0.50  # Clauses deleted for lack of memory   : 0
% 0.20/0.50  # Backward-subsumed                    : 1
% 0.20/0.50  # Backward-rewritten                   : 1
% 0.20/0.50  # Generated clauses                    : 18
% 0.20/0.50  # ...of the previous two non-redundant : 15
% 0.20/0.50  # ...aggressively subsumed             : 0
% 0.20/0.50  # Contextual simplify-reflections      : 0
% 0.20/0.50  # Paramodulations                      : 18
% 0.20/0.50  # Factorizations                       : 0
% 0.20/0.50  # NegExts                              : 0
% 0.20/0.50  # Equation resolutions                 : 0
% 0.20/0.50  # Disequality decompositions           : 0
% 0.20/0.50  # Total rewrite steps                  : 4
% 0.20/0.50  # ...of those cached                   : 1
% 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  : 12
% 0.20/0.50  #    Positive orientable unit clauses  : 4
% 0.20/0.50  #    Positive unorientable unit clauses: 0
% 0.20/0.50  #    Negative unit clauses             : 2
% 0.20/0.50  #    Non-unit-clauses                  : 6
% 0.20/0.50  # Current number of unprocessed clauses: 6
% 0.20/0.50  # ...number of literals in the above   : 27
% 0.20/0.50  # Current number of archived formulas  : 0
% 0.20/0.50  # Current number of archived clauses   : 10
% 0.20/0.50  # Clause-clause subsumption calls (NU) : 42
% 0.20/0.50  # Rec. Clause-clause subsumption calls : 25
% 0.20/0.50  # Non-unit clause-clause subsumptions  : 2
% 0.20/0.50  # Unit Clause-clause subsumption calls : 0
% 0.20/0.50  # Rewrite failures with RHS unbound    : 0
% 0.20/0.50  # BW rewrite match attempts            : 5
% 0.20/0.50  # BW rewrite match successes           : 1
% 0.20/0.50  # Condensation attempts                : 23
% 0.20/0.50  # Condensation successes               : 0
% 0.20/0.50  # Termbank termtop insertions          : 2528
% 0.20/0.50  # Search garbage collected termcells   : 589
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.004 s
% 0.20/0.50  # System time              : 0.004 s
% 0.20/0.50  # Total time               : 0.008 s
% 0.20/0.50  # Maximum resident set size: 1912 pages
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.006 s
% 0.20/0.50  # System time              : 0.006 s
% 0.20/0.50  # Total time               : 0.012 s
% 0.20/0.50  # Maximum resident set size: 1756 pages
% 0.20/0.50  % E---3.1 exiting
% 0.20/0.50  % E exiting
%------------------------------------------------------------------------------