TSTP Solution File: SYO396^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO396^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n014.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 08:45:52 EDT 2024

% Result   : Theorem 0.20s 0.48s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   46 (  24 unt;  13 typ;   0 def)
%            Number of atoms       :  116 (  20 equ;   0 cnn)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  253 (  64   ~;  46   |;   8   &; 135   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  65   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   61 (  45   ^  16   !;   0   ?;  61   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_24,type,
    mnot: ( $i > $o ) > $i > $o ).

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

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

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

thf(decl_29,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(decl_49,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_53,type,
    rel_k: $i > $i > $o ).

thf(decl_54,type,
    mbox_k: ( $i > $o ) > $i > $o ).

thf(decl_55,type,
    mdia_k: ( $i > $o ) > $i > $o ).

thf(decl_56,type,
    p: $i > $o ).

thf(decl_57,type,
    esk1_0: $i ).

thf(decl_58,type,
    esk2_0: $i ).

thf(decl_59,type,
    esk3_0: $i ).

thf(mand,axiom,
    ( mand
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X6: $i > $o,X3: $i] :
          ~ ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
          ( ( X6 @ X3 )
          | ( X7 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).

thf(mequiv,axiom,
    ( mequiv
    = ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).

thf(mdia_k,axiom,
    ( mdia_k
    = ( ^ [X6: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X6 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mdia_k) ).

thf(mbox_k,axiom,
    ( mbox_k
    = ( ^ [X6: $i > $o,X3: $i] :
        ! [X14: $i] :
          ( ~ ( rel_k @ X3 @ X14 )
          | ( X6 @ X14 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mbox_k) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X6: $i > $o] :
        ! [X3: $i] : ( X6 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).

thf(prove,conjecture,
    mvalid @ ( mequiv @ ( mbox_k @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia_k @ p ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(c_0_9,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mand]) ).

thf(c_0_10,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

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

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

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

thf(c_0_14,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

thf(c_0_15,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_12,c_0_10]),c_0_11]) ).

thf(c_0_16,plain,
    ( mdia_k
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ! [X21: $i] :
              ( ~ ( rel_k @ Z1 @ X21 )
              | ~ ( Z0 @ X21 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mdia_k]) ).

thf(c_0_17,plain,
    ( mbox_k
    = ( ^ [Z0: $i > $o,Z1: $i] :
        ! [X14: $i] :
          ( ~ ( rel_k @ Z1 @ X14 )
          | ( Z0 @ X14 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mbox_k]) ).

thf(c_0_18,plain,
    ( mequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( ~ ( Z0 @ Z2 )
                | ( Z1 @ Z2 ) )
            | ~ ( ~ ( Z1 @ Z2 )
                | ( Z0 @ Z2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

thf(c_0_19,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_20,plain,
    ( mdia_k
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ! [X21: $i] :
              ( ~ ( rel_k @ Z1 @ X21 )
              | ~ ( Z0 @ X21 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_10]),c_0_17]) ).

thf(c_0_21,negated_conjecture,
    ~ ! [X24: $i] :
        ~ ( ~ ( ~ ! [X22: $i] :
                    ( ~ ( rel_k @ X24 @ X22 )
                    | ~ ( p @ X22 ) )
              | ~ ~ ! [X23: $i] :
                      ( ~ ( rel_k @ X24 @ X23 )
                      | ~ ( p @ X23 ) ) )
          | ~ ( ~ ~ ~ ! [X23: $i] :
                        ( ~ ( rel_k @ X24 @ X23 )
                        | ~ ( p @ X23 ) )
              | ! [X22: $i] :
                  ( ~ ( rel_k @ X24 @ X22 )
                  | ~ ( p @ X22 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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)],[prove]),c_0_10]),c_0_15]),c_0_18]),c_0_19]),c_0_17]),c_0_20])]) ).

thf(c_0_22,negated_conjecture,
    ! [X26: $i,X28: $i] :
      ( ( ~ ( rel_k @ esk1_0 @ X28 )
        | ~ ( p @ X28 )
        | ~ ( rel_k @ esk1_0 @ X26 )
        | ~ ( p @ X26 ) )
      & ( ( rel_k @ esk1_0 @ esk3_0 )
        | ~ ( rel_k @ esk1_0 @ X26 )
        | ~ ( p @ X26 ) )
      & ( ( p @ esk3_0 )
        | ~ ( rel_k @ esk1_0 @ X26 )
        | ~ ( p @ X26 ) )
      & ( ~ ( rel_k @ esk1_0 @ X28 )
        | ~ ( p @ X28 )
        | ( rel_k @ esk1_0 @ esk2_0 ) )
      & ( ( rel_k @ esk1_0 @ esk3_0 )
        | ( rel_k @ esk1_0 @ esk2_0 ) )
      & ( ( p @ esk3_0 )
        | ( rel_k @ esk1_0 @ esk2_0 ) )
      & ( ~ ( rel_k @ esk1_0 @ X28 )
        | ~ ( p @ X28 )
        | ( p @ esk2_0 ) )
      & ( ( rel_k @ 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_21])])])])])]) ).

thf(c_0_23,negated_conjecture,
    ! [X3: $i,X14: $i] :
      ( ~ ( rel_k @ esk1_0 @ X3 )
      | ~ ( p @ X3 )
      | ~ ( rel_k @ esk1_0 @ X14 )
      | ~ ( p @ X14 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_24,negated_conjecture,
    ! [X3: $i] :
      ( ~ ( rel_k @ esk1_0 @ X3 )
      | ~ ( p @ X3 ) ),
    inference(condense,[status(thm)],[c_0_23]) ).

thf(c_0_25,negated_conjecture,
    ( ( rel_k @ esk1_0 @ esk3_0 )
    | ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_26,negated_conjecture,
    ( ( p @ esk3_0 )
    | ( p @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_27,negated_conjecture,
    ( ( rel_k @ esk1_0 @ esk3_0 )
    | ( rel_k @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_28,negated_conjecture,
    p @ esk2_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

thf(c_0_29,negated_conjecture,
    ( ( p @ esk3_0 )
    | ( rel_k @ esk1_0 @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_30,negated_conjecture,
    rel_k @ esk1_0 @ esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_27]),c_0_28])]) ).

thf(c_0_31,negated_conjecture,
    p @ esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_29]),c_0_28])]) ).

thf(c_0_32,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO396^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n014.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon May 20 09:39:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.46  Running higher-order theorem proving
% 0.20/0.46  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
% 0.20/0.48  # Version: 3.1.0-ho
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.48  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.48  # Starting almost_fo_3_lam with 300s (1) cores
% 0.20/0.48  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.48  # ehoh_best2_full_lfho with pid 14314 completed with status 0
% 0.20/0.48  # Result found by ehoh_best2_full_lfho
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.48  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HGHNF-FFSS00-SHSSMFNN
% 0.20/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.48  # new_ho_10 with pid 14318 completed with status 0
% 0.20/0.48  # Result found by new_ho_10
% 0.20/0.48  # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.20/0.48  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.20/0.48  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.48  # No SInE strategy applied
% 0.20/0.48  # Search class: HGHNF-FFSS00-SHSSMFNN
% 0.20/0.48  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.48  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.48  # Preprocessing time       : 0.001 s
% 0.20/0.48  # Presaturation interreduction done
% 0.20/0.48  
% 0.20/0.48  # Proof found!
% 0.20/0.48  # SZS status Theorem
% 0.20/0.48  # SZS output start CNFRefutation
% See solution above
% 0.20/0.48  # Parsed axioms                        : 70
% 0.20/0.48  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.48  # Initial clauses                      : 45
% 0.20/0.48  # Removed in clause preprocessing      : 36
% 0.20/0.48  # Initial clauses in saturation        : 9
% 0.20/0.48  # Processed clauses                    : 17
% 0.20/0.48  # ...of these trivial                  : 0
% 0.20/0.48  # ...subsumed                          : 0
% 0.20/0.48  # ...remaining for further processing  : 17
% 0.20/0.48  # Other redundant clauses eliminated   : 0
% 0.20/0.48  # Clauses deleted for lack of memory   : 0
% 0.20/0.48  # Backward-subsumed                    : 5
% 0.20/0.48  # Backward-rewritten                   : 3
% 0.20/0.48  # Generated clauses                    : 4
% 0.20/0.48  # ...of the previous two non-redundant : 3
% 0.20/0.48  # ...aggressively subsumed             : 0
% 0.20/0.48  # Contextual simplify-reflections      : 1
% 0.20/0.48  # Paramodulations                      : 4
% 0.20/0.48  # Factorizations                       : 0
% 0.20/0.48  # NegExts                              : 0
% 0.20/0.48  # Equation resolutions                 : 0
% 0.20/0.48  # Disequality decompositions           : 0
% 0.20/0.48  # Total rewrite steps                  : 6
% 0.20/0.48  # ...of those cached                   : 3
% 0.20/0.48  # Propositional unsat checks           : 0
% 0.20/0.48  #    Propositional check models        : 0
% 0.20/0.48  #    Propositional check unsatisfiable : 0
% 0.20/0.48  #    Propositional clauses             : 0
% 0.20/0.48  #    Propositional clauses after purity: 0
% 0.20/0.48  #    Propositional unsat core size     : 0
% 0.20/0.48  #    Propositional preprocessing time  : 0.000
% 0.20/0.48  #    Propositional encoding time       : 0.000
% 0.20/0.48  #    Propositional solver time         : 0.000
% 0.20/0.48  #    Success case prop preproc time    : 0.000
% 0.20/0.48  #    Success case prop encoding time   : 0.000
% 0.20/0.48  #    Success case prop solver time     : 0.000
% 0.20/0.48  # Current number of processed clauses  : 4
% 0.20/0.48  #    Positive orientable unit clauses  : 3
% 0.20/0.48  #    Positive unorientable unit clauses: 0
% 0.20/0.48  #    Negative unit clauses             : 0
% 0.20/0.48  #    Non-unit-clauses                  : 1
% 0.20/0.48  # Current number of unprocessed clauses: 0
% 0.20/0.48  # ...number of literals in the above   : 0
% 0.20/0.48  # Current number of archived formulas  : 0
% 0.20/0.48  # Current number of archived clauses   : 13
% 0.20/0.48  # Clause-clause subsumption calls (NU) : 8
% 0.20/0.48  # Rec. Clause-clause subsumption calls : 8
% 0.20/0.48  # Non-unit clause-clause subsumptions  : 6
% 0.20/0.48  # Unit Clause-clause subsumption calls : 1
% 0.20/0.48  # Rewrite failures with RHS unbound    : 0
% 0.20/0.48  # BW rewrite match attempts            : 3
% 0.20/0.48  # BW rewrite match successes           : 3
% 0.20/0.48  # Condensation attempts                : 17
% 0.20/0.48  # Condensation successes               : 1
% 0.20/0.48  # Termbank termtop insertions          : 2549
% 0.20/0.48  # Search garbage collected termcells   : 501
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.007 s
% 0.20/0.48  # System time              : 0.000 s
% 0.20/0.48  # Total time               : 0.007 s
% 0.20/0.48  # Maximum resident set size: 1920 pages
% 0.20/0.48  
% 0.20/0.48  # -------------------------------------------------
% 0.20/0.48  # User time                : 0.011 s
% 0.20/0.48  # System time              : 0.001 s
% 0.20/0.48  # Total time               : 0.012 s
% 0.20/0.48  # Maximum resident set size: 1800 pages
% 0.20/0.48  % E---3.1 exiting
% 0.20/0.48  % E exiting
%------------------------------------------------------------------------------