TSTP Solution File: PLA053_2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 02:19:22 EDT 2024

% Result   : Theorem 0.15s 0.41s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   33 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :   70 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   77 (  30   ~;  26   |;  11   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  33   !;   3   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    '$ki_world': $tType ).

tff(decl_22,type,
    '$ki_local_world': '$ki_world' ).

tff(decl_23,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(decl_24,type,
    h: ( '$ki_world' * $i ) > $o ).

tff(decl_25,type,
    bomb: ( '$ki_world' * $i ) > $o ).

tff(decl_26,type,
    defused: ( '$ki_world' * $i ) > $o ).

tff(decl_27,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(decl_28,type,
    esk1_0: '$ki_world' ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_2: ( '$ki_world' * $i ) > $i ).

tff(verify,conjecture,
    ! [X1: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X1)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X1,X2)
         => ? [X6] :
              ( '$ki_exists_in_world_$i'(X1,X6)
              & ( ( bomb(X1,X2)
                  & h(X1,X6) )
               => defused(X1,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(ax3,axiom,
    ! [X1: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X1)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X1,X2)
         => ? [X6] :
              ( '$ki_exists_in_world_$i'(X1,X6)
              & ! [X5: '$ki_world'] :
                  ( '$ki_accessible'(X1,X5)
                 => ( ( bomb(X5,X2)
                      & h(X5,X6) )
                   => defused(X5,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff('$ki_exists_in_world_$i_const',axiom,
    ! [X1: '$ki_world',X2] : '$ki_exists_in_world_$i'(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(mrel_reflexive,axiom,
    ! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(c_0_4,negated_conjecture,
    ~ ! [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
       => ! [X2] :
            ( '$ki_exists_in_world_$i'(X1,X2)
           => ? [X6] :
                ( '$ki_exists_in_world_$i'(X1,X6)
                & ( ( bomb(X1,X2)
                    & h(X1,X6) )
                 => defused(X1,X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[verify]) ).

tff(c_0_5,plain,
    ! [X10: '$ki_world',X11,X13: '$ki_world'] :
      ( ( '$ki_exists_in_world_$i'(X10,esk3_2(X10,X11))
        | ~ '$ki_exists_in_world_$i'(X10,X11)
        | ~ '$ki_accessible'('$ki_local_world',X10) )
      & ( ~ '$ki_accessible'(X10,X13)
        | ~ bomb(X13,X11)
        | ~ h(X13,esk3_2(X10,X11))
        | defused(X13,X11)
        | ~ '$ki_exists_in_world_$i'(X10,X11)
        | ~ '$ki_accessible'('$ki_local_world',X10) ) ),
    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)],[ax3])])])])])]) ).

tff(c_0_6,plain,
    ! [X20: '$ki_world',X21] : '$ki_exists_in_world_$i'(X20,X21),
    inference(variable_rename,[status(thm)],['$ki_exists_in_world_$i_const']) ).

tff(c_0_7,negated_conjecture,
    ! [X9] :
      ( '$ki_accessible'('$ki_local_world',esk1_0)
      & '$ki_exists_in_world_$i'(esk1_0,esk2_0)
      & ( bomb(esk1_0,esk2_0)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X9) )
      & ( h(esk1_0,X9)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X9) )
      & ( ~ defused(esk1_0,esk2_0)
        | ~ '$ki_exists_in_world_$i'(esk1_0,X9) ) ),
    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_4])])])])])]) ).

tcf(c_0_8,plain,
    ! [X5: '$ki_world',X2,X1: '$ki_world'] :
      ( defused(X5,X2)
      | ~ '$ki_accessible'(X1,X5)
      | ~ bomb(X5,X2)
      | ~ h(X5,esk3_2(X1,X2))
      | ~ '$ki_exists_in_world_$i'(X1,X2)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

tcf(c_0_9,plain,
    ! [X1: '$ki_world',X2] : '$ki_exists_in_world_$i'(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

tcf(c_0_10,negated_conjecture,
    ! [X2] :
      ( h(esk1_0,X2)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_11,plain,
    ! [X5: '$ki_world',X2,X1: '$ki_world'] :
      ( defused(X1,X2)
      | ~ bomb(X1,X2)
      | ~ h(X1,esk3_2(X5,X2))
      | ~ '$ki_accessible'('$ki_local_world',X5)
      | ~ '$ki_accessible'(X5,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]) ).

tcf(c_0_12,negated_conjecture,
    ! [X2] : h(esk1_0,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_9])]) ).

tff(c_0_13,plain,
    ! [X24: '$ki_world'] : '$ki_accessible'(X24,X24),
    inference(variable_rename,[status(thm)],[mrel_reflexive]) ).

tcf(c_0_14,negated_conjecture,
    ! [X2] :
      ( ~ defused(esk1_0,esk2_0)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_15,negated_conjecture,
    ! [X2,X1: '$ki_world'] :
      ( defused(esk1_0,X2)
      | ~ bomb(esk1_0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X1)
      | ~ '$ki_accessible'(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

tcf(c_0_16,plain,
    ! [X1: '$ki_world'] : '$ki_accessible'(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_17,negated_conjecture,
    '$ki_accessible'('$ki_local_world',esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_18,negated_conjecture,
    ! [X2] :
      ( bomb(esk1_0,esk2_0)
      | ~ '$ki_exists_in_world_$i'(esk1_0,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_19,negated_conjecture,
    ~ defused(esk1_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_9])]) ).

tcf(c_0_20,negated_conjecture,
    ! [X2] :
      ( defused(esk1_0,X2)
      | ~ bomb(esk1_0,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

tcf(c_0_21,negated_conjecture,
    bomb(esk1_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_9])]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n021.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Sat May 18 13:44:38 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.40  Running first-order theorem proving
% 0.15/0.40  Running: /export/starexec/sandbox/solver/bin/eprover --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
% 0.15/0.41  # Version: 3.1.0
% 0.15/0.41  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41  # Starting new_bool_3 with 300s (1) cores
% 0.15/0.41  # Starting new_bool_1 with 300s (1) cores
% 0.15/0.41  # Starting sh5l with 300s (1) cores
% 0.15/0.41  # new_bool_3 with pid 21654 completed with status 0
% 0.15/0.41  # Result found by new_bool_3
% 0.15/0.41  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41  # Starting new_bool_3 with 300s (1) cores
% 0.15/0.41  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.41  # Search class: FHHNS-FFSS21-SFFFFFNN
% 0.15/0.41  # partial match(1): FHHNS-FFSF21-SFFFFFNN
% 0.15/0.41  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.15/0.41  # SAT001_MinMin_p005000_rr_RG with pid 21658 completed with status 0
% 0.15/0.41  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.15/0.41  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41  # Starting new_bool_3 with 300s (1) cores
% 0.15/0.41  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.41  # Search class: FHHNS-FFSS21-SFFFFFNN
% 0.15/0.41  # partial match(1): FHHNS-FFSF21-SFFFFFNN
% 0.15/0.41  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.41  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.15/0.41  # Preprocessing time       : 0.001 s
% 0.15/0.41  # Presaturation interreduction done
% 0.15/0.41  
% 0.15/0.41  # Proof found!
% 0.15/0.41  # SZS status Theorem
% 0.15/0.41  # SZS output start CNFRefutation
% See solution above
% 0.15/0.41  # Parsed axioms                        : 14
% 0.15/0.41  # Removed by relevancy pruning/SinE    : 7
% 0.15/0.41  # Initial clauses                      : 14
% 0.15/0.41  # Removed in clause preprocessing      : 0
% 0.15/0.41  # Initial clauses in saturation        : 14
% 0.15/0.41  # Processed clauses                    : 26
% 0.15/0.41  # ...of these trivial                  : 3
% 0.15/0.41  # ...subsumed                          : 0
% 0.15/0.41  # ...remaining for further processing  : 23
% 0.15/0.41  # Other redundant clauses eliminated   : 0
% 0.15/0.41  # Clauses deleted for lack of memory   : 0
% 0.15/0.41  # Backward-subsumed                    : 1
% 0.15/0.41  # Backward-rewritten                   : 4
% 0.15/0.41  # Generated clauses                    : 4
% 0.15/0.41  # ...of the previous two non-redundant : 5
% 0.15/0.41  # ...aggressively subsumed             : 0
% 0.15/0.41  # Contextual simplify-reflections      : 0
% 0.15/0.41  # Paramodulations                      : 4
% 0.15/0.41  # Factorizations                       : 0
% 0.15/0.41  # NegExts                              : 0
% 0.15/0.41  # Equation resolutions                 : 0
% 0.15/0.41  # Disequality decompositions           : 0
% 0.15/0.41  # Total rewrite steps                  : 14
% 0.15/0.41  # ...of those cached                   : 4
% 0.15/0.41  # Propositional unsat checks           : 0
% 0.15/0.41  #    Propositional check models        : 0
% 0.15/0.41  #    Propositional check unsatisfiable : 0
% 0.15/0.41  #    Propositional clauses             : 0
% 0.15/0.41  #    Propositional clauses after purity: 0
% 0.15/0.41  #    Propositional unsat core size     : 0
% 0.15/0.41  #    Propositional preprocessing time  : 0.000
% 0.15/0.41  #    Propositional encoding time       : 0.000
% 0.15/0.41  #    Propositional solver time         : 0.000
% 0.15/0.41  #    Success case prop preproc time    : 0.000
% 0.15/0.41  #    Success case prop encoding time   : 0.000
% 0.15/0.41  #    Success case prop solver time     : 0.000
% 0.15/0.41  # Current number of processed clauses  : 9
% 0.15/0.41  #    Positive orientable unit clauses  : 5
% 0.15/0.41  #    Positive unorientable unit clauses: 0
% 0.15/0.41  #    Negative unit clauses             : 1
% 0.15/0.41  #    Non-unit-clauses                  : 3
% 0.15/0.41  # Current number of unprocessed clauses: 2
% 0.15/0.41  # ...number of literals in the above   : 7
% 0.15/0.41  # Current number of archived formulas  : 0
% 0.15/0.41  # Current number of archived clauses   : 14
% 0.15/0.41  # Clause-clause subsumption calls (NU) : 3
% 0.15/0.41  # Rec. Clause-clause subsumption calls : 2
% 0.15/0.41  # Non-unit clause-clause subsumptions  : 1
% 0.15/0.41  # Unit Clause-clause subsumption calls : 0
% 0.15/0.42  # Rewrite failures with RHS unbound    : 0
% 0.15/0.42  # BW rewrite match attempts            : 5
% 0.15/0.42  # BW rewrite match successes           : 3
% 0.15/0.42  # Condensation attempts                : 0
% 0.15/0.42  # Condensation successes               : 0
% 0.15/0.42  # Termbank termtop insertions          : 1051
% 0.15/0.42  # Search garbage collected termcells   : 253
% 0.15/0.42  
% 0.15/0.42  # -------------------------------------------------
% 0.15/0.42  # User time                : 0.004 s
% 0.15/0.42  # System time              : 0.002 s
% 0.15/0.42  # Total time               : 0.005 s
% 0.15/0.42  # Maximum resident set size: 1724 pages
% 0.15/0.42  
% 0.15/0.42  # -------------------------------------------------
% 0.15/0.42  # User time                : 0.004 s
% 0.15/0.42  # System time              : 0.004 s
% 0.15/0.42  # Total time               : 0.008 s
% 0.15/0.42  # Maximum resident set size: 1712 pages
% 0.15/0.42  % E---3.1 exiting
% 0.15/0.42  % E exiting
%------------------------------------------------------------------------------