TSTP Solution File: SEU472^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 03:27:31 EDT 2024

% Result   : Theorem 0.17s 0.44s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   36 (  20 unt;  12 typ;   0 def)
%            Number of atoms       :   68 (  25 equ;   0 cnn)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  278 (  13   ~;  20   |;  27   &; 186   @)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  114 ( 114   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  118 (  37   ^  81   !;   0   ?; 118   :)

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

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

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

thf(decl_33,type,
    sc: ( $i > $i > $o ) > $i > $i > $o ).

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

thf(decl_35,type,
    tc: ( $i > $i > $o ) > $i > $i > $o ).

thf(decl_37,type,
    trsc: ( $i > $i > $o ) > $i > $i > $o ).

thf(decl_51,type,
    epred1_0: $i > $i > $o ).

thf(decl_52,type,
    esk1_0: $i ).

thf(decl_53,type,
    esk2_0: $i ).

thf(decl_54,type,
    epred2_0: $i > $i > $o ).

thf(decl_55,type,
    epred3_0: $i > $i > $o ).

thf(transitive_closure,axiom,
    ( tc
    = ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ( trans @ X2 )
            & ( subrel @ X1 @ X2 ) )
         => ( X2 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_closure) ).

thf(subrel,axiom,
    ( subrel
    = ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( X1 @ X3 @ X4 )
         => ( X2 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).

thf(transitive,axiom,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( X1 @ X3 @ X4 )
            & ( X1 @ X4 @ X6 ) )
         => ( X1 @ X3 @ X6 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).

thf(inflationary,axiom,
    ( infl
    = ( ^ [X5: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X5 @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',inflationary) ).

thf(transitive_reflexive_symmetric_closure,axiom,
    ( trsc
    = ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_reflexive_symmetric_closure) ).

thf(reflexive_closure,axiom,
    ( rc
    = ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
          ( ( X3 = X4 )
          | ( X1 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).

thf(symmetric_closure,axiom,
    ( sc
    = ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
          ( ( X1 @ X4 @ X3 )
          | ( X1 @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).

thf(transitive_reflexive_symmetric_closure_op_is_inflationary,conjecture,
    infl @ trsc,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_inflationary) ).

thf(c_0_8,plain,
    ( tc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ! [X15: $i,X16: $i,X17: $i] :
                ( ( ( X2 @ X15 @ X16 )
                  & ( X2 @ X16 @ X17 ) )
               => ( X2 @ X15 @ X17 ) )
            & ! [X18: $i,X19: $i] :
                ( ( Z0 @ X18 @ X19 )
               => ( X2 @ X18 @ X19 ) ) )
         => ( X2 @ Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive_closure]) ).

thf(c_0_9,plain,
    ( subrel
    = ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ( Z0 @ X3 @ X4 )
         => ( Z1 @ X3 @ X4 ) ) ) ),
    inference(fof_simplification,[status(thm)],[subrel]) ).

thf(c_0_10,plain,
    ( trans
    = ( ^ [Z0: $i > $i > $o] :
        ! [X3: $i,X4: $i,X6: $i] :
          ( ( ( Z0 @ X3 @ X4 )
            & ( Z0 @ X4 @ X6 ) )
         => ( Z0 @ X3 @ X6 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive]) ).

thf(c_0_11,plain,
    ( infl
    = ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X1: $i > $i > $o,X9: $i,X10: $i] :
          ( ( X1 @ X9 @ X10 )
         => ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inflationary]) ).

thf(c_0_12,plain,
    ( trsc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
          ( Z2
          | ! [X26: $i > $i > $o] :
              ( ( ! [X27: $i,X28: $i,X29: $i] :
                    ( ( ( X26 @ X27 @ X28 )
                      & ( X26 @ X28 @ X29 ) )
                   => ( X26 @ X27 @ X29 ) )
                & ! [X30: $i,X31: $i] :
                    ( ( Z0 @ X30 @ X31 )
                   => ( X26 @ X30 @ X31 ) ) )
             => ( X26 @ Z2 @ Z1 ) )
          | ( Z1 = Z2 )
          | ! [X26: $i > $i > $o] :
              ( ( ! [X27: $i,X28: $i,X29: $i] :
                    ( ( ( X26 @ X27 @ X28 )
                      & ( X26 @ X28 @ X29 ) )
                   => ( X26 @ X27 @ X29 ) )
                & ! [X30: $i,X31: $i] :
                    ( ( Z0 @ X30 @ X31 )
                   => ( X26 @ X30 @ X31 ) ) )
             => ( X26 @ Z1 @ Z2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitive_reflexive_symmetric_closure]) ).

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

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

thf(c_0_15,plain,
    ( tc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
        ! [X2: $i > $i > $o] :
          ( ( ! [X15: $i,X16: $i,X17: $i] :
                ( ( ( X2 @ X15 @ X16 )
                  & ( X2 @ X16 @ X17 ) )
               => ( X2 @ X15 @ X17 ) )
            & ! [X18: $i,X19: $i] :
                ( ( Z0 @ X18 @ X19 )
               => ( X2 @ X18 @ X19 ) ) )
         => ( X2 @ Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).

thf(c_0_16,plain,
    ( infl
    = ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X1: $i > $i > $o,X9: $i,X10: $i] :
          ( ( X1 @ X9 @ X10 )
         => ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_11,c_0_9]) ).

thf(c_0_17,plain,
    ( trsc
    = ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
          ( Z2
          | ! [X26: $i > $i > $o] :
              ( ( ! [X27: $i,X28: $i,X29: $i] :
                    ( ( ( X26 @ X27 @ X28 )
                      & ( X26 @ X28 @ X29 ) )
                   => ( X26 @ X27 @ X29 ) )
                & ! [X30: $i,X31: $i] :
                    ( ( Z0 @ X30 @ X31 )
                   => ( X26 @ X30 @ X31 ) ) )
             => ( X26 @ Z2 @ Z1 ) )
          | ( Z1 = Z2 )
          | ! [X26: $i > $i > $o] :
              ( ( ! [X27: $i,X28: $i,X29: $i] :
                    ( ( ( X26 @ X27 @ X28 )
                      & ( X26 @ X28 @ X29 ) )
                   => ( X26 @ X27 @ X29 ) )
                & ! [X30: $i,X31: $i] :
                    ( ( Z0 @ X30 @ X31 )
                   => ( X26 @ X30 @ X31 ) ) )
             => ( X26 @ Z1 @ Z2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).

thf(c_0_18,negated_conjecture,
    ~ ! [X169: $i > $i > $o,X170: $i,X171: $i] :
        ( ( X169 @ X170 @ X171 )
       => ( ( X171 = X170 )
          | ! [X157: $i > $i > $o] :
              ( ( ! [X158: $i,X159: $i,X160: $i] :
                    ( ( ( X157 @ X158 @ X159 )
                      & ( X157 @ X159 @ X160 ) )
                   => ( X157 @ X158 @ X160 ) )
                & ! [X161: $i,X162: $i] :
                    ( ( X169 @ X161 @ X162 )
                   => ( X157 @ X161 @ X162 ) ) )
             => ( X157 @ X171 @ X170 ) )
          | ( X170 = X171 )
          | ! [X163: $i > $i > $o] :
              ( ( ! [X164: $i,X165: $i,X166: $i] :
                    ( ( ( X163 @ X164 @ X165 )
                      & ( X163 @ X165 @ X166 ) )
                   => ( X163 @ X164 @ X166 ) )
                & ! [X167: $i,X168: $i] :
                    ( ( X169 @ X167 @ X168 )
                   => ( X163 @ X167 @ X168 ) ) )
             => ( X163 @ X170 @ X171 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[transitive_reflexive_symmetric_closure_op_is_inflationary]),c_0_16]),c_0_17]) ).

thf(c_0_19,negated_conjecture,
    ! [X176: $i,X177: $i,X178: $i,X179: $i,X180: $i,X182: $i,X183: $i,X184: $i,X185: $i,X186: $i] :
      ( ( epred1_0 @ esk1_0 @ esk2_0 )
      & ( esk2_0 != esk1_0 )
      & ( ~ ( epred2_0 @ X176 @ X177 )
        | ~ ( epred2_0 @ X177 @ X178 )
        | ( epred2_0 @ X176 @ X178 ) )
      & ( ~ ( epred1_0 @ X179 @ X180 )
        | ( epred2_0 @ X179 @ X180 ) )
      & ~ ( epred2_0 @ esk2_0 @ esk1_0 )
      & ( esk1_0 != esk2_0 )
      & ( ~ ( epred3_0 @ X182 @ X183 )
        | ~ ( epred3_0 @ X183 @ X184 )
        | ( epred3_0 @ X182 @ X184 ) )
      & ( ~ ( epred1_0 @ X185 @ X186 )
        | ( epred3_0 @ X185 @ X186 ) )
      & ~ ( epred3_0 @ esk1_0 @ esk2_0 ) ),
    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_18])])])])]) ).

thf(c_0_20,negated_conjecture,
    ! [X3: $i,X4: $i] :
      ( ( epred3_0 @ X3 @ X4 )
      | ~ ( epred1_0 @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_21,negated_conjecture,
    epred1_0 @ esk1_0 @ esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_22,negated_conjecture,
    ~ ( epred3_0 @ esk1_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_23,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n013.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sun May 19 18:10:23 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.17/0.42  Running higher-order theorem proving
% 0.17/0.42  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
% 0.17/0.44  # Version: 3.1.0-ho
% 0.17/0.44  # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44  # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44  # Starting ho_unfolding_1 with 300s (1) cores
% 0.17/0.44  # post_as_ho11 with pid 14001 completed with status 0
% 0.17/0.44  # Result found by post_as_ho11
% 0.17/0.44  # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44  # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44  # No SInE strategy applied
% 0.17/0.44  # Search class: HHUSF-FFSF00-SHHSMFNN
% 0.17/0.44  # partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.17/0.44  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44  # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44  # new_ho_10 with pid 14005 completed with status 0
% 0.17/0.44  # Result found by new_ho_10
% 0.17/0.44  # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44  # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44  # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44  # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44  # No SInE strategy applied
% 0.17/0.44  # Search class: HHUSF-FFSF00-SHHSMFNN
% 0.17/0.44  # partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.17/0.44  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44  # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44  # Preprocessing time       : 0.001 s
% 0.17/0.44  # Presaturation interreduction done
% 0.17/0.44  
% 0.17/0.44  # Proof found!
% 0.17/0.44  # SZS status Theorem
% 0.17/0.44  # SZS output start CNFRefutation
% See solution above
% 0.17/0.44  # Parsed axioms                        : 59
% 0.17/0.44  # Removed by relevancy pruning/SinE    : 0
% 0.17/0.44  # Initial clauses                      : 38
% 0.17/0.44  # Removed in clause preprocessing      : 29
% 0.17/0.44  # Initial clauses in saturation        : 9
% 0.17/0.44  # Processed clauses                    : 15
% 0.17/0.44  # ...of these trivial                  : 0
% 0.17/0.44  # ...subsumed                          : 1
% 0.17/0.44  # ...remaining for further processing  : 14
% 0.17/0.44  # Other redundant clauses eliminated   : 0
% 0.17/0.44  # Clauses deleted for lack of memory   : 0
% 0.17/0.44  # Backward-subsumed                    : 0
% 0.17/0.44  # Backward-rewritten                   : 0
% 0.17/0.44  # Generated clauses                    : 2
% 0.17/0.44  # ...of the previous two non-redundant : 1
% 0.17/0.44  # ...aggressively subsumed             : 0
% 0.17/0.44  # Contextual simplify-reflections      : 0
% 0.17/0.44  # Paramodulations                      : 2
% 0.17/0.44  # Factorizations                       : 0
% 0.17/0.44  # NegExts                              : 0
% 0.17/0.44  # Equation resolutions                 : 0
% 0.17/0.44  # Disequality decompositions           : 0
% 0.17/0.44  # Total rewrite steps                  : 0
% 0.17/0.44  # ...of those cached                   : 0
% 0.17/0.44  # Propositional unsat checks           : 0
% 0.17/0.44  #    Propositional check models        : 0
% 0.17/0.44  #    Propositional check unsatisfiable : 0
% 0.17/0.44  #    Propositional clauses             : 0
% 0.17/0.44  #    Propositional clauses after purity: 0
% 0.17/0.44  #    Propositional unsat core size     : 0
% 0.17/0.44  #    Propositional preprocessing time  : 0.000
% 0.17/0.44  #    Propositional encoding time       : 0.000
% 0.17/0.44  #    Propositional solver time         : 0.000
% 0.17/0.44  #    Success case prop preproc time    : 0.000
% 0.17/0.44  #    Success case prop encoding time   : 0.000
% 0.17/0.44  #    Success case prop solver time     : 0.000
% 0.17/0.44  # Current number of processed clauses  : 6
% 0.17/0.44  #    Positive orientable unit clauses  : 1
% 0.17/0.44  #    Positive unorientable unit clauses: 0
% 0.17/0.44  #    Negative unit clauses             : 3
% 0.17/0.44  #    Non-unit-clauses                  : 2
% 0.17/0.44  # Current number of unprocessed clauses: 3
% 0.17/0.44  # ...number of literals in the above   : 7
% 0.17/0.44  # Current number of archived formulas  : 0
% 0.17/0.44  # Current number of archived clauses   : 8
% 0.17/0.44  # Clause-clause subsumption calls (NU) : 2
% 0.17/0.44  # Rec. Clause-clause subsumption calls : 2
% 0.17/0.44  # Non-unit clause-clause subsumptions  : 0
% 0.17/0.44  # Unit Clause-clause subsumption calls : 0
% 0.17/0.44  # Rewrite failures with RHS unbound    : 0
% 0.17/0.44  # BW rewrite match attempts            : 0
% 0.17/0.44  # BW rewrite match successes           : 0
% 0.17/0.44  # Condensation attempts                : 15
% 0.17/0.44  # Condensation successes               : 0
% 0.17/0.44  # Termbank termtop insertions          : 3447
% 0.17/0.44  # Search garbage collected termcells   : 993
% 0.17/0.44  
% 0.17/0.44  # -------------------------------------------------
% 0.17/0.44  # User time                : 0.002 s
% 0.17/0.44  # System time              : 0.004 s
% 0.17/0.44  # Total time               : 0.006 s
% 0.17/0.44  # Maximum resident set size: 2156 pages
% 0.17/0.44  
% 0.17/0.44  # -------------------------------------------------
% 0.17/0.44  # User time                : 0.005 s
% 0.17/0.44  # System time              : 0.005 s
% 0.17/0.44  # Total time               : 0.010 s
% 0.17/0.44  # Maximum resident set size: 1788 pages
% 0.17/0.44  % E---3.1 exiting
% 0.17/0.44  % E exiting
%------------------------------------------------------------------------------