TSTP Solution File: QUA002^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% 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 02:30:20 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   23 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   45 (  37 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   42 (   6   ~;  14   |;   0   &;  21   @)
%                                         (   0 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   30 (  26   ^   4   !;   0   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

thf(decl_29,type,
    addition: $i > $i > $i ).

thf(decl_34,type,
    esk1_0: $i ).

thf(decl_35,type,
    esk2_0: $i ).

thf(decl_36,type,
    esk3_0: $i ).

thf(addition_def,axiom,
    ( addition
    = ( ^ [X1: $i,X7: $i] : ( sup @ ( union @ ( singleton @ X1 ) @ ( singleton @ X7 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',addition_def) ).

thf(union_def,axiom,
    ( union
    = ( ^ [X2: $i > $o,X3: $i > $o,X4: $i] :
          ( ( X2 @ X4 )
          | ( X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',union_def) ).

thf(singleton_def,axiom,
    ( singleton
    = ( ^ [X1: $i,X4: $i] : ( X4 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',singleton_def) ).

thf(addition_comm,conjecture,
    ! [X8: $i,X9: $i] :
      ( ( addition @ X8 @ X9 )
      = ( addition @ X9 @ X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_comm) ).

thf(c_0_4,plain,
    ( addition
    = ( ^ [Z0: $i,Z1: $i] :
          ( sup
          @ ^ [Z2: $i] :
              ( ( Z2 = Z0 )
              | Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[addition_def]) ).

thf(c_0_5,plain,
    ( union
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[union_def]) ).

thf(c_0_6,plain,
    ( singleton
    = ( ^ [Z0: $i,Z1: $i] : Z1 ) ),
    inference(fof_simplification,[status(thm)],[singleton_def]) ).

thf(c_0_7,plain,
    ( addition
    = ( ^ [Z0: $i,Z1: $i] :
          ( sup
          @ ^ [Z2: $i] :
              ( ( Z2 = Z0 )
              | Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ~ ! [X8: $i,X9: $i] :
        ( ( sup
          @ ^ [Z0: $i] :
              ( ( Z0 = X8 )
              | ( Z0 = X9 ) ) )
        = ( sup
          @ ^ [Z0: $i] :
              ( ( Z0 = X9 )
              | ( Z0 = X8 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[addition_comm]),c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ( ( sup
      @ ^ [Z0: $i] :
          ( ( Z0 = esk1_0 )
          | ( Z0 = esk2_0 ) ) )
   != ( sup
      @ ^ [Z0: $i] :
          ( ( Z0 = esk2_0 )
          | ( Z0 = esk1_0 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

thf(c_0_10,negated_conjecture,
    ( ( sup
      @ ^ [Z0: $i] :
          ( ( Z0 = esk1_0 )
          | ( Z0 = esk2_0 ) ) )
   != ( sup
      @ ^ [Z0: $i] :
          ( ( Z0 = esk2_0 )
          | ( Z0 = esk1_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_11,negated_conjecture,
    ( ( ^ [Z0: $i] :
          ( ( Z0 = esk1_0 )
          | ( Z0 = esk2_0 ) ) )
   != ( ^ [Z0: $i] :
          ( ( Z0 = esk2_0 )
          | ( Z0 = esk1_0 ) ) ) ),
    inference(ext_eqres,[status(thm)],[c_0_10]) ).

thf(c_0_12,negated_conjecture,
    ( ( ( esk3_0 = esk1_0 )
      | ( esk3_0 = esk2_0 ) )
  <~> ( ( esk3_0 = esk2_0 )
      | ( esk3_0 = esk1_0 ) ) ),
    inference(neg_ext,[status(thm)],[c_0_11]) ).

thf(c_0_13,negated_conjecture,
    esk1_0 != esk3_0,
    inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]) ).

thf(c_0_14,negated_conjecture,
    esk2_0 != esk3_0,
    inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]) ).

thf(c_0_15,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_12])]),c_0_13]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.08  % Problem    : QUA002^1 : TPTP v8.2.0. Released v4.1.0.
% 0.05/0.09  % Command    : run_E %s %d THM
% 0.08/0.28  % Computer : n013.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Mon May 20 13:37:52 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.13/0.37  Running higher-order theorem proving
% 0.13/0.37  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
% 0.13/0.39  # Version: 3.1.0-ho
% 0.13/0.39  # Preprocessing class: HSSSSMSSSLSCHFN.
% 0.13/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.39  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.13/0.39  # Starting sh2lt with 300s (1) cores
% 0.13/0.39  # Starting sh5l with 300s (1) cores
% 0.13/0.39  # Starting pre_casc_6 with 300s (1) cores
% 0.13/0.39  # sh5l with pid 26891 completed with status 0
% 0.13/0.39  # Result found by sh5l
% 0.13/0.39  # Preprocessing class: HSSSSMSSSLSCHFN.
% 0.13/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.39  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.13/0.39  # Starting sh2lt with 300s (1) cores
% 0.13/0.39  # Starting sh5l with 300s (1) cores
% 0.13/0.39  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.39  # Search class: HHUSM-FFSF21-DHFFMFBN
% 0.13/0.39  # partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.13/0.39  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.39  # Starting new_ho_10 with 181s (1) cores
% 0.13/0.39  # new_ho_10 with pid 26896 completed with status 9
% 0.13/0.39  # Starting sh5l with 31s (1) cores
% 0.13/0.39  # sh5l with pid 26902 completed with status 0
% 0.13/0.39  # Result found by sh5l
% 0.13/0.39  # Preprocessing class: HSSSSMSSSLSCHFN.
% 0.13/0.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.39  # Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.13/0.39  # Starting sh2lt with 300s (1) cores
% 0.13/0.39  # Starting sh5l with 300s (1) cores
% 0.13/0.39  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.39  # Search class: HHUSM-FFSF21-DHFFMFBN
% 0.13/0.39  # partial match(3): HHUSM-FFSF21-MSFSMFBN
% 0.13/0.39  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.39  # Starting new_ho_10 with 181s (1) cores
% 0.13/0.39  # new_ho_10 with pid 26896 completed with status 9
% 0.13/0.39  # Starting sh5l with 31s (1) cores
% 0.13/0.39  # Preprocessing time       : 0.001 s
% 0.13/0.39  # Presaturation interreduction done
% 0.13/0.39  
% 0.13/0.39  # Proof found!
% 0.13/0.39  # SZS status Theorem
% 0.13/0.39  # SZS output start CNFRefutation
% See solution above
% 0.13/0.39  # Parsed axioms                        : 27
% 0.13/0.39  # Removed by relevancy pruning/SinE    : 14
% 0.13/0.39  # Initial clauses                      : 8
% 0.13/0.39  # Removed in clause preprocessing      : 0
% 0.13/0.39  # Initial clauses in saturation        : 8
% 0.13/0.39  # Processed clauses                    : 18
% 0.13/0.39  # ...of these trivial                  : 0
% 0.13/0.39  # ...subsumed                          : 0
% 0.13/0.39  # ...remaining for further processing  : 17
% 0.13/0.39  # Other redundant clauses eliminated   : 2
% 0.13/0.39  # Clauses deleted for lack of memory   : 0
% 0.13/0.39  # Backward-subsumed                    : 0
% 0.13/0.39  # Backward-rewritten                   : 0
% 0.13/0.39  # Generated clauses                    : 25
% 0.13/0.39  # ...of the previous two non-redundant : 23
% 0.13/0.39  # ...aggressively subsumed             : 0
% 0.13/0.39  # Contextual simplify-reflections      : 0
% 0.13/0.39  # Paramodulations                      : 3
% 0.13/0.39  # Factorizations                       : 0
% 0.13/0.39  # NegExts                              : 1
% 0.13/0.39  # Equation resolutions                 : 2
% 0.13/0.39  # Disequality decompositions           : 0
% 0.13/0.39  # Total rewrite steps                  : 0
% 0.13/0.39  # ...of those cached                   : 0
% 0.13/0.39  # Propositional unsat checks           : 0
% 0.13/0.39  #    Propositional check models        : 0
% 0.13/0.39  #    Propositional check unsatisfiable : 0
% 0.13/0.39  #    Propositional clauses             : 0
% 0.13/0.39  #    Propositional clauses after purity: 0
% 0.13/0.39  #    Propositional unsat core size     : 0
% 0.13/0.39  #    Propositional preprocessing time  : 0.000
% 0.13/0.39  #    Propositional encoding time       : 0.000
% 0.13/0.39  #    Propositional solver time         : 0.000
% 0.13/0.39  #    Success case prop preproc time    : 0.000
% 0.13/0.39  #    Success case prop encoding time   : 0.000
% 0.13/0.39  #    Success case prop solver time     : 0.000
% 0.13/0.39  # Current number of processed clauses  : 8
% 0.13/0.39  #    Positive orientable unit clauses  : 2
% 0.13/0.39  #    Positive unorientable unit clauses: 2
% 0.13/0.39  #    Negative unit clauses             : 4
% 0.13/0.39  #    Non-unit-clauses                  : 0
% 0.13/0.39  # Current number of unprocessed clauses: 21
% 0.13/0.39  # ...number of literals in the above   : 36
% 0.13/0.39  # Current number of archived formulas  : 0
% 0.13/0.39  # Current number of archived clauses   : 9
% 0.13/0.39  # Clause-clause subsumption calls (NU) : 0
% 0.13/0.39  # Rec. Clause-clause subsumption calls : 0
% 0.13/0.39  # Non-unit clause-clause subsumptions  : 0
% 0.13/0.39  # Unit Clause-clause subsumption calls : 5
% 0.13/0.39  # Rewrite failures with RHS unbound    : 0
% 0.13/0.39  # BW rewrite match attempts            : 12
% 0.13/0.39  # BW rewrite match successes           : 8
% 0.13/0.39  # Condensation attempts                : 18
% 0.13/0.39  # Condensation successes               : 0
% 0.13/0.39  # Termbank termtop insertions          : 3225
% 0.13/0.39  # Search garbage collected termcells   : 203
% 0.13/0.39  
% 0.13/0.39  # -------------------------------------------------
% 0.13/0.39  # User time                : 0.005 s
% 0.13/0.39  # System time              : 0.004 s
% 0.13/0.39  # Total time               : 0.009 s
% 0.13/0.39  # Maximum resident set size: 1912 pages
% 0.13/0.39  
% 0.13/0.39  # -------------------------------------------------
% 0.13/0.39  # User time                : 0.006 s
% 0.13/0.39  # System time              : 0.007 s
% 0.13/0.39  # Total time               : 0.013 s
% 0.13/0.39  # Maximum resident set size: 1760 pages
% 0.13/0.39  % E---3.1 exiting
% 0.13/0.39  % E exiting
%------------------------------------------------------------------------------