TSTP Solution File: NUM741^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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 : Sat May  4 08:56:31 EDT 2024

% Result   : Theorem 0.58s 0.55s
% Output   : CNFRefutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   40 (  19 unt;   9 typ;   0 def)
%            Number of atoms       :   46 (   8 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  326 (  15   ~;  12   |;   0   &; 296   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   63 (   0   ^  63   !;   0   ?;  63   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    frac: $tType ).

thf(decl_sort2,type,
    nat: $tType ).

thf(decl_22,type,
    x: frac ).

thf(decl_23,type,
    y: frac ).

thf(decl_24,type,
    z: frac ).

thf(decl_25,type,
    less: nat > nat > $o ).

thf(decl_26,type,
    ts: nat > nat > nat ).

thf(decl_27,type,
    num: frac > nat ).

thf(decl_28,type,
    den: frac > nat ).

thf(satz33c,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X3 ) )
     => ( less @ X1 @ X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',satz33c) ).

thf(satz29,axiom,
    ! [X1: nat,X2: nat] :
      ( ( ts @ X1 @ X2 )
      = ( ts @ X2 @ X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',satz29) ).

thf(satz31,axiom,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ts @ ( ts @ X1 @ X2 ) @ X3 )
      = ( ts @ X1 @ ( ts @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',satz31) ).

thf(satz34a,axiom,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( ( less @ X1 @ X2 )
     => ( ( less @ X3 @ X4 )
       => ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',satz34a) ).

thf(l,axiom,
    less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',l) ).

thf(k,axiom,
    less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',k) ).

thf(satz50,conjecture,
    less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bopbGG6Duz/E---3.1_8909.p',satz50) ).

thf(c_0_7,plain,
    ! [X17: nat,X18: nat,X19: nat] :
      ( ~ ( less @ ( ts @ X17 @ X19 ) @ ( ts @ X18 @ X19 ) )
      | ( less @ X17 @ X18 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz33c])])]) ).

thf(c_0_8,plain,
    ! [X24: nat,X25: nat] :
      ( ( ts @ X24 @ X25 )
      = ( ts @ X25 @ X24 ) ),
    inference(variable_rename,[status(thm)],[satz29]) ).

thf(c_0_9,plain,
    ! [X1: nat,X3: nat,X2: nat] :
      ( ( less @ X1 @ X3 )
      | ~ ( less @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_10,plain,
    ! [X2: nat,X1: nat] :
      ( ( ts @ X1 @ X2 )
      = ( ts @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_11,plain,
    ! [X26: nat,X27: nat,X28: nat] :
      ( ( ts @ ( ts @ X26 @ X27 ) @ X28 )
      = ( ts @ X26 @ ( ts @ X27 @ X28 ) ) ),
    inference(variable_rename,[status(thm)],[satz31]) ).

thf(c_0_12,plain,
    ! [X20: nat,X21: nat,X22: nat,X23: nat] :
      ( ~ ( less @ X20 @ X21 )
      | ~ ( less @ X22 @ X23 )
      | ( less @ ( ts @ X20 @ X22 ) @ ( ts @ X21 @ X23 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz34a])])]) ).

thf(c_0_13,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( less @ X1 @ X2 )
      | ~ ( less @ ( ts @ X3 @ X1 ) @ ( ts @ X2 @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_14,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ts @ ( ts @ X1 @ X2 ) @ X3 )
      = ( ts @ X1 @ ( ts @ X2 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_15,plain,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) )
      | ~ ( less @ X1 @ X2 )
      | ~ ( less @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_16,plain,
    less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
    inference(split_conjunct,[status(thm)],[l]) ).

thf(c_0_17,plain,
    ! [X1: nat,X3: nat,X2: nat] :
      ( ( less @ X1 @ X2 )
      | ~ ( less @ ( ts @ X3 @ X1 ) @ ( ts @ X3 @ X2 ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_10]) ).

thf(c_0_18,plain,
    ! [X1: nat,X3: nat,X2: nat] :
      ( ( ts @ X1 @ ( ts @ X2 @ X3 ) )
      = ( ts @ X3 @ ( ts @ X1 @ X2 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

thf(c_0_19,plain,
    ! [X1: nat,X2: nat] :
      ( ( less @ ( ts @ X1 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ X2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
      | ~ ( less @ X1 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_20,plain,
    less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
    inference(split_conjunct,[status(thm)],[k]) ).

thf(c_0_21,plain,
    ! [X1: nat,X2: nat,X3: nat] :
      ( ( ts @ X1 @ ( ts @ X2 @ X3 ) )
      = ( ts @ X2 @ ( ts @ X1 @ X3 ) ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_14]) ).

thf(c_0_22,negated_conjecture,
    ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz50])]) ).

thf(c_0_23,plain,
    ! [X1: nat,X2: nat,X3: nat,X4: nat] :
      ( ( less @ X1 @ ( ts @ X2 @ X3 ) )
      | ~ ( less @ ( ts @ X4 @ X1 ) @ ( ts @ X2 @ ( ts @ X3 @ X4 ) ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_24,plain,
    ! [X2: nat,X1: nat,X4: nat,X3: nat] :
      ( ( less @ ( ts @ X1 @ X2 ) @ X3 )
      | ~ ( less @ ( ts @ X2 @ ( ts @ X4 @ X1 ) ) @ ( ts @ X4 @ X3 ) ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_25,plain,
    less @ ( ts @ ( num @ x ) @ ( ts @ ( num @ y ) @ ( ts @ ( den @ y ) @ ( den @ z ) ) ) ) @ ( ts @ ( num @ y ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_14]),c_0_21]),c_0_10]),c_0_21]),c_0_21]),c_0_10]),c_0_21]) ).

thf(c_0_26,negated_conjecture,
    ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_22]) ).

thf(c_0_27,plain,
    ! [X2: nat,X1: nat,X3: nat,X4: nat,X5: nat] :
      ( ( less @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X4 ) )
      | ~ ( less @ ( ts @ X2 @ ( ts @ X5 @ X1 ) ) @ ( ts @ X3 @ ( ts @ X4 @ X5 ) ) ) ),
    inference(spm,[status(thm)],[c_0_23,c_0_18]) ).

thf(c_0_28,plain,
    less @ ( ts @ ( num @ x ) @ ( ts @ ( den @ y ) @ ( den @ z ) ) ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_10]),c_0_21]) ).

thf(c_0_29,negated_conjecture,
    ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_30,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_10]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 09:34:35 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  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/tmp/tmp.bopbGG6Duz/E---3.1_8909.p
% 0.58/0.55  # Version: 3.1.0-ho
% 0.58/0.55  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.58/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.58/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.58/0.55  # Starting full_lambda_5 with 300s (1) cores
% 0.58/0.55  # Starting new_ho_10_unif with 300s (1) cores
% 0.58/0.55  # new_ho_10 with pid 9049 completed with status 0
% 0.58/0.55  # Result found by new_ho_10
% 0.58/0.55  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.58/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.58/0.55  # No SInE strategy applied
% 0.58/0.55  # Search class: HHUSS-FFSF21-SFFFFFNN
% 0.58/0.55  # partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.58/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.55  # Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S071I with 811s (1) cores
% 0.58/0.55  # Starting new_ho_10 with 151s (1) cores
% 0.58/0.55  # Starting new_bool_3 with 136s (1) cores
% 0.58/0.55  # Starting new_bool_1 with 136s (1) cores
% 0.58/0.55  # Starting sh5l with 136s (1) cores
% 0.58/0.55  # new_bool_1 with pid 9062 completed with status 0
% 0.58/0.55  # Result found by new_bool_1
% 0.58/0.55  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.58/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.55  # Starting new_ho_10 with 1500s (5) cores
% 0.58/0.55  # No SInE strategy applied
% 0.58/0.55  # Search class: HHUSS-FFSF21-SFFFFFNN
% 0.58/0.55  # partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.58/0.55  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.55  # Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S071I with 811s (1) cores
% 0.58/0.55  # Starting new_ho_10 with 151s (1) cores
% 0.58/0.55  # Starting new_bool_3 with 136s (1) cores
% 0.58/0.55  # Starting new_bool_1 with 136s (1) cores
% 0.58/0.55  # Preprocessing time       : 0.001 s
% 0.58/0.55  # Presaturation interreduction done
% 0.58/0.55  
% 0.58/0.55  # Proof found!
% 0.58/0.55  # SZS status Theorem
% 0.58/0.55  # SZS output start CNFRefutation
% See solution above
% 0.58/0.55  # Parsed axioms                        : 16
% 0.58/0.55  # Removed by relevancy pruning/SinE    : 0
% 0.58/0.55  # Initial clauses                      : 16
% 0.58/0.55  # Removed in clause preprocessing      : 9
% 0.58/0.55  # Initial clauses in saturation        : 7
% 0.58/0.55  # Processed clauses                    : 589
% 0.58/0.55  # ...of these trivial                  : 12
% 0.58/0.55  # ...subsumed                          : 488
% 0.58/0.55  # ...remaining for further processing  : 89
% 0.58/0.55  # Other redundant clauses eliminated   : 0
% 0.58/0.55  # Clauses deleted for lack of memory   : 0
% 0.58/0.55  # Backward-subsumed                    : 0
% 0.58/0.55  # Backward-rewritten                   : 0
% 0.58/0.55  # Generated clauses                    : 2498
% 0.58/0.55  # ...of the previous two non-redundant : 2478
% 0.58/0.55  # ...aggressively subsumed             : 0
% 0.58/0.55  # Contextual simplify-reflections      : 0
% 0.58/0.55  # Paramodulations                      : 2498
% 0.58/0.55  # Factorizations                       : 0
% 0.58/0.55  # NegExts                              : 0
% 0.58/0.55  # Equation resolutions                 : 0
% 0.58/0.55  # Disequality decompositions           : 0
% 0.58/0.55  # Total rewrite steps                  : 1124
% 0.58/0.55  # ...of those cached                   : 914
% 0.58/0.55  # Propositional unsat checks           : 0
% 0.58/0.55  #    Propositional check models        : 0
% 0.58/0.55  #    Propositional check unsatisfiable : 0
% 0.58/0.55  #    Propositional clauses             : 0
% 0.58/0.55  #    Propositional clauses after purity: 0
% 0.58/0.55  #    Propositional unsat core size     : 0
% 0.58/0.55  #    Propositional preprocessing time  : 0.000
% 0.58/0.55  #    Propositional encoding time       : 0.000
% 0.58/0.55  #    Propositional solver time         : 0.000
% 0.58/0.55  #    Success case prop preproc time    : 0.000
% 0.58/0.55  #    Success case prop encoding time   : 0.000
% 0.58/0.55  #    Success case prop solver time     : 0.000
% 0.58/0.55  # Current number of processed clauses  : 82
% 0.58/0.55  #    Positive orientable unit clauses  : 7
% 0.58/0.55  #    Positive unorientable unit clauses: 4
% 0.58/0.55  #    Negative unit clauses             : 1
% 0.58/0.55  #    Non-unit-clauses                  : 70
% 0.58/0.55  # Current number of unprocessed clauses: 1867
% 0.58/0.55  # ...number of literals in the above   : 3676
% 0.58/0.55  # Current number of archived formulas  : 0
% 0.58/0.55  # Current number of archived clauses   : 7
% 0.58/0.55  # Clause-clause subsumption calls (NU) : 6880
% 0.58/0.55  # Rec. Clause-clause subsumption calls : 6880
% 0.58/0.55  # Non-unit clause-clause subsumptions  : 451
% 0.58/0.55  # Unit Clause-clause subsumption calls : 10
% 0.58/0.55  # Rewrite failures with RHS unbound    : 0
% 0.58/0.55  # BW rewrite match attempts            : 94
% 0.58/0.55  # BW rewrite match successes           : 82
% 0.58/0.55  # Condensation attempts                : 0
% 0.58/0.55  # Condensation successes               : 0
% 0.58/0.55  # Termbank termtop insertions          : 62491
% 0.58/0.55  # Search garbage collected termcells   : 78
% 0.58/0.55  
% 0.58/0.55  # -------------------------------------------------
% 0.58/0.55  # User time                : 0.045 s
% 0.58/0.55  # System time              : 0.009 s
% 0.58/0.55  # Total time               : 0.054 s
% 0.58/0.55  # Maximum resident set size: 1796 pages
% 0.58/0.55  
% 0.58/0.55  # -------------------------------------------------
% 0.58/0.55  # User time                : 0.219 s
% 0.58/0.55  # System time              : 0.022 s
% 0.58/0.55  # Total time               : 0.241 s
% 0.58/0.55  # Maximum resident set size: 1720 pages
% 0.58/0.55  % E---3.1 exiting
% 0.58/0.55  % E exiting
%------------------------------------------------------------------------------