TSTP Solution File: NUM345+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM345+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n005.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  : 600s
% DateTime : Mon Jul 18 09:31:45 EDT 2022

% Result   : Theorem 0.41s 23.60s
% Output   : CNFRefutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   42 (  20 unt;   0 def)
%            Number of atoms       :   92 (   5 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   89 (  39   ~;  36   |;   8   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :   75 (   0 sgn  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(add_digit_digit_digit,axiom,
    ! [X21,X22,X23,X24,X25] :
      ( ( rdn_digit_add(rdnn(X22),rdnn(X23),rdnn(X25),rdnn(n0))
        & rdn_digit_add(rdnn(X25),rdnn(X21),rdnn(X24),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X21),rdnn(X22),rdnn(X23),rdnn(X24)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).

fof(sum_entry_point_pos_pos,axiom,
    ! [X1,X2,X3,X10,X11,X12] :
      ( ( rdn_translate(X1,rdn_pos(X10))
        & rdn_translate(X2,rdn_pos(X11))
        & rdn_add_with_carry(rdnn(n0),X10,X11,X12)
        & rdn_translate(X3,rdn_pos(X12)) )
     => sum(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).

fof(rdn_digit_add_n5_n0_n5_n0,axiom,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).

fof(rdn_digit_add_n2_n3_n5_n0,axiom,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).

fof(sum_n2_n3_less_n6,conjecture,
    ! [X1] :
      ( sum(n2,n3,X1)
     => less(X1,n6) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sum_n2_n3_less_n6) ).

fof(rdn5,axiom,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).

fof(unique_sum,axiom,
    ! [X1,X2,X15,X16] :
      ( ( sum(X1,X2,X15)
        & sum(X1,X2,X16) )
     => X15 = X16 ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_sum) ).

fof(rdn3,axiom,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).

fof(less_entry_point_pos_pos,axiom,
    ! [X1,X2,X10,X11] :
      ( ( rdn_translate(X1,rdn_pos(X10))
        & rdn_translate(X2,rdn_pos(X11))
        & rdn_positive_less(X10,X11) )
     => less(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).

fof(rdn2,axiom,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).

fof(rdn6,axiom,
    rdn_translate(n6,rdn_pos(rdnn(n6))),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn6) ).

fof(rdn_positive_less56,axiom,
    rdn_positive_less(rdnn(n5),rdnn(n6)),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less56) ).

fof(c_0_12,plain,
    ! [X26,X27,X28,X29,X30] :
      ( ~ rdn_digit_add(rdnn(X27),rdnn(X28),rdnn(X30),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X30),rdnn(X26),rdnn(X29),rdnn(n0))
      | rdn_add_with_carry(rdnn(X26),rdnn(X27),rdnn(X28),rdnn(X29)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])])]) ).

fof(c_0_13,plain,
    ! [X13,X14,X15,X16,X17,X18] :
      ( ~ rdn_translate(X13,rdn_pos(X16))
      | ~ rdn_translate(X14,rdn_pos(X17))
      | ~ rdn_add_with_carry(rdnn(n0),X16,X17,X18)
      | ~ rdn_translate(X15,rdn_pos(X18))
      | sum(X13,X14,X15) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])])]) ).

cnf(c_0_14,plain,
    ( rdn_add_with_carry(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X4))
    | ~ rdn_digit_add(rdnn(X5),rdnn(X1),rdnn(X4),rdnn(n0))
    | ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X5),rdnn(n0)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_15,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n0_n5_n0]) ).

cnf(c_0_16,plain,
    ( sum(X1,X2,X3)
    | ~ rdn_translate(X3,rdn_pos(X4))
    | ~ rdn_add_with_carry(rdnn(n0),X5,X6,X4)
    | ~ rdn_translate(X2,rdn_pos(X6))
    | ~ rdn_translate(X1,rdn_pos(X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n5))
    | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n5),rdnn(n0)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    ( sum(X1,X2,X3)
    | ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n5),rdnn(n0))
    | ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(X4))) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,plain,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    inference(split_conjunct,[status(thm)],[rdn_digit_add_n2_n3_n5_n0]) ).

fof(c_0_20,negated_conjecture,
    ~ ! [X1] :
        ( sum(n2,n3,X1)
       => less(X1,n6) ),
    inference(assume_negation,[status(cth)],[sum_n2_n3_less_n6]) ).

cnf(c_0_21,plain,
    ( sum(X1,X2,X3)
    | ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n2))) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(split_conjunct,[status(thm)],[rdn5]) ).

fof(c_0_23,plain,
    ! [X17,X18,X19,X20] :
      ( ~ sum(X17,X18,X19)
      | ~ sum(X17,X18,X20)
      | X19 = X20 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unique_sum])]) ).

fof(c_0_24,negated_conjecture,
    ( sum(n2,n3,esk1_0)
    & ~ less(esk1_0,n6) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).

cnf(c_0_25,plain,
    ( sum(X1,X2,n5)
    | ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
    | ~ rdn_translate(X1,rdn_pos(rdnn(n2))) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,plain,
    rdn_translate(n3,rdn_pos(rdnn(n3))),
    inference(split_conjunct,[status(thm)],[rdn3]) ).

fof(c_0_27,plain,
    ! [X12,X13,X14,X15] :
      ( ~ rdn_translate(X12,rdn_pos(X14))
      | ~ rdn_translate(X13,rdn_pos(X15))
      | ~ rdn_positive_less(X14,X15)
      | less(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])])])]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | ~ sum(X3,X4,X2)
    | ~ sum(X3,X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    sum(n2,n3,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,plain,
    ( sum(X1,n3,n5)
    | ~ rdn_translate(X1,rdn_pos(rdnn(n2))) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    inference(split_conjunct,[status(thm)],[rdn2]) ).

cnf(c_0_32,plain,
    ( less(X1,X2)
    | ~ rdn_positive_less(X3,X4)
    | ~ rdn_translate(X2,rdn_pos(X4))
    | ~ rdn_translate(X1,rdn_pos(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,plain,
    rdn_translate(n6,rdn_pos(rdnn(n6))),
    inference(split_conjunct,[status(thm)],[rdn6]) ).

cnf(c_0_34,negated_conjecture,
    ( X1 = esk1_0
    | ~ sum(n2,n3,X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,plain,
    sum(n2,n3,n5),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,plain,
    ( less(X1,n6)
    | ~ rdn_positive_less(X2,rdnn(n6))
    | ~ rdn_translate(X1,rdn_pos(X2)) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,plain,
    rdn_positive_less(rdnn(n5),rdnn(n6)),
    inference(split_conjunct,[status(thm)],[rdn_positive_less56]) ).

cnf(c_0_38,negated_conjecture,
    ~ less(esk1_0,n6),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_39,negated_conjecture,
    esk1_0 = n5,
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    less(n5,n6),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_37])]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM345+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 12:39:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.41/23.43  eprover: CPU time limit exceeded, terminating
% 0.41/23.44  eprover: CPU time limit exceeded, terminating
% 0.41/23.47  eprover: CPU time limit exceeded, terminating
% 0.41/23.60  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.41/23.60  
% 0.41/23.60  # Failure: Resource limit exceeded (time)
% 0.41/23.60  # OLD status Res
% 0.41/23.60  # Preprocessing time       : 0.026 s
% 0.41/23.60  # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.41/23.60  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.41/23.60  # Preprocessing time       : 0.027 s
% 0.41/23.60  
% 0.41/23.60  # Proof found!
% 0.41/23.60  # SZS status Theorem
% 0.41/23.60  # SZS output start CNFRefutation
% See solution above
% 0.41/23.60  # Proof object total steps             : 42
% 0.41/23.60  # Proof object clause steps            : 24
% 0.41/23.60  # Proof object formula steps           : 18
% 0.41/23.60  # Proof object conjectures             : 8
% 0.41/23.60  # Proof object clause conjectures      : 5
% 0.41/23.60  # Proof object formula conjectures     : 3
% 0.41/23.60  # Proof object initial clauses used    : 13
% 0.41/23.60  # Proof object initial formulas used   : 12
% 0.41/23.60  # Proof object generating inferences   : 10
% 0.41/23.60  # Proof object simplifying inferences  : 5
% 0.41/23.60  # Training examples: 0 positive, 0 negative
% 0.41/23.60  # Parsed axioms                        : 402
% 0.41/23.60  # Removed by relevancy pruning/SinE    : 262
% 0.41/23.60  # Initial clauses                      : 143
% 0.41/23.60  # Removed in clause preprocessing      : 0
% 0.41/23.60  # Initial clauses in saturation        : 143
% 0.41/23.60  # Processed clauses                    : 1011
% 0.41/23.60  # ...of these trivial                  : 0
% 0.41/23.60  # ...subsumed                          : 164
% 0.41/23.60  # ...remaining for further processing  : 847
% 0.41/23.60  # Other redundant clauses eliminated   : 1
% 0.41/23.60  # Clauses deleted for lack of memory   : 0
% 0.41/23.60  # Backward-subsumed                    : 0
% 0.41/23.60  # Backward-rewritten                   : 9
% 0.41/23.60  # Generated clauses                    : 1148
% 0.41/23.60  # ...of the previous two non-trivial   : 1133
% 0.41/23.60  # Contextual simplify-reflections      : 35
% 0.41/23.60  # Paramodulations                      : 1145
% 0.41/23.60  # Factorizations                       : 2
% 0.41/23.60  # Equation resolutions                 : 1
% 0.41/23.60  # Current number of processed clauses  : 837
% 0.41/23.60  #    Positive orientable unit clauses  : 180
% 0.41/23.60  #    Positive unorientable unit clauses: 0
% 0.41/23.60  #    Negative unit clauses             : 29
% 0.41/23.60  #    Non-unit-clauses                  : 628
% 0.41/23.60  # Current number of unprocessed clauses: 262
% 0.41/23.60  # ...number of literals in the above   : 1084
% 0.41/23.60  # Current number of archived formulas  : 0
% 0.41/23.60  # Current number of archived clauses   : 9
% 0.41/23.60  # Clause-clause subsumption calls (NU) : 75139
% 0.41/23.60  # Rec. Clause-clause subsumption calls : 55701
% 0.41/23.60  # Non-unit clause-clause subsumptions  : 188
% 0.41/23.60  # Unit Clause-clause subsumption calls : 5944
% 0.41/23.60  # Rewrite failures with RHS unbound    : 0
% 0.41/23.60  # BW rewrite match attempts            : 6
% 0.41/23.60  # BW rewrite match successes           : 4
% 0.41/23.60  # Condensation attempts                : 0
% 0.41/23.60  # Condensation successes               : 0
% 0.41/23.60  # Termbank termtop insertions          : 33919
% 0.41/23.60  
% 0.41/23.60  # -------------------------------------------------
% 0.41/23.60  # User time                : 0.098 s
% 0.41/23.60  # System time              : 0.010 s
% 0.41/23.60  # Total time               : 0.108 s
% 0.41/23.60  # Maximum resident set size: 5864 pages
% 0.41/27.14  eprover: CPU time limit exceeded, terminating
% 0.41/27.16  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.16  eprover: No such file or directory
% 0.41/27.16  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.16  eprover: No such file or directory
% 0.41/27.17  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.17  eprover: No such file or directory
% 0.41/27.18  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.18  eprover: No such file or directory
% 0.41/27.18  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.18  eprover: No such file or directory
% 0.41/27.19  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.19  eprover: No such file or directory
% 0.41/27.19  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.19  eprover: No such file or directory
% 0.41/27.20  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.41/27.20  eprover: No such file or directory
% 0.41/46.49  eprover: CPU time limit exceeded, terminating
% 0.41/46.49  eprover: CPU time limit exceeded, terminating
% 0.41/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.50  eprover: No such file or directory
% 0.41/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.50  eprover: No such file or directory
% 0.41/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51  eprover: No such file or directory
% 0.41/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51  eprover: No such file or directory
% 0.41/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51  eprover: No such file or directory
% 0.41/46.51  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.51  eprover: No such file or directory
% 0.41/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.52  eprover: No such file or directory
% 0.41/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.52  eprover: No such file or directory
% 0.41/46.52  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.52  eprover: No such file or directory
% 0.41/46.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.53  eprover: No such file or directory
% 0.41/46.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.53  eprover: No such file or directory
% 0.41/46.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.53  eprover: No such file or directory
% 0.41/46.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.53  eprover: No such file or directory
% 0.41/46.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.54  eprover: No such file or directory
% 0.41/46.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.54  eprover: No such file or directory
% 0.41/46.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.54  eprover: No such file or directory
% 0.41/46.55  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.55  eprover: No such file or directory
% 0.41/46.55  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.41/46.55  eprover: No such file or directory
%------------------------------------------------------------------------------