TSTP Solution File: NUM926+5 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n025.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 09:37:54 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   42 (  26 unt;   0 def)
%            Number of atoms       :   70 (  39 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   51 (  23   ~;  20   |;   3   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   9 con; 0-3 aty)
%            Number of variables   :   52 (   4 sgn  28   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).

fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
    ( t = one_one(int)
   => ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
    ( ord_less(int,one_one(int),t)
   => ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).

fof(fact_37_nat__1__add__1,axiom,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_37_nat__1__add__1) ).

fof(fact_54_Numeral1__eq1__nat,axiom,
    one_one(nat) = number_number_of(nat,bit1(pls)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_54_Numeral1__eq1__nat) ).

fof(fact_34_zpower__zadd__distrib,axiom,
    ! [X8,X9,X15] : power_power(int,X8,plus_plus(nat,X9,X15)) = times_times(int,power_power(int,X8,X9),power_power(int,X8,X15)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_34_zpower__zadd__distrib) ).

fof(fact_86_number__of__is__id,axiom,
    ! [X18] : number_number_of(int,X18) = X18,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_86_number__of__is__id) ).

fof(fact_85_zmult__commute,axiom,
    ! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_85_zmult__commute) ).

fof(fact_25_zle__antisym,axiom,
    ! [X15,X11] :
      ( ord_less_eq(int,X15,X11)
     => ( ord_less_eq(int,X11,X15)
       => X15 = X11 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_25_zle__antisym) ).

fof(fact_0_tpos,axiom,
    ord_less_eq(int,one_one(int),t),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_0_tpos) ).

fof(fact_22_zless__le,axiom,
    ! [X16,X17] :
      ( ord_less(int,X16,X17)
    <=> ( ord_less_eq(int,X16,X17)
        & X16 != X17 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_22_zless__le) ).

fof(fact_23_zless__linear,axiom,
    ! [X8,X9] :
      ( ord_less(int,X8,X9)
      | X8 = X9
      | ord_less(int,X9,X8) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_23_zless__linear) ).

fof(c_0_12,negated_conjecture,
    ~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_13,plain,
    ( t != one_one(int)
    | plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).

fof(c_0_14,negated_conjecture,
    ! [X6,X7] : plus_plus(int,power_power(int,X6,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).

fof(c_0_15,plain,
    ( ~ ord_less(int,one_one(int),t)
    | plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).

cnf(c_0_16,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    inference(split_conjunct,[status(thm)],[fact_37_nat__1__add__1]) ).

cnf(c_0_17,plain,
    one_one(nat) = number_number_of(nat,bit1(pls)),
    inference(split_conjunct,[status(thm)],[fact_54_Numeral1__eq1__nat]) ).

fof(c_0_18,plain,
    ! [X16,X17,X18] : power_power(int,X16,plus_plus(nat,X17,X18)) = times_times(int,power_power(int,X16,X17),power_power(int,X16,X18)),
    inference(variable_rename,[status(thm)],[fact_34_zpower__zadd__distrib]) ).

fof(c_0_19,plain,
    ! [X19] : number_number_of(int,X19) = X19,
    inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).

fof(c_0_20,plain,
    ! [X16,X17] : times_times(int,X16,X17) = times_times(int,X17,X16),
    inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).

fof(c_0_21,plain,
    ! [X16,X17] :
      ( ~ ord_less_eq(int,X16,X17)
      | ~ ord_less_eq(int,X17,X16)
      | X16 = X17 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_zle__antisym])]) ).

cnf(c_0_22,plain,
    ( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
    | t != one_one(int) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,negated_conjecture,
    plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,plain,
    ( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
    | ~ ord_less(int,one_one(int),t) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_25,plain,
    number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).

cnf(c_0_26,plain,
    power_power(int,X1,plus_plus(nat,X2,X3)) = times_times(int,power_power(int,X1,X2),power_power(int,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,plain,
    number_number_of(int,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    times_times(int,X1,X2) = times_times(int,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ ord_less_eq(int,X2,X1)
    | ~ ord_less_eq(int,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    ord_less_eq(int,one_one(int),t),
    inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).

cnf(c_0_31,plain,
    one_one(int) != t,
    inference(sr,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_32,plain,
    ! [X18,X19,X18,X19] :
      ( ( ord_less_eq(int,X18,X19)
        | ~ ord_less(int,X18,X19) )
      & ( X18 != X19
        | ~ ord_less(int,X18,X19) )
      & ( ~ ord_less_eq(int,X18,X19)
        | X18 = X19
        | ord_less(int,X18,X19) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_zless__le])])])])]) ).

cnf(c_0_33,plain,
    ( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,esk3_0,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),power_power(int,esk4_0,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))
    | ~ ord_less(int,one_one(int),t) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).

cnf(c_0_34,negated_conjecture,
    plus_plus(int,times_times(int,power_power(int,X1,number_number_of(nat,bit1(pls))),power_power(int,X1,number_number_of(nat,bit1(pls)))),times_times(int,power_power(int,X2,number_number_of(nat,bit1(pls))),power_power(int,X2,number_number_of(nat,bit1(pls))))) != plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_27]),c_0_28]) ).

fof(c_0_35,plain,
    ! [X10,X11] :
      ( ord_less(int,X10,X11)
      | X10 = X11
      | ord_less(int,X11,X10) ),
    inference(variable_rename,[status(thm)],[fact_23_zless__linear]) ).

cnf(c_0_36,plain,
    ~ ord_less_eq(int,t,one_one(int)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_37,plain,
    ( ord_less_eq(int,X1,X2)
    | ~ ord_less(int,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_38,plain,
    ~ ord_less(int,one_one(int),t),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_27]),c_0_28]),c_0_26]),c_0_26]),c_0_34]) ).

cnf(c_0_39,plain,
    ( ord_less(int,X1,X2)
    | X2 = X1
    | ord_less(int,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,plain,
    ~ ord_less(int,t,one_one(int)),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_41,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.12/0.32  % Computer : n025.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Thu Jul  7 16:31:29 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.023 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 42
% 0.22/1.40  # Proof object clause steps            : 20
% 0.22/1.40  # Proof object formula steps           : 22
% 0.22/1.40  # Proof object conjectures             : 5
% 0.22/1.40  # Proof object clause conjectures      : 2
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 12
% 0.22/1.40  # Proof object initial formulas used   : 12
% 0.22/1.40  # Proof object generating inferences   : 3
% 0.22/1.40  # Proof object simplifying inferences  : 19
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 142
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 48
% 0.22/1.40  # Initial clauses                      : 126
% 0.22/1.40  # Removed in clause preprocessing      : 2
% 0.22/1.40  # Initial clauses in saturation        : 124
% 0.22/1.40  # Processed clauses                    : 135
% 0.22/1.40  # ...of these trivial                  : 5
% 0.22/1.40  # ...subsumed                          : 19
% 0.22/1.40  # ...remaining for further processing  : 111
% 0.22/1.40  # Other redundant clauses eliminated   : 1
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 3
% 0.22/1.40  # Backward-rewritten                   : 5
% 0.22/1.40  # Generated clauses                    : 435
% 0.22/1.40  # ...of the previous two non-trivial   : 387
% 0.22/1.40  # Contextual simplify-reflections      : 0
% 0.22/1.40  # Paramodulations                      : 428
% 0.22/1.40  # Factorizations                       : 4
% 0.22/1.40  # Equation resolutions                 : 3
% 0.22/1.40  # Current number of processed clauses  : 102
% 0.22/1.40  #    Positive orientable unit clauses  : 28
% 0.22/1.40  #    Positive unorientable unit clauses: 3
% 0.22/1.40  #    Negative unit clauses             : 8
% 0.22/1.40  #    Non-unit-clauses                  : 63
% 0.22/1.40  # Current number of unprocessed clauses: 372
% 0.22/1.40  # ...number of literals in the above   : 689
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 8
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 318
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 311
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 22
% 0.22/1.40  # Unit Clause-clause subsumption calls : 33
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 44
% 0.22/1.40  # BW rewrite match successes           : 30
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 17700
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.032 s
% 0.22/1.40  # System time              : 0.005 s
% 0.22/1.40  # Total time               : 0.037 s
% 0.22/1.40  # Maximum resident set size: 3872 pages
% 0.22/23.40  eprover: CPU time limit exceeded, terminating
% 0.22/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42  eprover: No such file or directory
% 0.22/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44  eprover: No such file or directory
% 0.22/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
% 0.22/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47  eprover: No such file or directory
%------------------------------------------------------------------------------