TSTP Solution File: NUM925_2 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:08:52 EDT 2023

% Result   : Theorem 0.52s 0.69s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   48 (  21 unt;  21 typ;   0 def)
%            Number of atoms       :   39 (  27 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   25 (  13   ~;   7   |;   3   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   18 (  13   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   8 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    one_one_int: int ).

tff(decl_23,type,
    one_one_nat: nat ).

tff(decl_25,type,
    plus_plus_int: int > fun_int_int ).

tff(decl_26,type,
    plus_plus_nat: nat > fun_nat_nat ).

tff(decl_29,type,
    zero_zero_int: int ).

tff(decl_33,type,
    bit0: int > int ).

tff(decl_34,type,
    bit1: int > int ).

tff(decl_35,type,
    pls: int ).

tff(decl_36,type,
    number_number_of_int: int > int ).

tff(decl_37,type,
    number_number_of_nat: int > nat ).

tff(decl_40,type,
    semiri1621563631at_int: fun_nat_int ).

tff(decl_44,type,
    ord_less_int: fun_int_fun_int_bool ).

tff(decl_47,type,
    ord_less_eq_int: fun_int_fun_int_bool ).

tff(decl_50,type,
    power_power_int: int > fun_nat_int ).

tff(decl_55,type,
    hAPP_int_bool: ( fun_int_bool * int ) > bool ).

tff(decl_56,type,
    hAPP_int_int: ( fun_int_int * int ) > int ).

tff(decl_57,type,
    hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).

tff(decl_59,type,
    hAPP_nat_int: ( fun_nat_int * nat ) > int ).

tff(decl_60,type,
    hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(decl_66,type,
    hBOOL: bool > $o ).

tff(decl_68,type,
    n: nat ).

tff(fact_176_number__of__is__id,axiom,
    ! [X22: int] : ( number_number_of_int(X22) = X22 ),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_176_number__of__is__id) ).

tff(conj_0,conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',conj_0) ).

tff(fact_25_semiring__norm_I110_J,axiom,
    one_one_int = number_number_of_int(bit1(pls)),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_25_semiring__norm_I110_J) ).

tff(fact_98_Pls__def,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_98_Pls__def) ).

tff(fact_19_semiring__one__add__one__is__two,axiom,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_19_semiring__one__add__one__is__two) ).

tff(fact_231_field__power__not__zero,axiom,
    ! [X132: nat,X134: int] :
      ( ( X134 != zero_zero_int )
     => ( hAPP_nat_int(power_power_int(X134),X132) != zero_zero_int ) ),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_231_field__power__not__zero) ).

tff(fact_447_zless__le,axiom,
    ! [X34: int,X26: int] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X34),X26))
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X34),X26))
        & ( X34 != X26 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_447_zless__le) ).

tff(fact_0_n1pos,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    file('/export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p',fact_0_n1pos) ).

tff(c_0_8,plain,
    ! [X1557: int] : ( number_number_of_int(X1557) = X1557 ),
    inference(variable_rename,[status(thm)],[fact_176_number__of__is__id]) ).

tff(c_0_9,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

tcf(c_0_10,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).

tcf(c_0_11,plain,
    pls = zero_zero_int,
    inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).

tcf(c_0_12,plain,
    ! [X1: int] : number_number_of_int(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

tcf(c_0_13,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

tcf(c_0_14,plain,
    bit1(zero_zero_int) = one_one_int,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

tcf(c_0_15,plain,
    hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).

tff(c_0_16,plain,
    ! [X995: nat,X996: int] :
      ( ( X996 = zero_zero_int )
      | ( hAPP_nat_int(power_power_int(X996),X995) != zero_zero_int ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).

tcf(c_0_17,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = zero_zero_int,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).

tcf(c_0_18,plain,
    number_number_of_nat(bit0(one_one_int)) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_14]) ).

tff(c_0_19,plain,
    ! [X1260: int,X1261: int] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1260),X1261))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1260),X1261)) )
      & ( ( X1260 != X1261 )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1260),X1261)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1260),X1261))
        | ( X1260 = X1261 )
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1260),X1261)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_zless__le])])]) ).

tcf(c_0_20,plain,
    ! [X1: int,X16: nat] :
      ( ( X1 = zero_zero_int )
      | ( hAPP_nat_int(power_power_int(X1),X16) != zero_zero_int ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

tcf(c_0_21,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = zero_zero_int,
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

tcf(c_0_22,plain,
    ! [X1: int,X2: int] :
      ( ( X1 != X2 )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

tcf(c_0_23,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).

tcf(c_0_24,negated_conjecture,
    hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

tcf(c_0_25,plain,
    ! [X1: int] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
    inference(er,[status(thm)],[c_0_22]) ).

cnf(c_0_26,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 2400
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Oct  2 14:34:14 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.56  Running first-order model finding
% 0.20/0.56  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.OzuVjLAs7s/E---3.1_2701.p
% 0.52/0.69  # Version: 3.1pre001
% 0.52/0.69  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.52/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.52/0.69  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.52/0.69  # Starting new_bool_3 with 300s (1) cores
% 0.52/0.69  # Starting new_bool_1 with 300s (1) cores
% 0.52/0.69  # Starting sh5l with 300s (1) cores
% 0.52/0.69  # new_bool_1 with pid 2780 completed with status 0
% 0.52/0.69  # Result found by new_bool_1
% 0.52/0.69  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.52/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.52/0.69  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.52/0.69  # Starting new_bool_3 with 300s (1) cores
% 0.52/0.69  # Starting new_bool_1 with 300s (1) cores
% 0.52/0.69  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.52/0.69  # Search class: FGHSM-FSLM31-DFFFFFNN
% 0.52/0.69  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.52/0.69  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.52/0.69  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2782 completed with status 0
% 0.52/0.69  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.52/0.69  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.52/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.52/0.69  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.52/0.69  # Starting new_bool_3 with 300s (1) cores
% 0.52/0.69  # Starting new_bool_1 with 300s (1) cores
% 0.52/0.69  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.52/0.69  # Search class: FGHSM-FSLM31-DFFFFFNN
% 0.52/0.69  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.52/0.69  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.52/0.69  # Preprocessing time       : 0.011 s
% 0.52/0.69  # Presaturation interreduction done
% 0.52/0.69  
% 0.52/0.69  # Proof found!
% 0.52/0.69  # SZS status Theorem
% 0.52/0.69  # SZS output start CNFRefutation
% See solution above
% 0.52/0.69  # Parsed axioms                        : 767
% 0.52/0.69  # Removed by relevancy pruning/SinE    : 244
% 0.52/0.69  # Initial clauses                      : 757
% 0.52/0.69  # Removed in clause preprocessing      : 69
% 0.52/0.69  # Initial clauses in saturation        : 688
% 0.52/0.69  # Processed clauses                    : 974
% 0.52/0.69  # ...of these trivial                  : 104
% 0.52/0.69  # ...subsumed                          : 303
% 0.52/0.69  # ...remaining for further processing  : 566
% 0.52/0.69  # Other redundant clauses eliminated   : 74
% 0.52/0.69  # Clauses deleted for lack of memory   : 0
% 0.52/0.69  # Backward-subsumed                    : 12
% 0.52/0.69  # Backward-rewritten                   : 18
% 0.52/0.69  # Generated clauses                    : 511
% 0.52/0.69  # ...of the previous two non-redundant : 410
% 0.52/0.69  # ...aggressively subsumed             : 0
% 0.52/0.69  # Contextual simplify-reflections      : 4
% 0.52/0.69  # Paramodulations                      : 439
% 0.52/0.69  # Factorizations                       : 0
% 0.52/0.69  # NegExts                              : 0
% 0.52/0.69  # Equation resolutions                 : 82
% 0.52/0.69  # Total rewrite steps                  : 892
% 0.52/0.69  # Propositional unsat checks           : 0
% 0.52/0.69  #    Propositional check models        : 0
% 0.52/0.69  #    Propositional check unsatisfiable : 0
% 0.52/0.69  #    Propositional clauses             : 0
% 0.52/0.69  #    Propositional clauses after purity: 0
% 0.52/0.69  #    Propositional unsat core size     : 0
% 0.52/0.69  #    Propositional preprocessing time  : 0.000
% 0.52/0.69  #    Propositional encoding time       : 0.000
% 0.52/0.69  #    Propositional solver time         : 0.000
% 0.52/0.69  #    Success case prop preproc time    : 0.000
% 0.52/0.69  #    Success case prop encoding time   : 0.000
% 0.52/0.69  #    Success case prop solver time     : 0.000
% 0.52/0.69  # Current number of processed clauses  : 128
% 0.52/0.69  #    Positive orientable unit clauses  : 47
% 0.52/0.69  #    Positive unorientable unit clauses: 1
% 0.52/0.69  #    Negative unit clauses             : 32
% 0.52/0.69  #    Non-unit-clauses                  : 48
% 0.52/0.69  # Current number of unprocessed clauses: 461
% 0.52/0.69  # ...number of literals in the above   : 1039
% 0.52/0.69  # Current number of archived formulas  : 0
% 0.52/0.69  # Current number of archived clauses   : 381
% 0.52/0.69  # Clause-clause subsumption calls (NU) : 15571
% 0.52/0.69  # Rec. Clause-clause subsumption calls : 13255
% 0.52/0.69  # Non-unit clause-clause subsumptions  : 185
% 0.52/0.69  # Unit Clause-clause subsumption calls : 723
% 0.52/0.69  # Rewrite failures with RHS unbound    : 0
% 0.52/0.69  # BW rewrite match attempts            : 198
% 0.52/0.69  # BW rewrite match successes           : 107
% 0.52/0.69  # Condensation attempts                : 0
% 0.52/0.69  # Condensation successes               : 0
% 0.52/0.69  # Termbank termtop insertions          : 67715
% 0.52/0.69  
% 0.52/0.69  # -------------------------------------------------
% 0.52/0.69  # User time                : 0.084 s
% 0.52/0.69  # System time              : 0.015 s
% 0.52/0.69  # Total time               : 0.099 s
% 0.52/0.69  # Maximum resident set size: 4928 pages
% 0.52/0.69  
% 0.52/0.69  # -------------------------------------------------
% 0.52/0.69  # User time                : 0.106 s
% 0.52/0.69  # System time              : 0.017 s
% 0.52/0.69  # Total time               : 0.123 s
% 0.52/0.69  # Maximum resident set size: 3040 pages
% 0.52/0.69  % E---3.1 exiting
%------------------------------------------------------------------------------