TSTP Solution File: NUM925+3 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 18:58:00 EDT 2023

% Result   : Theorem 3.32s 1.09s
% Output   : CNFRefutation 3.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (  24 unt;   0 def)
%            Number of atoms       :   66 (  30 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   53 (  25   ~;  19   |;   3   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   32 (   4 sgn;  19   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    hAPP_nat_int(power_power_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/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',conj_0) ).

fof(fact_98_Pls__def,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_98_Pls__def) ).

fof(fact_19_semiring__one__add__one__is__two,axiom,
    plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_19_semiring__one__add__one__is__two) ).

fof(fact_231_field__power__not__zero,axiom,
    ! [X65,X66] :
      ( is_int(X66)
     => ( X66 != zero_zero_int
       => hAPP_nat_int(power_power_int(X66),X65) != zero_zero_int ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_231_field__power__not__zero) ).

fof(fact_789_zle__iff__zadd,axiom,
    ! [X26,X31] :
      ( is_int(X31)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X26),X31))
      <=> ? [X91] : X31 = plus_plus_int(X26,hAPP_nat_int(semiri1621563631at_int,X91)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_789_zle__iff__zadd) ).

fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
    ! [X1,X2] :
      ( ( is_int(X1)
        & is_int(X2) )
     => is_int(plus_plus_int(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
    ! [X1,X2] : is_int(hAPP_nat_int(X1,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).

fof(fact_807_int__le__0__conv,axiom,
    ! [X19] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X19)),zero_zero_int))
    <=> X19 = zero_zero_nat ),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_807_int__le__0__conv) ).

fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
    is_int(one_one_int),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

fof(fact_254_transfer__int__nat__numerals_I2_J,axiom,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_254_transfer__int__nat__numerals_I2_J) ).

fof(fact_226_one__neq__zero,axiom,
    one_one_nat != zero_zero_nat,
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_226_one__neq__zero) ).

fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,hypothesis,
    is_int(zero_zero_int),
    file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).

fof(c_0_12,negated_conjecture,
    hAPP_nat_int(power_power_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])]) ).

cnf(c_0_13,negated_conjecture,
    hAPP_nat_int(power_power_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_12]) ).

cnf(c_0_14,plain,
    pls = zero_zero_int,
    inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).

cnf(c_0_15,plain,
    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]) ).

fof(c_0_16,plain,
    ! [X908,X909] :
      ( ~ is_int(X909)
      | X909 = zero_zero_int
      | hAPP_nat_int(power_power_int(X909),X908) != zero_zero_int ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).

cnf(c_0_17,negated_conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(zero_zero_int)))) = zero_zero_int,
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    number_number_of_nat(bit0(bit1(zero_zero_int))) = plus_plus_nat(one_one_nat,one_one_nat),
    inference(rw,[status(thm)],[c_0_15,c_0_14]) ).

fof(c_0_19,plain,
    ! [X1013,X1014,X1016] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1013),X1014))
        | X1014 = plus_plus_int(X1013,hAPP_nat_int(semiri1621563631at_int,esk10_2(X1013,X1014)))
        | ~ is_int(X1014) )
      & ( X1014 != plus_plus_int(X1013,hAPP_nat_int(semiri1621563631at_int,X1016))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1013),X1014))
        | ~ is_int(X1014) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_zle__iff__zadd])])])])]) ).

cnf(c_0_20,plain,
    ( X1 = zero_zero_int
    | ~ is_int(X1)
    | hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

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

fof(c_0_22,hypothesis,
    ! [X403,X404] :
      ( ~ is_int(X403)
      | ~ is_int(X404)
      | is_int(plus_plus_int(X403,X404)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint])]) ).

fof(c_0_23,hypothesis,
    ! [X407,X408] : is_int(hAPP_nat_int(X407,X408)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).

fof(c_0_24,plain,
    ! [X1017] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1017)),zero_zero_int))
        | X1017 = zero_zero_nat )
      & ( X1017 != zero_zero_nat
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1017)),zero_zero_int)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_int__le__0__conv])]) ).

cnf(c_0_25,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
    | X1 != plus_plus_int(X2,hAPP_nat_int(semiri1621563631at_int,X3))
    | ~ is_int(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
    | ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,hypothesis,
    ( is_int(plus_plus_int(X1,X2))
    | ~ is_int(X1)
    | ~ is_int(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,hypothesis,
    is_int(hAPP_nat_int(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,hypothesis,
    is_int(one_one_int),
    inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).

cnf(c_0_30,plain,
    ( X1 = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(split_conjunct,[status(thm)],[fact_254_transfer__int__nat__numerals_I2_J]) ).

cnf(c_0_32,plain,
    one_one_nat != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_226_one__neq__zero]) ).

cnf(c_0_33,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))))
    | ~ is_int(plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_34,hypothesis,
    plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).

cnf(c_0_35,hypothesis,
    is_int(zero_zero_int),
    inference(split_conjunct,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).

cnf(c_0_36,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_37,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23  % Problem    : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.24  % Command    : run_E %s %d THM
% 0.23/0.43  % Computer : n016.cluster.edu
% 0.23/0.43  % Model    : x86_64 x86_64
% 0.23/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43  % Memory   : 8042.1875MB
% 0.23/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43  % CPULimit   : 2400
% 0.23/0.43  % WCLimit    : 300
% 0.23/0.43  % DateTime   : Mon Oct  2 14:00:36 EDT 2023
% 0.23/0.43  % CPUTime    : 
% 0.44/0.63  Running first-order theorem proving
% 0.44/0.63  Running: /export/starexec/sandbox2/solver/bin/eprover --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.dOf1T2Dq8q/E---3.1_7572.p
% 3.32/1.09  # Version: 3.1pre001
% 3.32/1.09  # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09  # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09  # Starting new_bool_1 with 600s (2) cores
% 3.32/1.09  # Starting sh5l with 300s (1) cores
% 3.32/1.09  # new_bool_3 with pid 7652 completed with status 0
% 3.32/1.09  # Result found by new_bool_3
% 3.32/1.09  # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09  # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.32/1.09  # Search class: FGHSM-SSLM31-DFFFFFNN
% 3.32/1.09  # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 3.32/1.09  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 325s (1) cores
% 3.32/1.09  # Starting new_bool_3 with 61s (1) cores
% 3.32/1.09  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 7655 completed with status 0
% 3.32/1.09  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.32/1.09  # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09  # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.32/1.09  # Search class: FGHSM-SSLM31-DFFFFFNN
% 3.32/1.09  # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 3.32/1.09  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 325s (1) cores
% 3.32/1.09  # Preprocessing time       : 0.015 s
% 3.32/1.09  # Presaturation interreduction done
% 3.32/1.09  
% 3.32/1.09  # Proof found!
% 3.32/1.09  # SZS status Theorem
% 3.32/1.09  # SZS output start CNFRefutation
% See solution above
% 3.32/1.09  # Parsed axioms                        : 1233
% 3.32/1.09  # Removed by relevancy pruning/SinE    : 363
% 3.32/1.09  # Initial clauses                      : 1289
% 3.32/1.09  # Removed in clause preprocessing      : 98
% 3.32/1.09  # Initial clauses in saturation        : 1191
% 3.32/1.09  # Processed clauses                    : 2368
% 3.32/1.09  # ...of these trivial                  : 135
% 3.32/1.09  # ...subsumed                          : 527
% 3.32/1.09  # ...remaining for further processing  : 1706
% 3.32/1.09  # Other redundant clauses eliminated   : 196
% 3.32/1.09  # Clauses deleted for lack of memory   : 0
% 3.32/1.09  # Backward-subsumed                    : 9
% 3.32/1.09  # Backward-rewritten                   : 25
% 3.32/1.09  # Generated clauses                    : 11702
% 3.32/1.09  # ...of the previous two non-redundant : 10243
% 3.32/1.09  # ...aggressively subsumed             : 0
% 3.32/1.09  # Contextual simplify-reflections      : 2
% 3.32/1.09  # Paramodulations                      : 11490
% 3.32/1.09  # Factorizations                       : 9
% 3.32/1.09  # NegExts                              : 0
% 3.32/1.09  # Equation resolutions                 : 215
% 3.32/1.09  # Total rewrite steps                  : 5778
% 3.32/1.09  # Propositional unsat checks           : 0
% 3.32/1.09  #    Propositional check models        : 0
% 3.32/1.09  #    Propositional check unsatisfiable : 0
% 3.32/1.09  #    Propositional clauses             : 0
% 3.32/1.09  #    Propositional clauses after purity: 0
% 3.32/1.09  #    Propositional unsat core size     : 0
% 3.32/1.09  #    Propositional preprocessing time  : 0.000
% 3.32/1.09  #    Propositional encoding time       : 0.000
% 3.32/1.09  #    Propositional solver time         : 0.000
% 3.32/1.09  #    Success case prop preproc time    : 0.000
% 3.32/1.09  #    Success case prop encoding time   : 0.000
% 3.32/1.09  #    Success case prop solver time     : 0.000
% 3.32/1.09  # Current number of processed clauses  : 839
% 3.32/1.09  #    Positive orientable unit clauses  : 189
% 3.32/1.09  #    Positive unorientable unit clauses: 15
% 3.32/1.09  #    Negative unit clauses             : 75
% 3.32/1.09  #    Non-unit-clauses                  : 560
% 3.32/1.09  # Current number of unprocessed clauses: 9762
% 3.32/1.09  # ...number of literals in the above   : 23504
% 3.32/1.09  # Current number of archived formulas  : 0
% 3.32/1.09  # Current number of archived clauses   : 758
% 3.32/1.09  # Clause-clause subsumption calls (NU) : 112406
% 3.32/1.09  # Rec. Clause-clause subsumption calls : 60293
% 3.32/1.09  # Non-unit clause-clause subsumptions  : 293
% 3.32/1.09  # Unit Clause-clause subsumption calls : 14448
% 3.32/1.09  # Rewrite failures with RHS unbound    : 0
% 3.32/1.09  # BW rewrite match attempts            : 541
% 3.32/1.09  # BW rewrite match successes           : 205
% 3.32/1.09  # Condensation attempts                : 0
% 3.32/1.09  # Condensation successes               : 0
% 3.32/1.09  # Termbank termtop insertions          : 319548
% 3.32/1.09  
% 3.32/1.09  # -------------------------------------------------
% 3.32/1.09  # User time                : 0.399 s
% 3.32/1.09  # System time              : 0.015 s
% 3.32/1.09  # Total time               : 0.414 s
% 3.32/1.09  # Maximum resident set size: 7080 pages
% 3.32/1.09  
% 3.32/1.09  # -------------------------------------------------
% 3.32/1.09  # User time                : 0.783 s
% 3.32/1.09  # System time              : 0.020 s
% 3.32/1.09  # Total time               : 0.803 s
% 3.32/1.09  # Maximum resident set size: 3560 pages
% 3.32/1.09  % E---3.1 exiting
% 3.32/1.09  % E---3.1 exiting
%------------------------------------------------------------------------------