TSTP Solution File: NUM925+5 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n001.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 : Mon Jun 24 12:39:05 EDT 2024

% Result   : Theorem 0.19s 0.54s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   50 (  41 unt;   0 def)
%            Number of atoms       :   72 (  50 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   43 (  21   ~;  16   |;   3   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   39 (   4 sgn  20   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_92_Bit1__def,axiom,
    ! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_92_Bit1__def) ).

fof(fact_47_zadd__commute,axiom,
    ! [X15,X7] : plus_plus(int,X15,X7) = plus_plus(int,X7,X15),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_47_zadd__commute) ).

fof(fact_76_add__Pls,axiom,
    ! [X19] : plus_plus(int,pls,X19) = X19,
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_76_add__Pls) ).

fof(fact_75_add__Pls__right,axiom,
    ! [X19] : plus_plus(int,X19,pls) = X19,
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_75_add__Pls__right) ).

fof(fact_2_sum__power2__eq__zero__iff,axiom,
    ! [X1] :
      ( linordered_idom(X1)
     => ! [X4,X5] :
          ( plus_plus(X1,power_power(X1,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X5,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X1)
        <=> ( ti(X1,X4) = zero_zero(X1)
            & ti(X1,X5) = zero_zero(X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_2_sum__power2__eq__zero__iff) ).

fof(conj_0,conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',conj_0) ).

fof(fact_29_nat__1__add__1,axiom,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_29_nat__1__add__1) ).

fof(fact_73_Pls__def,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_73_Pls__def) ).

fof(fact_85_add__numeral__0__right,axiom,
    ! [X1] :
      ( number_ring(X1)
     => ! [X30] : plus_plus(X1,X30,number_number_of(X1,pls)) = ti(X1,X30) ),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_85_add__numeral__0__right) ).

fof(fact_19_zero__is__num__zero,axiom,
    zero_zero(int) = number_number_of(int,pls),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_19_zero__is__num__zero) ).

fof(arity_Int_Oint___Int_Onumber__ring,axiom,
    number_ring(int),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',arity_Int_Oint___Int_Onumber__ring) ).

fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
    linordered_idom(int),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',arity_Int_Oint___Rings_Olinordered__idom) ).

fof(fact_32_rel__simps_I2_J,axiom,
    ~ ord_less(int,pls,pls),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_32_rel__simps_I2_J) ).

fof(fact_0_n1pos,axiom,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_0_n1pos) ).

fof(c_0_14,plain,
    ! [X79] : bit1(X79) = plus_plus(int,plus_plus(int,one_one(int),X79),X79),
    inference(variable_rename,[status(thm)],[fact_92_Bit1__def]) ).

fof(c_0_15,plain,
    ! [X116,X117] : plus_plus(int,X116,X117) = plus_plus(int,X117,X116),
    inference(variable_rename,[status(thm)],[fact_47_zadd__commute]) ).

fof(c_0_16,plain,
    ! [X83] : plus_plus(int,pls,X83) = X83,
    inference(variable_rename,[status(thm)],[fact_76_add__Pls]) ).

cnf(c_0_17,plain,
    bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X82] : plus_plus(int,X82,pls) = X82,
    inference(variable_rename,[status(thm)],[fact_75_add__Pls__right]) ).

fof(c_0_20,plain,
    ! [X88,X89,X90] :
      ( ( ti(X88,X89) = zero_zero(X88)
        | plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X88)
        | ~ linordered_idom(X88) )
      & ( ti(X88,X90) = zero_zero(X88)
        | plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X88)
        | ~ linordered_idom(X88) )
      & ( ti(X88,X89) != zero_zero(X88)
        | ti(X88,X90) != zero_zero(X88)
        | plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X88)
        | ~ linordered_idom(X88) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_sum__power2__eq__zero__iff])])])])]) ).

cnf(c_0_21,plain,
    plus_plus(int,pls,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    plus_plus(int,X1,plus_plus(int,one_one(int),X1)) = bit1(X1),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    plus_plus(int,X1,pls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_24,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(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_25,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | plus_plus(X1,power_power(X1,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X1)
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
    inference(split_conjunct,[status(thm)],[fact_29_nat__1__add__1]) ).

cnf(c_0_27,plain,
    bit1(pls) = one_one(int),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    pls = zero_zero(int),
    inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).

fof(c_0_30,plain,
    ! [X178,X179] :
      ( ~ number_ring(X178)
      | plus_plus(X178,X179,number_number_of(X178,pls)) = ti(X178,X179) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_add__numeral__0__right])])])]) ).

cnf(c_0_31,plain,
    zero_zero(int) = number_number_of(int,pls),
    inference(split_conjunct,[status(thm)],[fact_19_zero__is__num__zero]) ).

cnf(c_0_32,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | plus_plus(X1,power_power(X1,X3,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X1,X2,plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(X1)
    | ~ linordered_idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).

cnf(c_0_33,plain,
    plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(one_one(int))),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = pls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).

cnf(c_0_35,plain,
    ( plus_plus(X1,X2,number_number_of(X1,pls)) = ti(X1,X2)
    | ~ number_ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_36,plain,
    number_ring(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).

cnf(c_0_37,plain,
    number_number_of(int,pls) = pls,
    inference(rw,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_38,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | plus_plus(X1,power_power(X1,X3,number_number_of(nat,bit0(one_one(int)))),power_power(X1,X2,number_number_of(nat,bit0(one_one(int))))) != zero_zero(X1)
    | ~ linordered_idom(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(one_one(int)))) = pls,
    inference(rw,[status(thm)],[c_0_34,c_0_33]) ).

cnf(c_0_40,plain,
    ti(int,X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_23]) ).

cnf(c_0_41,plain,
    linordered_idom(int),
    inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]) ).

fof(c_0_42,plain,
    ~ ord_less(int,pls,pls),
    inference(fof_simplification,[status(thm)],[fact_32_rel__simps_I2_J]) ).

cnf(c_0_43,plain,
    ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).

cnf(c_0_44,negated_conjecture,
    ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls
    | power_power(int,X1,number_number_of(nat,bit0(one_one(int)))) != pls ),
    inference(cn,[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_38,c_0_39]),c_0_40]),c_0_29]),c_0_23]),c_0_29]),c_0_41])]) ).

fof(c_0_45,plain,
    ~ ord_less(int,pls,pls),
    inference(fof_nnf,[status(thm)],[c_0_42]) ).

cnf(c_0_46,plain,
    ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
    inference(rw,[status(thm)],[c_0_43,c_0_29]) ).

cnf(c_0_47,negated_conjecture,
    plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
    inference(spm,[status(thm)],[c_0_44,c_0_39]) ).

cnf(c_0_48,plain,
    ~ ord_less(int,pls,pls),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_49,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n001.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    : 300
% 0.12/0.35  % DateTime   : Sat Jun 22 23:54:54 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.19/0.49  Running first-order theorem proving
% 0.19/0.49  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.9xVFQLMyCN/E---3.1_18066.p
% 0.19/0.54  # Version: 3.2.0
% 0.19/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54  # Starting sh5l with 300s (1) cores
% 0.19/0.54  # new_bool_1 with pid 18147 completed with status 0
% 0.19/0.54  # Result found by new_bool_1
% 0.19/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.54  # Search class: FGHSM-FFLM31-MFFFFFNN
% 0.19/0.54  # Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.54  # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 109s (1) cores
% 0.19/0.54  # 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 18154 completed with status 0
% 0.19/0.54  # Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.19/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.54  # Search class: FGHSM-FFLM31-MFFFFFNN
% 0.19/0.54  # Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.54  # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 109s (1) cores
% 0.19/0.54  # Preprocessing time       : 0.002 s
% 0.19/0.54  # Presaturation interreduction done
% 0.19/0.54  
% 0.19/0.54  # Proof found!
% 0.19/0.54  # SZS status Theorem
% 0.19/0.54  # SZS output start CNFRefutation
% See solution above
% 0.19/0.54  # Parsed axioms                        : 153
% 0.19/0.54  # Removed by relevancy pruning/SinE    : 43
% 0.19/0.54  # Initial clauses                      : 148
% 0.19/0.54  # Removed in clause preprocessing      : 3
% 0.19/0.54  # Initial clauses in saturation        : 145
% 0.19/0.54  # Processed clauses                    : 674
% 0.19/0.54  # ...of these trivial                  : 13
% 0.19/0.54  # ...subsumed                          : 320
% 0.19/0.54  # ...remaining for further processing  : 341
% 0.19/0.54  # Other redundant clauses eliminated   : 6
% 0.19/0.54  # Clauses deleted for lack of memory   : 0
% 0.19/0.54  # Backward-subsumed                    : 1
% 0.19/0.54  # Backward-rewritten                   : 24
% 0.19/0.54  # Generated clauses                    : 1218
% 0.19/0.54  # ...of the previous two non-redundant : 997
% 0.19/0.54  # ...aggressively subsumed             : 0
% 0.19/0.54  # Contextual simplify-reflections      : 0
% 0.19/0.54  # Paramodulations                      : 1207
% 0.19/0.54  # Factorizations                       : 2
% 0.19/0.54  # NegExts                              : 0
% 0.19/0.54  # Equation resolutions                 : 9
% 0.19/0.54  # Disequality decompositions           : 0
% 0.19/0.54  # Total rewrite steps                  : 1460
% 0.19/0.54  # ...of those cached                   : 1317
% 0.19/0.54  # Propositional unsat checks           : 0
% 0.19/0.54  #    Propositional check models        : 0
% 0.19/0.54  #    Propositional check unsatisfiable : 0
% 0.19/0.54  #    Propositional clauses             : 0
% 0.19/0.54  #    Propositional clauses after purity: 0
% 0.19/0.54  #    Propositional unsat core size     : 0
% 0.19/0.54  #    Propositional preprocessing time  : 0.000
% 0.19/0.54  #    Propositional encoding time       : 0.000
% 0.19/0.54  #    Propositional solver time         : 0.000
% 0.19/0.54  #    Success case prop preproc time    : 0.000
% 0.19/0.54  #    Success case prop encoding time   : 0.000
% 0.19/0.54  #    Success case prop solver time     : 0.000
% 0.19/0.54  # Current number of processed clauses  : 195
% 0.19/0.54  #    Positive orientable unit clauses  : 55
% 0.19/0.54  #    Positive unorientable unit clauses: 2
% 0.19/0.54  #    Negative unit clauses             : 35
% 0.19/0.54  #    Non-unit-clauses                  : 103
% 0.19/0.54  # Current number of unprocessed clauses: 575
% 0.19/0.54  # ...number of literals in the above   : 1228
% 0.19/0.54  # Current number of archived formulas  : 0
% 0.19/0.54  # Current number of archived clauses   : 142
% 0.19/0.54  # Clause-clause subsumption calls (NU) : 1664
% 0.19/0.54  # Rec. Clause-clause subsumption calls : 1409
% 0.19/0.54  # Non-unit clause-clause subsumptions  : 75
% 0.19/0.54  # Unit Clause-clause subsumption calls : 140
% 0.19/0.54  # Rewrite failures with RHS unbound    : 0
% 0.19/0.54  # BW rewrite match attempts            : 217
% 0.19/0.54  # BW rewrite match successes           : 43
% 0.19/0.54  # Condensation attempts                : 0
% 0.19/0.54  # Condensation successes               : 0
% 0.19/0.54  # Termbank termtop insertions          : 29932
% 0.19/0.54  # Search garbage collected termcells   : 1367
% 0.19/0.54  
% 0.19/0.54  # -------------------------------------------------
% 0.19/0.54  # User time                : 0.035 s
% 0.19/0.54  # System time              : 0.005 s
% 0.19/0.54  # Total time               : 0.040 s
% 0.19/0.54  # Maximum resident set size: 2220 pages
% 0.19/0.54  
% 0.19/0.54  # -------------------------------------------------
% 0.19/0.54  # User time                : 0.037 s
% 0.19/0.54  # System time              : 0.008 s
% 0.19/0.54  # Total time               : 0.044 s
% 0.19/0.54  # Maximum resident set size: 1856 pages
% 0.19/0.54  % E---3.1 exiting
% 0.19/0.54  % E exiting
%------------------------------------------------------------------------------