TSTP Solution File: NUN067+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : NUN067+1 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 : Tue May 21 02:15:52 EDT 2024

% Result   : Theorem 0.22s 0.50s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   35 (   8 unt;   0 def)
%            Number of atoms       :  107 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  135 (  63   ~;  50   |;  22   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   70 (   9 sgn  42   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_8,axiom,
    ! [X20,X21] :
      ( ~ id(X20,X21)
      | ( ~ r1(X20)
        & ~ r1(X21) )
      | ( r1(X20)
        & r1(X21) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).

fof(nonzerosexistid,conjecture,
    ? [X63] :
    ! [X46] :
      ( ~ id(X63,X46)
      | ~ r1(X46) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosexistid) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( id(X2,X1)
        & r1(X2) )
      | ( ~ r1(X2)
        & ~ id(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).

fof(axiom_6,axiom,
    ! [X15,X16] :
      ( ~ id(X15,X16)
      | id(X16,X15) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).

fof(axiom_7,axiom,
    ! [X17,X18,X19] :
      ( ~ id(X17,X18)
      | id(X17,X19)
      | ~ id(X18,X19) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( id(X5,X4)
        & r2(X3,X5) )
      | ( ~ r2(X3,X5)
        & ~ id(X5,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).

fof(axiom_7a,axiom,
    ! [X65,X66] :
      ( ! [X67] :
          ( ~ id(X67,X66)
          | ~ r1(X67) )
      | ~ r2(X65,X66) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).

fof(c_0_7,plain,
    ! [X20,X21] :
      ( ~ id(X20,X21)
      | ( ~ r1(X20)
        & ~ r1(X21) )
      | ( r1(X20)
        & r1(X21) ) ),
    inference(fof_simplification,[status(thm)],[axiom_8]) ).

fof(c_0_8,negated_conjecture,
    ~ ? [X63] :
      ! [X46] :
        ( ~ id(X63,X46)
        | ~ r1(X46) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nonzerosexistid])]) ).

fof(c_0_9,plain,
    ? [X1] :
    ! [X2] :
      ( ( id(X2,X1)
        & r1(X2) )
      | ( ~ r1(X2)
        & ~ id(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(c_0_10,plain,
    ! [X72,X73] :
      ( ( r1(X72)
        | ~ r1(X72)
        | ~ id(X72,X73) )
      & ( r1(X73)
        | ~ r1(X72)
        | ~ id(X72,X73) )
      & ( r1(X72)
        | ~ r1(X73)
        | ~ id(X72,X73) )
      & ( r1(X73)
        | ~ r1(X73)
        | ~ id(X72,X73) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,negated_conjecture,
    ! [X68] :
      ( id(X68,esk1_1(X68))
      & r1(esk1_1(X68)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_12,plain,
    ! [X15,X16] :
      ( ~ id(X15,X16)
      | id(X16,X15) ),
    inference(fof_simplification,[status(thm)],[axiom_6]) ).

fof(c_0_13,plain,
    ! [X71] :
      ( ( ~ r1(X71)
        | id(X71,esk2_0) )
      & ( ~ id(X71,esk2_0)
        | id(X71,esk2_0) )
      & ( ~ r1(X71)
        | r1(X71) )
      & ( ~ id(X71,esk2_0)
        | r1(X71) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])])]) ).

cnf(c_0_14,plain,
    ( r1(X1)
    | ~ r1(X2)
    | ~ id(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    id(X1,esk1_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    r1(esk1_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_17,plain,
    ! [X17,X18,X19] :
      ( ~ id(X17,X18)
      | id(X17,X19)
      | ~ id(X18,X19) ),
    inference(fof_simplification,[status(thm)],[axiom_7]) ).

fof(c_0_18,plain,
    ! [X85,X86] :
      ( ~ id(X85,X86)
      | id(X86,X85) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).

cnf(c_0_19,plain,
    ( id(X1,esk2_0)
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    r1(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).

fof(c_0_21,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( id(X5,X4)
        & r2(X3,X5) )
      | ( ~ r2(X3,X5)
        & ~ id(X5,X4) ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_22,plain,
    ! [X87,X88,X89] :
      ( ~ id(X87,X88)
      | id(X87,X89)
      | ~ id(X88,X89) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).

cnf(c_0_23,plain,
    ( id(X2,X1)
    | ~ id(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    id(X1,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).

fof(c_0_25,plain,
    ! [X65,X66] :
      ( ! [X67] :
          ( ~ id(X67,X66)
          | ~ r1(X67) )
      | ~ r2(X65,X66) ),
    inference(fof_simplification,[status(thm)],[axiom_7a]) ).

fof(c_0_26,plain,
    ! [X112,X114] :
      ( ( ~ r2(X112,X114)
        | id(X114,esk17_1(X112)) )
      & ( ~ id(X114,esk17_1(X112))
        | id(X114,esk17_1(X112)) )
      & ( ~ r2(X112,X114)
        | r2(X112,X114) )
      & ( ~ id(X114,esk17_1(X112))
        | r2(X112,X114) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])])]) ).

cnf(c_0_27,plain,
    ( id(X1,X3)
    | ~ id(X1,X2)
    | ~ id(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,plain,
    id(esk2_0,X1),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

fof(c_0_29,plain,
    ! [X81,X82,X83] :
      ( ~ id(X83,X82)
      | ~ r1(X83)
      | ~ r2(X81,X82) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_25])])]) ).

cnf(c_0_30,plain,
    ( r2(X2,X1)
    | ~ id(X1,esk17_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    id(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).

cnf(c_0_32,plain,
    ( ~ id(X1,X2)
    | ~ r1(X1)
    | ~ r2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,plain,
    r2(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).

cnf(c_0_34,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_20])]),c_0_33]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : NUN067+1 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 15:04:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.22/0.48  Running first-order model finding
% 0.22/0.48  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50  # Version: 3.1.0
% 0.22/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.50  # Starting sh5l with 300s (1) cores
% 0.22/0.50  # new_bool_3 with pid 29177 completed with status 0
% 0.22/0.50  # Result found by new_bool_3
% 0.22/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.50  # Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_S1S with 155s (1) cores
% 0.22/0.50  # H----_102_C18_F1_PI_AE_Q4_CS_SP_S1S with pid 29183 completed with status 0
% 0.22/0.50  # Result found by H----_102_C18_F1_PI_AE_Q4_CS_SP_S1S
% 0.22/0.50  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.50  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.50  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.50  # Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/0.50  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.50  # Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_S1S with 155s (1) cores
% 0.22/0.50  # Preprocessing time       : 0.001 s
% 0.22/0.50  
% 0.22/0.50  # Proof found!
% 0.22/0.50  # SZS status Theorem
% 0.22/0.50  # SZS output start CNFRefutation
% See solution above
% 0.22/0.50  # Parsed axioms                        : 19
% 0.22/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.22/0.50  # Initial clauses                      : 60
% 0.22/0.50  # Removed in clause preprocessing      : 16
% 0.22/0.50  # Initial clauses in saturation        : 44
% 0.22/0.50  # Processed clauses                    : 51
% 0.22/0.50  # ...of these trivial                  : 0
% 0.22/0.50  # ...subsumed                          : 0
% 0.22/0.50  # ...remaining for further processing  : 50
% 0.22/0.50  # Other redundant clauses eliminated   : 0
% 0.22/0.50  # Clauses deleted for lack of memory   : 0
% 0.22/0.50  # Backward-subsumed                    : 0
% 0.22/0.50  # Backward-rewritten                   : 43
% 0.22/0.50  # Generated clauses                    : 108
% 0.22/0.50  # ...of the previous two non-redundant : 111
% 0.22/0.50  # ...aggressively subsumed             : 0
% 0.22/0.50  # Contextual simplify-reflections      : 0
% 0.22/0.50  # Paramodulations                      : 108
% 0.22/0.50  # Factorizations                       : 0
% 0.22/0.50  # NegExts                              : 0
% 0.22/0.50  # Equation resolutions                 : 0
% 0.22/0.50  # Disequality decompositions           : 0
% 0.22/0.50  # Total rewrite steps                  : 70
% 0.22/0.50  # ...of those cached                   : 20
% 0.22/0.50  # Propositional unsat checks           : 0
% 0.22/0.50  #    Propositional check models        : 0
% 0.22/0.50  #    Propositional check unsatisfiable : 0
% 0.22/0.50  #    Propositional clauses             : 0
% 0.22/0.50  #    Propositional clauses after purity: 0
% 0.22/0.50  #    Propositional unsat core size     : 0
% 0.22/0.50  #    Propositional preprocessing time  : 0.000
% 0.22/0.50  #    Propositional encoding time       : 0.000
% 0.22/0.50  #    Propositional solver time         : 0.000
% 0.22/0.50  #    Success case prop preproc time    : 0.000
% 0.22/0.50  #    Success case prop encoding time   : 0.000
% 0.22/0.50  #    Success case prop solver time     : 0.000
% 0.22/0.50  # Current number of processed clauses  : 7
% 0.22/0.50  #    Positive orientable unit clauses  : 7
% 0.22/0.50  #    Positive unorientable unit clauses: 0
% 0.22/0.50  #    Negative unit clauses             : 0
% 0.22/0.50  #    Non-unit-clauses                  : 0
% 0.22/0.50  # Current number of unprocessed clauses: 53
% 0.22/0.50  # ...number of literals in the above   : 163
% 0.22/0.50  # Current number of archived formulas  : 0
% 0.22/0.50  # Current number of archived clauses   : 43
% 0.22/0.50  # Clause-clause subsumption calls (NU) : 105
% 0.22/0.50  # Rec. Clause-clause subsumption calls : 63
% 0.22/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.22/0.50  # Unit Clause-clause subsumption calls : 24
% 0.22/0.50  # Rewrite failures with RHS unbound    : 0
% 0.22/0.50  # BW rewrite match attempts            : 48
% 0.22/0.50  # BW rewrite match successes           : 45
% 0.22/0.50  # Condensation attempts                : 0
% 0.22/0.50  # Condensation successes               : 0
% 0.22/0.50  # Termbank termtop insertions          : 3553
% 0.22/0.50  # Search garbage collected termcells   : 364
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.008 s
% 0.22/0.50  # System time              : 0.003 s
% 0.22/0.50  # Total time               : 0.010 s
% 0.22/0.50  # Maximum resident set size: 1912 pages
% 0.22/0.50  
% 0.22/0.50  # -------------------------------------------------
% 0.22/0.50  # User time                : 0.009 s
% 0.22/0.50  # System time              : 0.005 s
% 0.22/0.50  # Total time               : 0.014 s
% 0.22/0.50  # Maximum resident set size: 1772 pages
% 0.22/0.50  % E---3.1 exiting
%------------------------------------------------------------------------------