TSTP Solution File: SEU212+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SEU212+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:30:55 EDT 2023

% Result   : Theorem 0.21s 0.52s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :  129 (  36 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  161 (  62   ~;  64   |;  18   &)
%                                         (   8 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   53 (   2 sgn;  29   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t8_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( in(ordered_pair(X1,X2),X3)
      <=> ( in(X1,relation_dom(X3))
          & X2 = apply(X3,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.o88yVTbVnU/E---3.1_18642.p',t8_funct_1) ).

fof(d4_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.o88yVTbVnU/E---3.1_18642.p',d4_funct_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/tmp/tmp.o88yVTbVnU/E---3.1_18642.p',d5_tarski) ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.o88yVTbVnU/E---3.1_18642.p',d4_relat_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( in(ordered_pair(X1,X2),X3)
        <=> ( in(X1,relation_dom(X3))
            & X2 = apply(X3,X1) ) ) ),
    inference(assume_negation,[status(cth)],[t8_funct_1]) ).

fof(c_0_5,plain,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_funct_1]) ).

fof(c_0_6,negated_conjecture,
    ( relation(esk15_0)
    & function(esk15_0)
    & ( ~ in(ordered_pair(esk13_0,esk14_0),esk15_0)
      | ~ in(esk13_0,relation_dom(esk15_0))
      | esk14_0 != apply(esk15_0,esk13_0) )
    & ( in(esk13_0,relation_dom(esk15_0))
      | in(ordered_pair(esk13_0,esk14_0),esk15_0) )
    & ( esk14_0 = apply(esk15_0,esk13_0)
      | in(ordered_pair(esk13_0,esk14_0),esk15_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_7,plain,
    ! [X24,X25] : ordered_pair(X24,X25) = unordered_pair(unordered_pair(X24,X25),singleton(X24)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_8,plain,
    ! [X11,X12,X13] :
      ( ( X13 != apply(X11,X12)
        | in(ordered_pair(X12,X13),X11)
        | ~ in(X12,relation_dom(X11))
        | ~ relation(X11)
        | ~ function(X11) )
      & ( ~ in(ordered_pair(X12,X13),X11)
        | X13 = apply(X11,X12)
        | ~ in(X12,relation_dom(X11))
        | ~ relation(X11)
        | ~ function(X11) )
      & ( X13 != apply(X11,X12)
        | X13 = empty_set
        | in(X12,relation_dom(X11))
        | ~ relation(X11)
        | ~ function(X11) )
      & ( X13 != empty_set
        | X13 = apply(X11,X12)
        | in(X12,relation_dom(X11))
        | ~ relation(X11)
        | ~ function(X11) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).

cnf(c_0_9,negated_conjecture,
    ( ~ in(ordered_pair(esk13_0,esk14_0),esk15_0)
    | ~ in(esk13_0,relation_dom(esk15_0))
    | esk14_0 != apply(esk15_0,esk13_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( in(ordered_pair(X3,X1),X2)
    | X1 != apply(X2,X3)
    | ~ in(X3,relation_dom(X2))
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( X2 = apply(X3,X1)
    | ~ in(ordered_pair(X1,X2),X3)
    | ~ in(X1,relation_dom(X3))
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( esk14_0 = apply(esk15_0,esk13_0)
    | in(ordered_pair(esk13_0,esk14_0),esk15_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    ( esk14_0 != apply(esk15_0,esk13_0)
    | ~ in(esk13_0,relation_dom(esk15_0))
    | ~ in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    ( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
    | X1 != apply(X2,X3)
    | ~ function(X2)
    | ~ relation(X2)
    | ~ in(X3,relation_dom(X2)) ),
    inference(rw,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    relation(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,negated_conjecture,
    function(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_18,plain,
    ! [X14,X15,X16,X18,X19,X20,X22] :
      ( ( ~ in(X16,X15)
        | in(ordered_pair(X16,esk1_3(X14,X15,X16)),X14)
        | X15 != relation_dom(X14)
        | ~ relation(X14) )
      & ( ~ in(ordered_pair(X18,X19),X14)
        | in(X18,X15)
        | X15 != relation_dom(X14)
        | ~ relation(X14) )
      & ( ~ in(esk2_2(X14,X20),X20)
        | ~ in(ordered_pair(esk2_2(X14,X20),X22),X14)
        | X20 = relation_dom(X14)
        | ~ relation(X14) )
      & ( in(esk2_2(X14,X20),X20)
        | in(ordered_pair(esk2_2(X14,X20),esk3_2(X14,X20)),X14)
        | X20 = relation_dom(X14)
        | ~ relation(X14) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).

cnf(c_0_19,negated_conjecture,
    ( in(esk13_0,relation_dom(esk15_0))
    | in(ordered_pair(esk13_0,esk14_0),esk15_0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,plain,
    ( X2 = apply(X3,X1)
    | ~ function(X3)
    | ~ relation(X3)
    | ~ in(X1,relation_dom(X3))
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_21,negated_conjecture,
    ( esk14_0 = apply(esk15_0,esk13_0)
    | in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
    inference(rw,[status(thm)],[c_0_13,c_0_10]) ).

cnf(c_0_22,negated_conjecture,
    ( apply(esk15_0,esk13_0) != esk14_0
    | ~ in(esk13_0,relation_dom(esk15_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_23,plain,
    ( in(X1,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,negated_conjecture,
    ( in(esk13_0,relation_dom(esk15_0))
    | in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0) ),
    inference(rw,[status(thm)],[c_0_19,c_0_10]) ).

cnf(c_0_25,negated_conjecture,
    ~ in(esk13_0,relation_dom(esk15_0)),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16]),c_0_17])]),c_0_22]) ).

cnf(c_0_26,plain,
    ( in(X1,X4)
    | X4 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_23,c_0_10]) ).

cnf(c_0_27,negated_conjecture,
    in(unordered_pair(unordered_pair(esk13_0,esk14_0),singleton(esk13_0)),esk15_0),
    inference(sr,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    ( in(esk13_0,X1)
    | X1 != relation_dom(esk15_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16])]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : SEU212+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % 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
% 0.15/0.37  % CPULimit   : 2400
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon Oct  2 08:36:05 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.21/0.50  Running first-order model finding
% 0.21/0.50  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.o88yVTbVnU/E---3.1_18642.p
% 0.21/0.52  # Version: 3.1pre001
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.52  # Starting sh5l with 300s (1) cores
% 0.21/0.52  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 18719 completed with status 0
% 0.21/0.52  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.21/0.52  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.52  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 113s (1) cores
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.21/0.52  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.21/0.52  # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.21/0.52  # Starting U----_206c_02_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 0.21/0.52  # G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 18729 completed with status 0
% 0.21/0.52  # Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 0.21/0.52  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.52  # No SInE strategy applied
% 0.21/0.52  # Search class: FGHSM-FFMM31-MFFFFFNN
% 0.21/0.52  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.52  # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 113s (1) cores
% 0.21/0.52  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.21/0.52  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 0.21/0.52  # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 0.21/0.52  # Preprocessing time       : 0.001 s
% 0.21/0.52  
% 0.21/0.52  # Proof found!
% 0.21/0.52  # SZS status Theorem
% 0.21/0.52  # SZS output start CNFRefutation
% See solution above
% 0.21/0.52  # Parsed axioms                        : 35
% 0.21/0.52  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.52  # Initial clauses                      : 56
% 0.21/0.52  # Removed in clause preprocessing      : 1
% 0.21/0.52  # Initial clauses in saturation        : 55
% 0.21/0.52  # Processed clauses                    : 77
% 0.21/0.52  # ...of these trivial                  : 3
% 0.21/0.52  # ...subsumed                          : 6
% 0.21/0.52  # ...remaining for further processing  : 68
% 0.21/0.52  # Other redundant clauses eliminated   : 0
% 0.21/0.52  # Clauses deleted for lack of memory   : 0
% 0.21/0.52  # Backward-subsumed                    : 9
% 0.21/0.52  # Backward-rewritten                   : 2
% 0.21/0.52  # Generated clauses                    : 104
% 0.21/0.52  # ...of the previous two non-redundant : 91
% 0.21/0.52  # ...aggressively subsumed             : 0
% 0.21/0.52  # Contextual simplify-reflections      : 2
% 0.21/0.52  # Paramodulations                      : 100
% 0.21/0.52  # Factorizations                       : 0
% 0.21/0.52  # NegExts                              : 0
% 0.21/0.52  # Equation resolutions                 : 3
% 0.21/0.52  # Total rewrite steps                  : 25
% 0.21/0.52  # Propositional unsat checks           : 0
% 0.21/0.52  #    Propositional check models        : 0
% 0.21/0.52  #    Propositional check unsatisfiable : 0
% 0.21/0.52  #    Propositional clauses             : 0
% 0.21/0.52  #    Propositional clauses after purity: 0
% 0.21/0.52  #    Propositional unsat core size     : 0
% 0.21/0.52  #    Propositional preprocessing time  : 0.000
% 0.21/0.52  #    Propositional encoding time       : 0.000
% 0.21/0.52  #    Propositional solver time         : 0.000
% 0.21/0.52  #    Success case prop preproc time    : 0.000
% 0.21/0.52  #    Success case prop encoding time   : 0.000
% 0.21/0.52  #    Success case prop solver time     : 0.000
% 0.21/0.52  # Current number of processed clauses  : 56
% 0.21/0.52  #    Positive orientable unit clauses  : 17
% 0.21/0.52  #    Positive unorientable unit clauses: 1
% 0.21/0.52  #    Negative unit clauses             : 8
% 0.21/0.52  #    Non-unit-clauses                  : 30
% 0.21/0.52  # Current number of unprocessed clauses: 65
% 0.21/0.52  # ...number of literals in the above   : 210
% 0.21/0.52  # Current number of archived formulas  : 0
% 0.21/0.52  # Current number of archived clauses   : 13
% 0.21/0.52  # Clause-clause subsumption calls (NU) : 203
% 0.21/0.52  # Rec. Clause-clause subsumption calls : 162
% 0.21/0.52  # Non-unit clause-clause subsumptions  : 8
% 0.21/0.52  # Unit Clause-clause subsumption calls : 77
% 0.21/0.52  # Rewrite failures with RHS unbound    : 0
% 0.21/0.52  # BW rewrite match attempts            : 4
% 0.21/0.52  # BW rewrite match successes           : 4
% 0.21/0.52  # Condensation attempts                : 0
% 0.21/0.52  # Condensation successes               : 0
% 0.21/0.52  # Termbank termtop insertions          : 3605
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.009 s
% 0.21/0.52  # System time              : 0.002 s
% 0.21/0.52  # Total time               : 0.011 s
% 0.21/0.52  # Maximum resident set size: 1848 pages
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.029 s
% 0.21/0.52  # System time              : 0.011 s
% 0.21/0.52  # Total time               : 0.040 s
% 0.21/0.52  # Maximum resident set size: 1700 pages
% 0.21/0.52  % E---3.1 exiting
%------------------------------------------------------------------------------