TSTP Solution File: SEU056+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n004.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  : 600s
% DateTime : Tue Jul 19 09:16:38 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   46 (  24 unt;   0 def)
%            Number of atoms       :   85 (  31 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   62 (  23   ~;  19   |;  10   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   57 (   6 sgn  32   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_xboole_0) ).

fof(t125_funct_1,conjecture,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( ( disjoint(X1,X2)
          & one_to_one(X3) )
       => disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t125_funct_1) ).

fof(t2_boole,axiom,
    ! [X1] : set_intersection2(X1,empty_set) = empty_set,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_boole) ).

fof(t121_funct_1,axiom,
    ! [X1,X2,X3] :
      ( ( relation(X3)
        & function(X3) )
     => ( one_to_one(X3)
       => relation_image(X3,set_intersection2(X1,X2)) = set_intersection2(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t121_funct_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).

fof(d7_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d7_xboole_0) ).

fof(symmetry_r1_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetry_r1_xboole_0) ).

fof(t149_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => relation_image(X1,empty_set) = empty_set ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t149_relat_1) ).

fof(c_0_9,plain,
    ! [X2] :
      ( ~ empty(X2)
      | X2 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_10,plain,
    empty(esk9_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( relation(X3)
          & function(X3) )
       => ( ( disjoint(X1,X2)
            & one_to_one(X3) )
         => disjoint(relation_image(X3,X1),relation_image(X3,X2)) ) ),
    inference(assume_negation,[status(cth)],[t125_funct_1]) ).

fof(c_0_12,plain,
    ! [X2] : set_intersection2(X2,empty_set) = empty_set,
    inference(variable_rename,[status(thm)],[t2_boole]) ).

cnf(c_0_13,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    empty(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,plain,
    ! [X4,X5,X6] :
      ( ~ relation(X6)
      | ~ function(X6)
      | ~ one_to_one(X6)
      | relation_image(X6,set_intersection2(X4,X5)) = set_intersection2(relation_image(X6,X4),relation_image(X6,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t121_funct_1])]) ).

fof(c_0_16,negated_conjecture,
    ( relation(esk3_0)
    & function(esk3_0)
    & disjoint(esk1_0,esk2_0)
    & one_to_one(esk3_0)
    & ~ disjoint(relation_image(esk3_0,esk1_0),relation_image(esk3_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_17,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_18,plain,
    set_intersection2(X1,empty_set) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    empty_set = esk9_0,
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_20,plain,
    ! [X3,X4,X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_intersection2(X3,X4) = empty_set )
      & ( set_intersection2(X3,X4) != empty_set
        | disjoint(X3,X4) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])])]) ).

fof(c_0_21,plain,
    ! [X3,X4] :
      ( ~ disjoint(X3,X4)
      | disjoint(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).

cnf(c_0_22,plain,
    ( relation_image(X1,set_intersection2(X2,X3)) = set_intersection2(relation_image(X1,X2),relation_image(X1,X3))
    | ~ one_to_one(X1)
    | ~ function(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,negated_conjecture,
    one_to_one(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    function(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,plain,
    set_intersection2(X1,esk9_0) = esk9_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).

fof(c_0_28,plain,
    ! [X2] :
      ( ~ relation(X2)
      | relation_image(X2,empty_set) = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t149_relat_1])]) ).

cnf(c_0_29,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,plain,
    ( disjoint(X1,X2)
    | ~ disjoint(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,negated_conjecture,
    disjoint(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_32,negated_conjecture,
    relation_image(esk3_0,set_intersection2(X1,X2)) = set_intersection2(relation_image(esk3_0,X1),relation_image(esk3_0,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).

cnf(c_0_33,plain,
    set_intersection2(esk9_0,X1) = esk9_0,
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,plain,
    ( relation_image(X1,empty_set) = empty_set
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_35,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_36,plain,
    ( set_intersection2(X1,X2) = esk9_0
    | ~ disjoint(X1,X2) ),
    inference(rw,[status(thm)],[c_0_29,c_0_19]) ).

cnf(c_0_37,negated_conjecture,
    disjoint(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    set_intersection2(relation_image(esk3_0,esk9_0),relation_image(esk3_0,X1)) = relation_image(esk3_0,esk9_0),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    ( relation_image(X1,esk9_0) = esk9_0
    | ~ relation(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_19]),c_0_19]) ).

cnf(c_0_40,negated_conjecture,
    ~ disjoint(relation_image(esk3_0,esk1_0),relation_image(esk3_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_41,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != esk9_0 ),
    inference(rw,[status(thm)],[c_0_35,c_0_19]) ).

cnf(c_0_42,negated_conjecture,
    set_intersection2(esk1_0,esk2_0) = esk9_0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26]) ).

cnf(c_0_43,negated_conjecture,
    relation_image(esk3_0,esk9_0) = esk9_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_27]),c_0_24])]) ).

cnf(c_0_44,negated_conjecture,
    set_intersection2(relation_image(esk3_0,esk1_0),relation_image(esk3_0,esk2_0)) != esk9_0,
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_42]),c_0_43]),c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 20:18:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.016 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 46
% 0.22/1.40  # Proof object clause steps            : 27
% 0.22/1.40  # Proof object formula steps           : 19
% 0.22/1.40  # Proof object conjectures             : 15
% 0.22/1.40  # Proof object clause conjectures      : 12
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 14
% 0.22/1.40  # Proof object initial formulas used   : 9
% 0.22/1.40  # Proof object generating inferences   : 9
% 0.22/1.40  # Proof object simplifying inferences  : 15
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 37
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 14
% 0.22/1.40  # Initial clauses                      : 38
% 0.22/1.40  # Removed in clause preprocessing      : 2
% 0.22/1.40  # Initial clauses in saturation        : 36
% 0.22/1.40  # Processed clauses                    : 67
% 0.22/1.40  # ...of these trivial                  : 4
% 0.22/1.40  # ...subsumed                          : 5
% 0.22/1.40  # ...remaining for further processing  : 58
% 0.22/1.40  # Other redundant clauses eliminated   : 0
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 0
% 0.22/1.40  # Backward-rewritten                   : 16
% 0.22/1.40  # Generated clauses                    : 77
% 0.22/1.40  # ...of the previous two non-trivial   : 62
% 0.22/1.40  # Contextual simplify-reflections      : 4
% 0.22/1.40  # Paramodulations                      : 77
% 0.22/1.40  # Factorizations                       : 0
% 0.22/1.40  # Equation resolutions                 : 0
% 0.22/1.40  # Current number of processed clauses  : 42
% 0.22/1.40  #    Positive orientable unit clauses  : 25
% 0.22/1.40  #    Positive unorientable unit clauses: 1
% 0.22/1.40  #    Negative unit clauses             : 4
% 0.22/1.40  #    Non-unit-clauses                  : 12
% 0.22/1.40  # Current number of unprocessed clauses: 12
% 0.22/1.40  # ...number of literals in the above   : 17
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 16
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 24
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 23
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 9
% 0.22/1.40  # Unit Clause-clause subsumption calls : 6
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 9
% 0.22/1.40  # BW rewrite match successes           : 9
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 2265
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.018 s
% 0.22/1.40  # System time              : 0.001 s
% 0.22/1.40  # Total time               : 0.019 s
% 0.22/1.40  # Maximum resident set size: 2968 pages
%------------------------------------------------------------------------------