TSTP Solution File: SET159+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n022.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 00:49:42 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   48 (  22 unt;   0 def)
%            Number of atoms       :   96 (  22 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   79 (  31   ~;  37   |;   7   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  129 (  13 sgn  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',subset_defn) ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',union_defn) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',equal_defn) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',commutativity_of_union) ).

fof(prove_associativity_of_union,conjecture,
    ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',prove_associativity_of_union) ).

fof(c_0_5,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])])]) ).

fof(c_0_6,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])])]) ).

cnf(c_0_7,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_9]) ).

cnf(c_0_14,plain,
    ( subset(union(X1,X2),X3)
    | member(esk1_2(union(X1,X2),X3),X1)
    | member(esk1_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( subset(X1,union(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_16,plain,
    ( subset(union(X1,X2),union(X2,X3))
    | member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_18,plain,
    subset(union(X1,X2),union(X2,union(X1,X3))),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_19,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])])]) ).

cnf(c_0_20,plain,
    ( subset(union(X1,X2),X2)
    | member(esk1_2(union(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_14]) ).

cnf(c_0_21,plain,
    ( member(X1,union(X2,union(X3,X4)))
    | ~ member(X1,union(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    ( subset(X1,union(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
    inference(spm,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_23,plain,
    ( subset(X1,union(union(X2,X3),X4))
    | ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_24,plain,
    ( subset(union(X1,X2),union(X3,X2))
    | member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

cnf(c_0_25,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    subset(union(X1,union(X1,X2)),union(X1,X2)),
    inference(spm,[status(thm)],[c_0_13,c_0_20]) ).

cnf(c_0_27,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

fof(c_0_28,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

fof(c_0_29,negated_conjecture,
    ~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    inference(assume_negation,[status(cth)],[prove_associativity_of_union]) ).

cnf(c_0_30,plain,
    ( subset(X1,union(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,union(X3,X4))),union(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_21]) ).

cnf(c_0_31,plain,
    ( subset(union(X1,X2),union(X3,union(X4,X1)))
    | member(esk1_2(union(X1,X2),union(X3,union(X4,X1))),X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_14]) ).

cnf(c_0_32,plain,
    subset(union(X1,X2),union(union(X3,X1),X2)),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_33,plain,
    union(X1,union(X1,X2)) = union(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_34,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_35,negated_conjecture,
    union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

cnf(c_0_36,plain,
    subset(union(X1,union(X2,X3)),union(X3,union(X2,X1))),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,plain,
    ( union(union(X1,X2),X3) = union(X2,X3)
    | ~ subset(union(union(X1,X2),X3),union(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_32]) ).

cnf(c_0_38,plain,
    union(X1,union(X2,X1)) = union(X2,X1),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,plain,
    union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_36])]) ).

cnf(c_0_41,plain,
    union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_27])]) ).

cnf(c_0_42,negated_conjecture,
    union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[c_0_39,c_0_34]) ).

cnf(c_0_43,plain,
    union(union(X1,X2),X3) = union(X2,union(X1,X3)),
    inference(spm,[status(thm)],[c_0_34,c_0_40]) ).

cnf(c_0_44,plain,
    union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
    inference(spm,[status(thm)],[c_0_41,c_0_34]) ).

cnf(c_0_45,negated_conjecture,
    union(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,union(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[c_0_42,c_0_40]) ).

cnf(c_0_46,plain,
    union(X1,union(X2,X3)) = union(X3,union(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_43]),c_0_44]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_34])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 02:12:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.23/1.41  # Preprocessing time       : 0.015 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 48
% 0.23/1.41  # Proof object clause steps            : 37
% 0.23/1.41  # Proof object formula steps           : 11
% 0.23/1.41  # Proof object conjectures             : 7
% 0.23/1.41  # Proof object clause conjectures      : 4
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 9
% 0.23/1.41  # Proof object initial formulas used   : 5
% 0.23/1.41  # Proof object generating inferences   : 25
% 0.23/1.41  # Proof object simplifying inferences  : 13
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 7
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 0
% 0.23/1.41  # Initial clauses                      : 16
% 0.23/1.41  # Removed in clause preprocessing      : 2
% 0.23/1.41  # Initial clauses in saturation        : 14
% 0.23/1.41  # Processed clauses                    : 2424
% 0.23/1.41  # ...of these trivial                  : 197
% 0.23/1.41  # ...subsumed                          : 1808
% 0.23/1.41  # ...remaining for further processing  : 419
% 0.23/1.41  # Other redundant clauses eliminated   : 2
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 1
% 0.23/1.41  # Backward-rewritten                   : 236
% 0.23/1.41  # Generated clauses                    : 37550
% 0.23/1.41  # ...of the previous two non-trivial   : 33817
% 0.23/1.41  # Contextual simplify-reflections      : 89
% 0.23/1.41  # Paramodulations                      : 37204
% 0.23/1.41  # Factorizations                       : 344
% 0.23/1.41  # Equation resolutions                 : 2
% 0.23/1.41  # Current number of processed clauses  : 180
% 0.23/1.41  #    Positive orientable unit clauses  : 33
% 0.23/1.41  #    Positive unorientable unit clauses: 3
% 0.23/1.41  #    Negative unit clauses             : 0
% 0.23/1.41  #    Non-unit-clauses                  : 144
% 0.23/1.41  # Current number of unprocessed clauses: 7196
% 0.23/1.41  # ...number of literals in the above   : 20195
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 237
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 68070
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 48288
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 1874
% 0.23/1.41  # Unit Clause-clause subsumption calls : 4123
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 2371
% 0.23/1.41  # BW rewrite match successes           : 438
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 745830
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.430 s
% 0.23/1.41  # System time              : 0.016 s
% 0.23/1.41  # Total time               : 0.446 s
% 0.23/1.41  # Maximum resident set size: 30224 pages
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
% 0.23/23.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48  eprover: No such file or directory
%------------------------------------------------------------------------------