TSTP Solution File: SET595+3 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SET595+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 19:19:29 EDT 2023

% Result   : Theorem 3.07s 0.88s
% Output   : CNFRefutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   39 (   8 unt;   0 def)
%            Number of atoms       :  101 (  13 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   96 (  34   ~;  42   |;  12   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   86 (   4 sgn;  35   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th54,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => X2 = union(X1,difference(X2,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',prove_th54) ).

fof(difference_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',difference_defn) ).

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',subset_defn) ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',union_defn) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',commutativity_of_union) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.EQm5IUj4RC/E---3.1_7995.p',equal_defn) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => X2 = union(X1,difference(X2,X1)) ),
    inference(assume_negation,[status(cth)],[prove_th54]) ).

fof(c_0_7,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[difference_defn]) ).

fof(c_0_8,plain,
    ! [X13,X14,X15,X16,X17] :
      ( ( ~ subset(X13,X14)
        | ~ member(X15,X13)
        | member(X15,X14) )
      & ( member(esk2_2(X16,X17),X16)
        | subset(X16,X17) )
      & ( ~ member(esk2_2(X16,X17),X17)
        | subset(X16,X17) ) ),
    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)],[subset_defn])])])])])]) ).

fof(c_0_9,negated_conjecture,
    ( subset(esk4_0,esk5_0)
    & esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_10,plain,
    ! [X7,X8,X9] :
      ( ( ~ member(X9,union(X7,X8))
        | member(X9,X7)
        | member(X9,X8) )
      & ( ~ member(X9,X7)
        | member(X9,union(X7,X8)) )
      & ( ~ member(X9,X8)
        | member(X9,union(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).

fof(c_0_11,plain,
    ! [X10,X11,X12] :
      ( ( member(X12,X10)
        | ~ member(X12,difference(X10,X11)) )
      & ( ~ member(X12,X11)
        | ~ member(X12,difference(X10,X11)) )
      & ( ~ member(X12,X10)
        | member(X12,X11)
        | member(X12,difference(X10,X11)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

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

cnf(c_0_13,negated_conjecture,
    subset(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( subset(X1,X2)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( member(X1,X3)
    | member(X1,difference(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( member(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    ( member(X1,esk5_0)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_20,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_21,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk2_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    ( subset(X1,X2)
    | member(esk2_2(X1,X2),difference(X1,X3))
    | member(esk2_2(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( subset(X1,esk5_0)
    | ~ member(esk2_2(X1,esk5_0),esk4_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_24,plain,
    ( subset(union(X1,X2),X3)
    | member(esk2_2(union(X1,X2),X3),X1)
    | member(esk2_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_17]) ).

fof(c_0_25,plain,
    ! [X21,X22] : union(X21,X22) = union(X22,X21),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

fof(c_0_26,plain,
    ! [X19,X20] :
      ( ( subset(X19,X20)
        | X19 != X20 )
      & ( subset(X20,X19)
        | X19 != X20 )
      & ( ~ subset(X19,X20)
        | ~ subset(X20,X19)
        | X19 = X20 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

cnf(c_0_27,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk2_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_20]) ).

cnf(c_0_28,plain,
    ( subset(X1,union(X2,difference(X1,X3)))
    | member(esk2_2(X1,union(X2,difference(X1,X3))),X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_29,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,negated_conjecture,
    ( subset(union(X1,esk4_0),esk5_0)
    | member(esk2_2(union(X1,esk4_0),esk5_0),X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    subset(X1,union(X2,difference(X1,X2))),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    ( subset(union(esk4_0,difference(X1,X2)),esk5_0)
    | member(esk2_2(union(esk4_0,difference(X1,X2)),esk5_0),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31]) ).

cnf(c_0_35,plain,
    ( union(X1,difference(X2,X1)) = X2
    | ~ subset(union(X1,difference(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    subset(union(esk4_0,difference(esk5_0,X1)),esk5_0),
    inference(spm,[status(thm)],[c_0_14,c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET595+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 2400
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Oct  2 17:38:51 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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.EQm5IUj4RC/E---3.1_7995.p
% 3.07/0.88  # Version: 3.1pre001
% 3.07/0.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.07/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.07/0.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.07/0.88  # Starting new_bool_3 with 300s (1) cores
% 3.07/0.88  # Starting new_bool_1 with 300s (1) cores
% 3.07/0.88  # Starting sh5l with 300s (1) cores
% 3.07/0.88  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8073 completed with status 0
% 3.07/0.88  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.07/0.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.07/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.07/0.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.07/0.88  # No SInE strategy applied
% 3.07/0.88  # Search class: FGHSS-FFSF22-SFFFFFNN
% 3.07/0.88  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.07/0.88  # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 3.07/0.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.07/0.88  # Starting new_bool_3 with 136s (1) cores
% 3.07/0.88  # Starting new_bool_1 with 136s (1) cores
% 3.07/0.88  # Starting sh5l with 136s (1) cores
% 3.07/0.88  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 8078 completed with status 0
% 3.07/0.88  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.07/0.88  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.07/0.88  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.07/0.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.07/0.88  # No SInE strategy applied
% 3.07/0.88  # Search class: FGHSS-FFSF22-SFFFFFNN
% 3.07/0.88  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.07/0.88  # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 811s (1) cores
% 3.07/0.88  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.07/0.88  # Preprocessing time       : 0.001 s
% 3.07/0.88  # Presaturation interreduction done
% 3.07/0.88  
% 3.07/0.88  # Proof found!
% 3.07/0.88  # SZS status Theorem
% 3.07/0.88  # SZS output start CNFRefutation
% See solution above
% 3.07/0.88  # Parsed axioms                        : 9
% 3.07/0.88  # Removed by relevancy pruning/SinE    : 0
% 3.07/0.88  # Initial clauses                      : 22
% 3.07/0.88  # Removed in clause preprocessing      : 2
% 3.07/0.88  # Initial clauses in saturation        : 20
% 3.07/0.88  # Processed clauses                    : 3494
% 3.07/0.88  # ...of these trivial                  : 337
% 3.07/0.88  # ...subsumed                          : 2543
% 3.07/0.88  # ...remaining for further processing  : 614
% 3.07/0.88  # Other redundant clauses eliminated   : 2
% 3.07/0.88  # Clauses deleted for lack of memory   : 0
% 3.07/0.88  # Backward-subsumed                    : 5
% 3.07/0.88  # Backward-rewritten                   : 70
% 3.07/0.88  # Generated clauses                    : 33621
% 3.07/0.88  # ...of the previous two non-redundant : 29873
% 3.07/0.88  # ...aggressively subsumed             : 0
% 3.07/0.88  # Contextual simplify-reflections      : 8
% 3.07/0.88  # Paramodulations                      : 33173
% 3.07/0.88  # Factorizations                       : 446
% 3.07/0.88  # NegExts                              : 0
% 3.07/0.88  # Equation resolutions                 : 2
% 3.07/0.88  # Total rewrite steps                  : 21670
% 3.07/0.88  # Propositional unsat checks           : 0
% 3.07/0.88  #    Propositional check models        : 0
% 3.07/0.88  #    Propositional check unsatisfiable : 0
% 3.07/0.88  #    Propositional clauses             : 0
% 3.07/0.88  #    Propositional clauses after purity: 0
% 3.07/0.88  #    Propositional unsat core size     : 0
% 3.07/0.88  #    Propositional preprocessing time  : 0.000
% 3.07/0.88  #    Propositional encoding time       : 0.000
% 3.07/0.88  #    Propositional solver time         : 0.000
% 3.07/0.88  #    Success case prop preproc time    : 0.000
% 3.07/0.88  #    Success case prop encoding time   : 0.000
% 3.07/0.88  #    Success case prop solver time     : 0.000
% 3.07/0.88  # Current number of processed clauses  : 519
% 3.07/0.88  #    Positive orientable unit clauses  : 104
% 3.07/0.88  #    Positive unorientable unit clauses: 15
% 3.07/0.88  #    Negative unit clauses             : 2
% 3.07/0.88  #    Non-unit-clauses                  : 398
% 3.07/0.88  # Current number of unprocessed clauses: 26282
% 3.07/0.88  # ...number of literals in the above   : 92677
% 3.07/0.88  # Current number of archived formulas  : 0
% 3.07/0.88  # Current number of archived clauses   : 93
% 3.07/0.88  # Clause-clause subsumption calls (NU) : 37486
% 3.07/0.88  # Rec. Clause-clause subsumption calls : 15628
% 3.07/0.88  # Non-unit clause-clause subsumptions  : 1502
% 3.07/0.88  # Unit Clause-clause subsumption calls : 5756
% 3.07/0.88  # Rewrite failures with RHS unbound    : 0
% 3.07/0.88  # BW rewrite match attempts            : 1091
% 3.07/0.88  # BW rewrite match successes           : 96
% 3.07/0.88  # Condensation attempts                : 0
% 3.07/0.88  # Condensation successes               : 0
% 3.07/0.88  # Termbank termtop insertions          : 564733
% 3.07/0.88  
% 3.07/0.88  # -------------------------------------------------
% 3.07/0.88  # User time                : 0.356 s
% 3.07/0.88  # System time              : 0.019 s
% 3.07/0.88  # Total time               : 0.374 s
% 3.07/0.88  # Maximum resident set size: 1736 pages
% 3.07/0.88  
% 3.07/0.88  # -------------------------------------------------
% 3.07/0.88  # User time                : 1.825 s
% 3.07/0.88  # System time              : 0.037 s
% 3.07/0.88  # Total time               : 1.862 s
% 3.07/0.88  # Maximum resident set size: 1680 pages
% 3.07/0.88  % E---3.1 exiting
% 3.07/0.88  % E---3.1 exiting
%------------------------------------------------------------------------------