TSTP Solution File: SEU327+2 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SEU327+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n005.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 19:31:39 EDT 2023

% Result   : Theorem 305.14s 39.09s
% Output   : CNFRefutation 305.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   46 (  20 unt;   0 def)
%            Number of atoms       :   82 (  39 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   65 (  29   ~;  21   |;   3   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :   59 (   0 sgn;  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t11_tops_2,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',t11_tops_2) ).

fof(redefinition_k5_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => union_of_subsets(X1,X2) = union(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',redefinition_k5_setfam_1) ).

fof(dt_k7_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',dt_k7_setfam_1) ).

fof(redefinition_k6_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => meet_of_subsets(X1,X2) = set_meet(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',redefinition_k6_setfam_1) ).

fof(dt_k5_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(union_of_subsets(X1,X2),powerset(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',dt_k5_setfam_1) ).

fof(t47_setfam_1,lemma,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',t47_setfam_1) ).

fof(d4_subset_1,axiom,
    ! [X1] : cast_to_subset(X1) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',d4_subset_1) ).

fof(d5_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',d5_subset_1) ).

fof(redefinition_k6_subset_1,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',redefinition_k6_subset_1) ).

fof(dt_k2_subset_1,axiom,
    ! [X1] : element(cast_to_subset(X1),powerset(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p',dt_k2_subset_1) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(powerset(X1)))
       => ( X2 != empty_set
         => meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
    inference(assume_negation,[status(cth)],[t11_tops_2]) ).

fof(c_0_11,plain,
    ! [X843,X844] :
      ( ~ element(X844,powerset(powerset(X843)))
      | union_of_subsets(X843,X844) = union(X844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).

fof(c_0_12,negated_conjecture,
    ( element(esk313_0,powerset(powerset(esk312_0)))
    & esk313_0 != empty_set
    & meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union_of_subsets(esk312_0,esk313_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X593,X594] :
      ( ~ element(X594,powerset(powerset(X593)))
      | element(complements_of_subsets(X593,X594),powerset(powerset(X593))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).

cnf(c_0_14,plain,
    ( union_of_subsets(X2,X1) = union(X1)
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    element(esk313_0,powerset(powerset(esk312_0))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X848,X849] :
      ( ~ element(X849,powerset(powerset(X848)))
      | meet_of_subsets(X848,X849) = set_meet(X849) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1])]) ).

cnf(c_0_17,plain,
    ( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X578,X579] :
      ( ~ element(X579,powerset(powerset(X578)))
      | element(union_of_subsets(X578,X579),powerset(X578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).

fof(c_0_19,lemma,
    ! [X1538,X1539] :
      ( ~ element(X1539,powerset(powerset(X1538)))
      | X1539 = empty_set
      | subset_difference(X1538,cast_to_subset(X1538),union_of_subsets(X1538,X1539)) = meet_of_subsets(X1538,complements_of_subsets(X1538,X1539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).

fof(c_0_20,plain,
    ! [X405] : cast_to_subset(X405) = X405,
    inference(variable_rename,[status(thm)],[d4_subset_1]) ).

cnf(c_0_21,negated_conjecture,
    meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union_of_subsets(esk312_0,esk313_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    union_of_subsets(esk312_0,esk313_0) = union(esk313_0),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_23,plain,
    ( meet_of_subsets(X2,X1) = set_meet(X1)
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    element(complements_of_subsets(esk312_0,esk313_0),powerset(powerset(esk312_0))),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

fof(c_0_25,plain,
    ! [X459,X460] :
      ( ~ element(X460,powerset(X459))
      | subset_complement(X459,X460) = set_difference(X459,X460) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).

cnf(c_0_26,plain,
    ( element(union_of_subsets(X2,X1),powerset(X2))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_27,plain,
    ! [X850,X851,X852] :
      ( ~ element(X851,powerset(X850))
      | ~ element(X852,powerset(X850))
      | subset_difference(X850,X851,X852) = set_difference(X851,X852) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).

fof(c_0_28,plain,
    ! [X558] : element(cast_to_subset(X558),powerset(X558)),
    inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).

cnf(c_0_29,lemma,
    ( X1 = empty_set
    | subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_30,plain,
    cast_to_subset(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_31,negated_conjecture,
    meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union(esk313_0)),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_32,negated_conjecture,
    meet_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) = set_meet(complements_of_subsets(esk312_0,esk313_0)),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_33,plain,
    ( subset_complement(X2,X1) = set_difference(X2,X1)
    | ~ element(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,negated_conjecture,
    element(union(esk313_0),powerset(esk312_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_15]),c_0_22]) ).

cnf(c_0_35,plain,
    ( subset_difference(X2,X1,X3) = set_difference(X1,X3)
    | ~ element(X1,powerset(X2))
    | ~ element(X3,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,plain,
    element(cast_to_subset(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,lemma,
    ( X1 = empty_set
    | subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,negated_conjecture,
    esk313_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_39,negated_conjecture,
    set_meet(complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,union(esk313_0)),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,negated_conjecture,
    subset_complement(esk312_0,union(esk313_0)) = set_difference(esk312_0,union(esk313_0)),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ( subset_difference(esk312_0,X1,union(esk313_0)) = set_difference(X1,union(esk313_0))
    | ~ element(X1,powerset(esk312_0)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_34]) ).

cnf(c_0_42,plain,
    element(X1,powerset(X1)),
    inference(rw,[status(thm)],[c_0_36,c_0_30]) ).

cnf(c_0_43,negated_conjecture,
    subset_difference(esk312_0,esk312_0,union(esk313_0)) = set_meet(complements_of_subsets(esk312_0,esk313_0)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_15]),c_0_22]),c_0_32]),c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    set_meet(complements_of_subsets(esk312_0,esk313_0)) != set_difference(esk312_0,union(esk313_0)),
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SEU327+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.10  % Command    : run_E %s %d THM
% 0.10/0.31  % Computer : n005.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 2400
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Oct  2 08:10:31 EDT 2023
% 0.10/0.31  % CPUTime    : 
% 0.16/0.46  Running first-order model finding
% 0.16/0.46  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/tmp/tmp.wdbXM8hjjj/E---3.1_18688.p
% 305.14/39.09  # Version: 3.1pre001
% 305.14/39.09  # Preprocessing class: FSLMSMSSSSSNFFN.
% 305.14/39.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 305.14/39.09  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 305.14/39.09  # Starting new_bool_3 with 600s (2) cores
% 305.14/39.09  # Starting new_bool_1 with 600s (2) cores
% 305.14/39.09  # Starting sh5l with 300s (1) cores
% 305.14/39.09  # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 18767 completed with status 0
% 305.14/39.09  # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 305.14/39.09  # Preprocessing class: FSLMSMSSSSSNFFN.
% 305.14/39.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 305.14/39.09  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 305.14/39.09  # No SInE strategy applied
% 305.14/39.09  # Search class: FGHSM-SMLM32-MFFFFFNN
% 305.14/39.09  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 305.14/39.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 305.14/39.09  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 305.14/39.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 305.14/39.09  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 18776 completed with status 0
% 305.14/39.09  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 305.14/39.09  # Preprocessing class: FSLMSMSSSSSNFFN.
% 305.14/39.09  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 305.14/39.09  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 305.14/39.09  # No SInE strategy applied
% 305.14/39.09  # Search class: FGHSM-SMLM32-MFFFFFNN
% 305.14/39.09  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 305.14/39.09  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 305.14/39.09  # Preprocessing time       : 0.029 s
% 305.14/39.09  # Presaturation interreduction done
% 305.14/39.09  
% 305.14/39.09  # Proof found!
% 305.14/39.09  # SZS status Theorem
% 305.14/39.09  # SZS output start CNFRefutation
% See solution above
% 305.14/39.09  # Parsed axioms                        : 540
% 305.14/39.09  # Removed by relevancy pruning/SinE    : 0
% 305.14/39.09  # Initial clauses                      : 2094
% 305.14/39.09  # Removed in clause preprocessing      : 40
% 305.14/39.09  # Initial clauses in saturation        : 2054
% 305.14/39.09  # Processed clauses                    : 68877
% 305.14/39.09  # ...of these trivial                  : 654
% 305.14/39.09  # ...subsumed                          : 43799
% 305.14/39.09  # ...remaining for further processing  : 24424
% 305.14/39.09  # Other redundant clauses eliminated   : 957
% 305.14/39.09  # Clauses deleted for lack of memory   : 0
% 305.14/39.09  # Backward-subsumed                    : 321
% 305.14/39.09  # Backward-rewritten                   : 1440
% 305.14/39.09  # Generated clauses                    : 784139
% 305.14/39.09  # ...of the previous two non-redundant : 748677
% 305.14/39.09  # ...aggressively subsumed             : 0
% 305.14/39.09  # Contextual simplify-reflections      : 261
% 305.14/39.09  # Paramodulations                      : 783278
% 305.14/39.09  # Factorizations                       : 35
% 305.14/39.09  # NegExts                              : 0
% 305.14/39.09  # Equation resolutions                 : 966
% 305.14/39.09  # Total rewrite steps                  : 130221
% 305.14/39.09  # Propositional unsat checks           : 4
% 305.14/39.09  #    Propositional check models        : 1
% 305.14/39.09  #    Propositional check unsatisfiable : 0
% 305.14/39.09  #    Propositional clauses             : 0
% 305.14/39.09  #    Propositional clauses after purity: 0
% 305.14/39.09  #    Propositional unsat core size     : 0
% 305.14/39.09  #    Propositional preprocessing time  : 0.000
% 305.14/39.09  #    Propositional encoding time       : 1.468
% 305.14/39.09  #    Propositional solver time         : 0.946
% 305.14/39.09  #    Success case prop preproc time    : 0.000
% 305.14/39.09  #    Success case prop encoding time   : 0.000
% 305.14/39.09  #    Success case prop solver time     : 0.000
% 305.14/39.09  # Current number of processed clauses  : 20367
% 305.14/39.09  #    Positive orientable unit clauses  : 2878
% 305.14/39.09  #    Positive unorientable unit clauses: 4
% 305.14/39.09  #    Negative unit clauses             : 2278
% 305.14/39.09  #    Non-unit-clauses                  : 15207
% 305.14/39.09  # Current number of unprocessed clauses: 679861
% 305.14/39.09  # ...number of literals in the above   : 2230970
% 305.14/39.09  # Current number of archived formulas  : 0
% 305.14/39.09  # Current number of archived clauses   : 3668
% 305.14/39.09  # Clause-clause subsumption calls (NU) : 36347998
% 305.14/39.09  # Rec. Clause-clause subsumption calls : 25283644
% 305.14/39.09  # Non-unit clause-clause subsumptions  : 19823
% 305.14/39.09  # Unit Clause-clause subsumption calls : 3924732
% 305.14/39.09  # Rewrite failures with RHS unbound    : 0
% 305.14/39.09  # BW rewrite match attempts            : 19933
% 305.14/39.09  # BW rewrite match successes           : 353
% 305.14/39.09  # Condensation attempts                : 0
% 305.14/39.09  # Condensation successes               : 0
% 305.14/39.09  # Termbank termtop insertions          : 21220121
% 305.14/39.09  
% 305.14/39.09  # -------------------------------------------------
% 305.14/39.09  # User time                : 37.464 s
% 305.14/39.09  # System time              : 0.615 s
% 305.14/39.09  # Total time               : 38.079 s
% 305.14/39.09  # Maximum resident set size: 7540 pages
% 305.14/39.09  
% 305.14/39.09  # -------------------------------------------------
% 305.14/39.09  # User time                : 112.202 s
% 305.14/39.09  # System time              : 2.013 s
% 305.14/39.09  # Total time               : 114.215 s
% 305.14/39.09  # Maximum resident set size: 2396 pages
% 305.14/39.09  % E---3.1 exiting
%------------------------------------------------------------------------------