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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---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 : n021.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 19:26:00 EDT 2023

% Result   : Theorem 184.30s 24.12s
% Output   : CNFRefutation 184.30s
% 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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.p',t47_setfam_1) ).

fof(d4_subset_1,axiom,
    ! [X1] : cast_to_subset(X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.p',redefinition_k6_subset_1) ).

fof(dt_k2_subset_1,axiom,
    ! [X1] : element(cast_to_subset(X1),powerset(X1)),
    file('/export/starexec/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.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,
    ! [X69,X70] :
      ( ~ element(X70,powerset(powerset(X69)))
      | union_of_subsets(X69,X70) = union(X70) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).

fof(c_0_12,negated_conjecture,
    ( element(esk2_0,powerset(powerset(esk1_0)))
    & esk2_0 != empty_set
    & meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union_of_subsets(esk1_0,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_13,plain,
    ! [X86,X87] :
      ( ~ element(X87,powerset(powerset(X86)))
      | element(complements_of_subsets(X86,X87),powerset(powerset(X86))) ),
    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(esk2_0,powerset(powerset(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X77,X78] :
      ( ~ element(X78,powerset(powerset(X77)))
      | meet_of_subsets(X77,X78) = set_meet(X78) ),
    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,
    ! [X67,X68] :
      ( ~ element(X68,powerset(powerset(X67)))
      | element(union_of_subsets(X67,X68),powerset(X67)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).

fof(c_0_19,lemma,
    ! [X71,X72] :
      ( ~ element(X72,powerset(powerset(X71)))
      | X72 = empty_set
      | subset_difference(X71,cast_to_subset(X71),union_of_subsets(X71,X72)) = meet_of_subsets(X71,complements_of_subsets(X71,X72)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).

fof(c_0_20,plain,
    ! [X612] : cast_to_subset(X612) = X612,
    inference(variable_rename,[status(thm)],[d4_subset_1]) ).

cnf(c_0_21,negated_conjecture,
    meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union_of_subsets(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    union_of_subsets(esk1_0,esk2_0) = union(esk2_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(esk1_0,esk2_0),powerset(powerset(esk1_0))),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

fof(c_0_25,plain,
    ! [X25,X26] :
      ( ~ element(X26,powerset(X25))
      | subset_complement(X25,X26) = set_difference(X25,X26) ),
    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,
    ! [X317,X318,X319] :
      ( ~ element(X318,powerset(X317))
      | ~ element(X319,powerset(X317))
      | subset_difference(X317,X318,X319) = set_difference(X318,X319) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).

fof(c_0_28,plain,
    ! [X613] : element(cast_to_subset(X613),powerset(X613)),
    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(esk1_0,complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union(esk2_0)),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_32,negated_conjecture,
    meet_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) = set_meet(complements_of_subsets(esk1_0,esk2_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(esk2_0),powerset(esk1_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,
    ( subset_difference(X1,X1,union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | X2 = empty_set
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,negated_conjecture,
    esk2_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_39,negated_conjecture,
    set_meet(complements_of_subsets(esk1_0,esk2_0)) != subset_complement(esk1_0,union(esk2_0)),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_40,negated_conjecture,
    subset_complement(esk1_0,union(esk2_0)) = set_difference(esk1_0,union(esk2_0)),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ( subset_difference(esk1_0,X1,union(esk2_0)) = set_difference(X1,union(esk2_0))
    | ~ element(X1,powerset(esk1_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(esk1_0,esk1_0,union(esk2_0)) = set_meet(complements_of_subsets(esk1_0,esk2_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(esk1_0,esk2_0)) != set_difference(esk1_0,union(esk2_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
% 0.12/0.18  % Problem    : SEU327+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.19  % Command    : run_E %s %d THM
% 0.19/0.40  % Computer : n021.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41  % CPULimit   : 2400
% 0.19/0.41  % WCLimit    : 300
% 0.19/0.41  % DateTime   : Mon Oct  2 08:14:29 EDT 2023
% 0.19/0.41  % CPUTime    : 
% 0.26/0.59  Running first-order theorem proving
% 0.26/0.59  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.lWntTudk80/E---3.1_7874.p
% 184.30/24.12  # Version: 3.1pre001
% 184.30/24.12  # Preprocessing class: FSLMSMSSSSSNFFN.
% 184.30/24.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.30/24.12  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 184.30/24.12  # Starting new_bool_3 with 600s (2) cores
% 184.30/24.12  # Starting new_bool_1 with 600s (2) cores
% 184.30/24.12  # Starting sh5l with 300s (1) cores
% 184.30/24.12  # sh5l with pid 7972 completed with status 0
% 184.30/24.12  # Result found by sh5l
% 184.30/24.12  # Preprocessing class: FSLMSMSSSSSNFFN.
% 184.30/24.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.30/24.12  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 184.30/24.12  # Starting new_bool_3 with 600s (2) cores
% 184.30/24.12  # Starting new_bool_1 with 600s (2) cores
% 184.30/24.12  # Starting sh5l with 300s (1) cores
% 184.30/24.12  # SinE strategy is gf500_gu_R04_F100_L20000
% 184.30/24.12  # Search class: FGHSM-SMLM32-MFFFFFNN
% 184.30/24.12  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 184.30/24.12  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 23s (1) cores
% 184.30/24.12  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 8025 completed with status 0
% 184.30/24.12  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 184.30/24.12  # Preprocessing class: FSLMSMSSSSSNFFN.
% 184.30/24.12  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 184.30/24.12  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 184.30/24.12  # Starting new_bool_3 with 600s (2) cores
% 184.30/24.12  # Starting new_bool_1 with 600s (2) cores
% 184.30/24.12  # Starting sh5l with 300s (1) cores
% 184.30/24.12  # SinE strategy is gf500_gu_R04_F100_L20000
% 184.30/24.12  # Search class: FGHSM-SMLM32-MFFFFFNN
% 184.30/24.12  # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 184.30/24.12  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 23s (1) cores
% 184.30/24.12  # Preprocessing time       : 0.033 s
% 184.30/24.12  # Presaturation interreduction done
% 184.30/24.12  
% 184.30/24.12  # Proof found!
% 184.30/24.12  # SZS status Theorem
% 184.30/24.12  # SZS output start CNFRefutation
% See solution above
% 184.30/24.12  # Parsed axioms                        : 540
% 184.30/24.12  # Removed by relevancy pruning/SinE    : 37
% 184.30/24.12  # Initial clauses                      : 2034
% 184.30/24.12  # Removed in clause preprocessing      : 7
% 184.30/24.12  # Initial clauses in saturation        : 2027
% 184.30/24.12  # Processed clauses                    : 67744
% 184.30/24.12  # ...of these trivial                  : 992
% 184.30/24.12  # ...subsumed                          : 42224
% 184.30/24.12  # ...remaining for further processing  : 24528
% 184.30/24.12  # Other redundant clauses eliminated   : 819
% 184.30/24.12  # Clauses deleted for lack of memory   : 0
% 184.30/24.12  # Backward-subsumed                    : 215
% 184.30/24.12  # Backward-rewritten                   : 1522
% 184.30/24.12  # Generated clauses                    : 793307
% 184.30/24.12  # ...of the previous two non-redundant : 763453
% 184.30/24.12  # ...aggressively subsumed             : 0
% 184.30/24.12  # Contextual simplify-reflections      : 278
% 184.30/24.12  # Paramodulations                      : 792576
% 184.30/24.12  # Factorizations                       : 40
% 184.30/24.12  # NegExts                              : 0
% 184.30/24.12  # Equation resolutions                 : 826
% 184.30/24.12  # Total rewrite steps                  : 119483
% 184.30/24.12  # Propositional unsat checks           : 4
% 184.30/24.12  #    Propositional check models        : 1
% 184.30/24.12  #    Propositional check unsatisfiable : 0
% 184.30/24.12  #    Propositional clauses             : 0
% 184.30/24.12  #    Propositional clauses after purity: 0
% 184.30/24.12  #    Propositional unsat core size     : 0
% 184.30/24.12  #    Propositional preprocessing time  : 0.000
% 184.30/24.12  #    Propositional encoding time       : 0.932
% 184.30/24.12  #    Propositional solver time         : 0.662
% 184.30/24.12  #    Success case prop preproc time    : 0.000
% 184.30/24.12  #    Success case prop encoding time   : 0.000
% 184.30/24.12  #    Success case prop solver time     : 0.000
% 184.30/24.12  # Current number of processed clauses  : 20506
% 184.30/24.12  #    Positive orientable unit clauses  : 3571
% 184.30/24.12  #    Positive unorientable unit clauses: 27
% 184.30/24.12  #    Negative unit clauses             : 2858
% 184.30/24.12  #    Non-unit-clauses                  : 14050
% 184.30/24.12  # Current number of unprocessed clauses: 695806
% 184.30/24.12  # ...number of literals in the above   : 2210810
% 184.30/24.12  # Current number of archived formulas  : 0
% 184.30/24.12  # Current number of archived clauses   : 3638
% 184.30/24.12  # Clause-clause subsumption calls (NU) : 22329686
% 184.30/24.12  # Rec. Clause-clause subsumption calls : 15209978
% 184.30/24.12  # Non-unit clause-clause subsumptions  : 14408
% 184.30/24.12  # Unit Clause-clause subsumption calls : 3663703
% 184.30/24.12  # Rewrite failures with RHS unbound    : 0
% 184.30/24.12  # BW rewrite match attempts            : 25356
% 184.30/24.12  # BW rewrite match successes           : 416
% 184.30/24.12  # Condensation attempts                : 0
% 184.30/24.12  # Condensation successes               : 0
% 184.30/24.12  # Termbank termtop insertions          : 20319239
% 184.30/24.12  
% 184.30/24.12  # -------------------------------------------------
% 184.30/24.12  # User time                : 22.446 s
% 184.30/24.12  # System time              : 0.491 s
% 184.30/24.12  # Total time               : 22.937 s
% 184.30/24.12  # Maximum resident set size: 7560 pages
% 184.30/24.12  
% 184.30/24.12  # -------------------------------------------------
% 184.30/24.12  # User time                : 22.464 s
% 184.30/24.12  # System time              : 0.494 s
% 184.30/24.12  # Total time               : 22.957 s
% 184.30/24.12  # Maximum resident set size: 2404 pages
% 184.30/24.12  % E---3.1 exiting
% 184.30/24.13  % E---3.1 exiting
%------------------------------------------------------------------------------