TSTP Solution File: SEU147+2 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 19:24:56 EDT 2023

% Result   : Theorem 0.16s 0.46s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   44 (  10 unt;   0 def)
%            Number of atoms       :  118 (  47 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  127 (  53   ~;  52   |;  11   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-2 aty)
%            Number of variables   :   83 (   0 sgn;  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',antisymmetry_r2_hidden) ).

fof(d1_zfmisc_1,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',d1_zfmisc_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',d3_tarski) ).

fof(l32_xboole_1,lemma,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',l32_xboole_1) ).

fof(t3_xboole_1,lemma,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',t3_xboole_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',d1_tarski) ).

fof(t3_boole,axiom,
    ! [X1] : set_difference(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',t3_boole) ).

fof(l4_zfmisc_1,lemma,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',l4_zfmisc_1) ).

fof(t1_zfmisc_1,conjecture,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox2/tmp/tmp.LK3Xgz4JBv/E---3.1_6880.p',t1_zfmisc_1) ).

fof(c_0_9,plain,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).

fof(c_0_10,plain,
    ! [X34,X35,X36,X37,X38,X39] :
      ( ( ~ in(X36,X35)
        | subset(X36,X34)
        | X35 != powerset(X34) )
      & ( ~ subset(X37,X34)
        | in(X37,X35)
        | X35 != powerset(X34) )
      & ( ~ in(esk3_2(X38,X39),X39)
        | ~ subset(esk3_2(X38,X39),X38)
        | X39 = powerset(X38) )
      & ( in(esk3_2(X38,X39),X39)
        | subset(esk3_2(X38,X39),X38)
        | X39 = powerset(X38) ) ),
    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)],[d1_zfmisc_1])])])])])]) ).

fof(c_0_11,plain,
    ! [X41,X42] :
      ( ~ in(X41,X42)
      | ~ in(X42,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

cnf(c_0_12,plain,
    ( in(X1,X3)
    | ~ subset(X1,X2)
    | X3 != powerset(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    ( ~ in(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_14,plain,
    ( in(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_15,plain,
    ( subset(X1,X3)
    | ~ in(X1,X2)
    | X2 != powerset(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X52,X53,X54,X55,X56] :
      ( ( ~ subset(X52,X53)
        | ~ in(X54,X52)
        | in(X54,X53) )
      & ( in(esk5_2(X55,X56),X55)
        | subset(X55,X56) )
      & ( ~ in(esk5_2(X55,X56),X56)
        | subset(X55,X56) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_17,plain,
    ( ~ subset(X1,X2)
    | ~ in(powerset(X2),X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_18,lemma,
    ! [X24,X25] :
      ( ( set_difference(X24,X25) != empty_set
        | subset(X24,X25) )
      & ( ~ subset(X24,X25)
        | set_difference(X24,X25) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).

fof(c_0_19,lemma,
    ! [X32] :
      ( ~ subset(X32,empty_set)
      | X32 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).

cnf(c_0_20,plain,
    ( subset(X1,X2)
    | ~ in(X1,powerset(X2)) ),
    inference(er,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( in(esk5_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( ~ subset(powerset(X1),X2)
    | ~ subset(powerset(X2),X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_23,lemma,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,lemma,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( subset(esk5_2(powerset(X1),X2),X1)
    | subset(powerset(X1),X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

fof(c_0_26,plain,
    ! [X5,X6,X7,X8,X9,X10] :
      ( ( ~ in(X7,X6)
        | X7 = X5
        | X6 != singleton(X5) )
      & ( X8 != X5
        | in(X8,X6)
        | X6 != singleton(X5) )
      & ( ~ in(esk1_2(X9,X10),X10)
        | esk1_2(X9,X10) != X9
        | X10 = singleton(X9) )
      & ( in(esk1_2(X9,X10),X10)
        | esk1_2(X9,X10) = X9
        | X10 = singleton(X9) ) ),
    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)],[d1_tarski])])])])])]) ).

cnf(c_0_27,lemma,
    ( set_difference(powerset(X1),X2) != empty_set
    | ~ subset(powerset(X2),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_28,plain,
    ! [X31] : set_difference(X31,empty_set) = X31,
    inference(variable_rename,[status(thm)],[t3_boole]) ).

cnf(c_0_29,plain,
    ( subset(X1,X2)
    | ~ in(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_30,lemma,
    ( esk5_2(powerset(empty_set),X1) = empty_set
    | subset(powerset(empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,lemma,
    ( set_difference(powerset(X1),X2) != empty_set
    | set_difference(powerset(X2),X1) != empty_set ),
    inference(spm,[status(thm)],[c_0_27,c_0_23]) ).

cnf(c_0_33,plain,
    set_difference(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_34,lemma,
    ! [X18,X19] :
      ( ( ~ subset(X18,singleton(X19))
        | X18 = empty_set
        | X18 = singleton(X19) )
      & ( X18 != empty_set
        | subset(X18,singleton(X19)) )
      & ( X18 != singleton(X19)
        | subset(X18,singleton(X19)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).

cnf(c_0_35,lemma,
    ( subset(powerset(empty_set),X1)
    | ~ in(empty_set,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_31])]) ).

fof(c_0_37,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t1_zfmisc_1])]) ).

cnf(c_0_38,lemma,
    ( set_difference(powerset(empty_set),X1) != empty_set
    | powerset(X1) != empty_set ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,lemma,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_40,lemma,
    subset(powerset(empty_set),singleton(empty_set)),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_42,lemma,
    powerset(empty_set) != empty_set,
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_43,lemma,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n028.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 2400
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon Oct  2 09:30:51 EDT 2023
% 0.11/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  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.LK3Xgz4JBv/E---3.1_6880.p
% 0.16/0.46  # Version: 3.1pre001
% 0.16/0.46  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.16/0.46  # Starting sh5l with 300s (1) cores
% 0.16/0.46  # new_bool_3 with pid 6959 completed with status 0
% 0.16/0.46  # Result found by new_bool_3
% 0.16/0.46  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46  # Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46  # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 163s (1) cores
% 0.16/0.46  # G-E--_300_C01_F1_SE_CS_SP_S0Y with pid 6963 completed with status 0
% 0.16/0.46  # Result found by G-E--_300_C01_F1_SE_CS_SP_S0Y
% 0.16/0.46  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.46  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.46  # Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.46  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.46  # Starting G-E--_300_C01_F1_SE_CS_SP_S0Y with 163s (1) cores
% 0.16/0.46  # Preprocessing time       : 0.002 s
% 0.16/0.46  
% 0.16/0.46  # Proof found!
% 0.16/0.46  # SZS status Theorem
% 0.16/0.46  # SZS output start CNFRefutation
% See solution above
% 0.16/0.46  # Parsed axioms                        : 70
% 0.16/0.46  # Removed by relevancy pruning/SinE    : 20
% 0.16/0.46  # Initial clauses                      : 82
% 0.16/0.46  # Removed in clause preprocessing      : 0
% 0.16/0.46  # Initial clauses in saturation        : 82
% 0.16/0.46  # Processed clauses                    : 578
% 0.16/0.46  # ...of these trivial                  : 55
% 0.16/0.46  # ...subsumed                          : 329
% 0.16/0.46  # ...remaining for further processing  : 194
% 0.16/0.46  # Other redundant clauses eliminated   : 35
% 0.16/0.46  # Clauses deleted for lack of memory   : 0
% 0.16/0.46  # Backward-subsumed                    : 1
% 0.16/0.46  # Backward-rewritten                   : 7
% 0.16/0.46  # Generated clauses                    : 2268
% 0.16/0.46  # ...of the previous two non-redundant : 1059
% 0.16/0.46  # ...aggressively subsumed             : 0
% 0.16/0.46  # Contextual simplify-reflections      : 0
% 0.16/0.46  # Paramodulations                      : 2230
% 0.16/0.46  # Factorizations                       : 2
% 0.16/0.46  # NegExts                              : 0
% 0.16/0.46  # Equation resolutions                 : 35
% 0.16/0.46  # Total rewrite steps                  : 2013
% 0.16/0.46  # Propositional unsat checks           : 0
% 0.16/0.46  #    Propositional check models        : 0
% 0.16/0.46  #    Propositional check unsatisfiable : 0
% 0.16/0.46  #    Propositional clauses             : 0
% 0.16/0.46  #    Propositional clauses after purity: 0
% 0.16/0.46  #    Propositional unsat core size     : 0
% 0.16/0.46  #    Propositional preprocessing time  : 0.000
% 0.16/0.46  #    Propositional encoding time       : 0.000
% 0.16/0.46  #    Propositional solver time         : 0.000
% 0.16/0.46  #    Success case prop preproc time    : 0.000
% 0.16/0.46  #    Success case prop encoding time   : 0.000
% 0.16/0.46  #    Success case prop solver time     : 0.000
% 0.16/0.46  # Current number of processed clauses  : 167
% 0.16/0.46  #    Positive orientable unit clauses  : 63
% 0.16/0.46  #    Positive unorientable unit clauses: 2
% 0.16/0.46  #    Negative unit clauses             : 18
% 0.16/0.46  #    Non-unit-clauses                  : 84
% 0.16/0.46  # Current number of unprocessed clauses: 534
% 0.16/0.46  # ...number of literals in the above   : 1109
% 0.16/0.46  # Current number of archived formulas  : 0
% 0.16/0.46  # Current number of archived clauses   : 10
% 0.16/0.46  # Clause-clause subsumption calls (NU) : 1094
% 0.16/0.46  # Rec. Clause-clause subsumption calls : 849
% 0.16/0.46  # Non-unit clause-clause subsumptions  : 178
% 0.16/0.46  # Unit Clause-clause subsumption calls : 137
% 0.16/0.46  # Rewrite failures with RHS unbound    : 0
% 0.16/0.46  # BW rewrite match attempts            : 51
% 0.16/0.46  # BW rewrite match successes           : 20
% 0.16/0.46  # Condensation attempts                : 0
% 0.16/0.46  # Condensation successes               : 0
% 0.16/0.46  # Termbank termtop insertions          : 18149
% 0.16/0.46  
% 0.16/0.46  # -------------------------------------------------
% 0.16/0.46  # User time                : 0.026 s
% 0.16/0.46  # System time              : 0.002 s
% 0.16/0.46  # Total time               : 0.028 s
% 0.16/0.46  # Maximum resident set size: 1912 pages
% 0.16/0.46  
% 0.16/0.46  # -------------------------------------------------
% 0.16/0.46  # User time                : 0.029 s
% 0.16/0.46  # System time              : 0.003 s
% 0.16/0.46  # Total time               : 0.031 s
% 0.16/0.46  # Maximum resident set size: 1728 pages
% 0.16/0.46  % E---3.1 exiting
% 0.16/0.46  % E---3.1 exiting
%------------------------------------------------------------------------------