TSTP Solution File: SET980+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 19:24:31 EDT 2023

% Result   : Theorem 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   45 (   9 unt;   0 def)
%            Number of atoms       :  119 (  40 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  125 (  51   ~;  57   |;  10   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   75 (  15 sgn;  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t134_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
     => ( X1 = empty_set
        | X2 = empty_set
        | ( X1 = X3
          & X2 = X4 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ltCRdBVcbs/E---3.1_31911.p',t134_zfmisc_1) ).

fof(l55_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ltCRdBVcbs/E---3.1_31911.p',l55_zfmisc_1) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.ltCRdBVcbs/E---3.1_31911.p',d1_xboole_0) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.ltCRdBVcbs/E---3.1_31911.p',t2_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
       => ( X1 = empty_set
          | X2 = empty_set
          | ( X1 = X3
            & X2 = X4 ) ) ),
    inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X15,X16,X17,X18] :
      ( ( in(X15,X17)
        | ~ in(ordered_pair(X15,X16),cartesian_product2(X17,X18)) )
      & ( in(X16,X18)
        | ~ in(ordered_pair(X15,X16),cartesian_product2(X17,X18)) )
      & ( ~ in(X15,X17)
        | ~ in(X16,X18)
        | in(ordered_pair(X15,X16),cartesian_product2(X17,X18)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).

fof(c_0_6,negated_conjecture,
    ( cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0)
    & esk1_0 != empty_set
    & esk2_0 != empty_set
    & ( esk1_0 != esk3_0
      | esk2_0 != esk4_0 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_7,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    cartesian_product2(esk1_0,esk2_0) = cartesian_product2(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

cnf(c_0_10,plain,
    ( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
    | ~ in(X1,X2)
    | ~ in(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(ordered_pair(X2,X1),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

fof(c_0_12,plain,
    ! [X9,X10,X11] :
      ( ( X9 != empty_set
        | ~ in(X10,X9) )
      & ( in(esk5_1(X11),X11)
        | X11 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
    | ~ in(X2,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk2_0)
    | ~ in(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_16,plain,
    ( in(esk5_1(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    esk1_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_18,negated_conjecture,
    ( in(X1,esk1_0)
    | ~ in(X2,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk2_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

fof(c_0_20,plain,
    ! [X21,X22] :
      ( ( ~ in(esk6_2(X21,X22),X21)
        | ~ in(esk6_2(X21,X22),X22)
        | X21 = X22 )
      & ( in(esk6_2(X21,X22),X21)
        | in(esk6_2(X21,X22),X22)
        | X21 = X22 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).

cnf(c_0_21,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,negated_conjecture,
    ( in(X1,esk1_0)
    | ~ in(X1,esk3_0)
    | ~ in(X2,esk2_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    ( in(esk6_2(X1,X2),X1)
    | in(esk6_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,plain,
    ~ in(X1,empty_set),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( esk3_0 = X1
    | in(esk6_2(esk3_0,X1),esk1_0)
    | in(esk6_2(esk3_0,X1),X1)
    | ~ in(X2,esk2_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,plain,
    ( empty_set = X1
    | in(esk6_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    esk2_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_28,negated_conjecture,
    ( esk3_0 = X1
    | in(esk6_2(esk3_0,X1),esk1_0)
    | in(esk6_2(esk3_0,X1),X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_8]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | ~ in(esk6_2(X1,X2),X1)
    | ~ in(esk6_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_31,negated_conjecture,
    ( esk3_0 = esk1_0
    | in(esk6_2(esk3_0,esk1_0),esk1_0) ),
    inference(ef,[status(thm)],[c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X2,esk2_0)
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_10]) ).

cnf(c_0_33,negated_conjecture,
    ( esk3_0 = esk1_0
    | ~ in(esk6_2(esk3_0,esk1_0),esk3_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_27]) ).

cnf(c_0_35,negated_conjecture,
    esk3_0 = esk1_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
    | ~ in(X2,esk4_0)
    | ~ in(X1,esk1_0) ),
    inference(rw,[status(thm)],[c_0_14,c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    ( in(X1,esk2_0)
    | ~ in(X1,esk4_0)
    | ~ in(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_36]) ).

cnf(c_0_38,negated_conjecture,
    ( esk4_0 = X1
    | in(esk6_2(esk4_0,X1),esk2_0)
    | in(esk6_2(esk4_0,X1),X1)
    | ~ in(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_37,c_0_23]) ).

cnf(c_0_39,negated_conjecture,
    ( esk1_0 != esk3_0
    | esk2_0 != esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_40,negated_conjecture,
    ( esk4_0 = X1
    | in(esk6_2(esk4_0,X1),esk2_0)
    | in(esk6_2(esk4_0,X1),X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_17]) ).

cnf(c_0_41,negated_conjecture,
    esk4_0 != esk2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35])]) ).

cnf(c_0_42,negated_conjecture,
    in(esk6_2(esk4_0,esk2_0),esk2_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_40]),c_0_41]) ).

cnf(c_0_43,negated_conjecture,
    ~ in(esk6_2(esk4_0,esk2_0),esk4_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.15  % Command    : run_E %s %d THM
% 0.13/0.37  % Computer : n007.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit   : 2400
% 0.13/0.37  % WCLimit    : 300
% 0.13/0.37  % DateTime   : Mon Oct  2 17:12:54 EDT 2023
% 0.13/0.37  % CPUTime    : 
% 0.21/0.51  Running first-order model finding
% 0.21/0.51  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.ltCRdBVcbs/E---3.1_31911.p
% 0.21/0.53  # Version: 3.1pre001
% 0.21/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # sh5l with pid 31991 completed with status 0
% 0.21/0.53  # Result found by sh5l
% 0.21/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.21/0.53  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.53  # SAT001_MinMin_p005000_rr_RG with pid 31997 completed with status 0
% 0.21/0.53  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.53  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.53  # Search class: FGHSS-FFSS21-SFFFFFNN
% 0.21/0.53  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.53  # Preprocessing time       : 0.001 s
% 0.21/0.53  # Presaturation interreduction done
% 0.21/0.53  
% 0.21/0.53  # Proof found!
% 0.21/0.53  # SZS status Theorem
% 0.21/0.53  # SZS output start CNFRefutation
% See solution above
% 0.21/0.53  # Parsed axioms                        : 12
% 0.21/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.53  # Initial clauses                      : 21
% 0.21/0.53  # Removed in clause preprocessing      : 0
% 0.21/0.53  # Initial clauses in saturation        : 21
% 0.21/0.53  # Processed clauses                    : 167
% 0.21/0.53  # ...of these trivial                  : 7
% 0.21/0.53  # ...subsumed                          : 32
% 0.21/0.53  # ...remaining for further processing  : 128
% 0.21/0.53  # Other redundant clauses eliminated   : 3
% 0.21/0.53  # Clauses deleted for lack of memory   : 0
% 0.21/0.53  # Backward-subsumed                    : 16
% 0.21/0.53  # Backward-rewritten                   : 25
% 0.21/0.53  # Generated clauses                    : 242
% 0.21/0.53  # ...of the previous two non-redundant : 232
% 0.21/0.53  # ...aggressively subsumed             : 0
% 0.21/0.53  # Contextual simplify-reflections      : 1
% 0.21/0.53  # Paramodulations                      : 233
% 0.21/0.53  # Factorizations                       : 6
% 0.21/0.53  # NegExts                              : 0
% 0.21/0.53  # Equation resolutions                 : 3
% 0.21/0.53  # Total rewrite steps                  : 68
% 0.21/0.53  # Propositional unsat checks           : 0
% 0.21/0.53  #    Propositional check models        : 0
% 0.21/0.53  #    Propositional check unsatisfiable : 0
% 0.21/0.53  #    Propositional clauses             : 0
% 0.21/0.53  #    Propositional clauses after purity: 0
% 0.21/0.53  #    Propositional unsat core size     : 0
% 0.21/0.53  #    Propositional preprocessing time  : 0.000
% 0.21/0.53  #    Propositional encoding time       : 0.000
% 0.21/0.53  #    Propositional solver time         : 0.000
% 0.21/0.53  #    Success case prop preproc time    : 0.000
% 0.21/0.53  #    Success case prop encoding time   : 0.000
% 0.21/0.53  #    Success case prop solver time     : 0.000
% 0.21/0.53  # Current number of processed clauses  : 63
% 0.21/0.53  #    Positive orientable unit clauses  : 17
% 0.21/0.53  #    Positive unorientable unit clauses: 1
% 0.21/0.53  #    Negative unit clauses             : 13
% 0.21/0.53  #    Non-unit-clauses                  : 32
% 0.21/0.53  # Current number of unprocessed clauses: 62
% 0.21/0.53  # ...number of literals in the above   : 150
% 0.21/0.53  # Current number of archived formulas  : 0
% 0.21/0.53  # Current number of archived clauses   : 62
% 0.21/0.53  # Clause-clause subsumption calls (NU) : 921
% 0.21/0.53  # Rec. Clause-clause subsumption calls : 740
% 0.21/0.53  # Non-unit clause-clause subsumptions  : 33
% 0.21/0.53  # Unit Clause-clause subsumption calls : 161
% 0.21/0.53  # Rewrite failures with RHS unbound    : 0
% 0.21/0.53  # BW rewrite match attempts            : 7
% 0.21/0.53  # BW rewrite match successes           : 5
% 0.21/0.53  # Condensation attempts                : 0
% 0.21/0.53  # Condensation successes               : 0
% 0.21/0.53  # Termbank termtop insertions          : 3799
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.014 s
% 0.21/0.53  # System time              : 0.000 s
% 0.21/0.53  # Total time               : 0.014 s
% 0.21/0.53  # Maximum resident set size: 1728 pages
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.014 s
% 0.21/0.53  # System time              : 0.003 s
% 0.21/0.53  # Total time               : 0.017 s
% 0.21/0.53  # Maximum resident set size: 1680 pages
% 0.21/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------