TSTP Solution File: SET918+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET918+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:56:31 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (  13 unt;   0 def)
%            Number of atoms       :  105 (  58 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  122 (  46   ~;  50   |;  20   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   71 (   2 sgn  47   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t59_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
        & in(X2,X3)
        & X1 != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(d3_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(d2_tarski,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
          & in(X2,X3)
          & X1 != X2 ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t59_zfmisc_1])]) ).

fof(c_0_7,negated_conjecture,
    ( set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0)
    & in(esk2_0,esk3_0)
    & esk1_0 != esk2_0 ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_8,plain,
    ! [X38,X39] : unordered_pair(X38,X39) = unordered_pair(X39,X38),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_9,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( ~ in(X12,X11)
        | X12 = X10
        | X11 != singleton(X10) )
      & ( X13 != X10
        | in(X13,X11)
        | X11 != singleton(X10) )
      & ( ~ in(esk4_2(X14,X15),X15)
        | esk4_2(X14,X15) != X14
        | X15 = singleton(X14) )
      & ( in(esk4_2(X14,X15),X15)
        | esk4_2(X14,X15) = X14
        | X15 = singleton(X14) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_10,negated_conjecture,
    set_intersection2(unordered_pair(esk1_0,esk2_0),esk3_0) = singleton(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X35,X36] : set_intersection2(X35,X36) = set_intersection2(X36,X35),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_13,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    singleton(esk1_0) = set_intersection2(unordered_pair(esk2_0,esk1_0),esk3_0),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X26,X27,X28,X29,X30,X31,X32,X33] :
      ( ( in(X29,X26)
        | ~ in(X29,X28)
        | X28 != set_intersection2(X26,X27) )
      & ( in(X29,X27)
        | ~ in(X29,X28)
        | X28 != set_intersection2(X26,X27) )
      & ( ~ in(X30,X26)
        | ~ in(X30,X27)
        | in(X30,X28)
        | X28 != set_intersection2(X26,X27) )
      & ( ~ in(esk6_3(X31,X32,X33),X33)
        | ~ in(esk6_3(X31,X32,X33),X31)
        | ~ in(esk6_3(X31,X32,X33),X32)
        | X33 = set_intersection2(X31,X32) )
      & ( in(esk6_3(X31,X32,X33),X31)
        | in(esk6_3(X31,X32,X33),X33)
        | X33 = set_intersection2(X31,X32) )
      & ( in(esk6_3(X31,X32,X33),X32)
        | in(esk6_3(X31,X32,X33),X33)
        | X33 = set_intersection2(X31,X32) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_xboole_0])])])])])])]) ).

cnf(c_0_17,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    singleton(esk1_0) = set_intersection2(esk3_0,unordered_pair(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    ( in(X1,X4)
    | ~ in(X1,X2)
    | ~ in(X1,X3)
    | X4 != set_intersection2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_20,plain,
    ! [X17,X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ in(X20,X19)
        | X20 = X17
        | X20 = X18
        | X19 != unordered_pair(X17,X18) )
      & ( X21 != X17
        | in(X21,X19)
        | X19 != unordered_pair(X17,X18) )
      & ( X21 != X18
        | in(X21,X19)
        | X19 != unordered_pair(X17,X18) )
      & ( esk5_3(X22,X23,X24) != X22
        | ~ in(esk5_3(X22,X23,X24),X24)
        | X24 = unordered_pair(X22,X23) )
      & ( esk5_3(X22,X23,X24) != X23
        | ~ in(esk5_3(X22,X23,X24),X24)
        | X24 = unordered_pair(X22,X23) )
      & ( in(esk5_3(X22,X23,X24),X24)
        | esk5_3(X22,X23,X24) = X22
        | esk5_3(X22,X23,X24) = X23
        | X24 = unordered_pair(X22,X23) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d2_tarski])])])])])])]) ).

cnf(c_0_21,negated_conjecture,
    ( X1 = esk1_0
    | ~ in(X1,set_intersection2(esk3_0,unordered_pair(esk2_0,esk1_0))) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != unordered_pair(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    ( X1 = esk1_0
    | ~ in(X1,unordered_pair(esk2_0,esk1_0))
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).

cnf(c_0_26,negated_conjecture,
    in(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_27,negated_conjecture,
    esk1_0 != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET918+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 12:55:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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/benchmark/theBenchmark.p
% 0.19/0.49  # Version: 3.1.0
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.49  # Starting sh5l with 300s (1) cores
% 0.19/0.49  # sh5l with pid 5088 completed with status 0
% 0.19/0.49  # Result found by sh5l
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.49  # Starting sh5l with 300s (1) cores
% 0.19/0.49  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.49  # Search class: FGHSS-FFMF32-SFFFFFNN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 103s (1) cores
% 0.19/0.49  # G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 5096 completed with status 0
% 0.19/0.49  # Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.49  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.49  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.49  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.49  # Starting sh5l with 300s (1) cores
% 0.19/0.49  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.49  # Search class: FGHSS-FFMF32-SFFFFFNN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 103s (1) cores
% 0.19/0.49  # Preprocessing time       : 0.001 s
% 0.19/0.49  # Presaturation interreduction done
% 0.19/0.49  
% 0.19/0.49  # Proof found!
% 0.19/0.49  # SZS status Theorem
% 0.19/0.49  # SZS output start CNFRefutation
% See solution above
% 0.19/0.49  # Parsed axioms                        : 10
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 2
% 0.19/0.49  # Initial clauses                      : 23
% 0.19/0.49  # Removed in clause preprocessing      : 0
% 0.19/0.49  # Initial clauses in saturation        : 23
% 0.19/0.49  # Processed clauses                    : 69
% 0.19/0.49  # ...of these trivial                  : 0
% 0.19/0.49  # ...subsumed                          : 8
% 0.19/0.49  # ...remaining for further processing  : 61
% 0.19/0.49  # Other redundant clauses eliminated   : 11
% 0.19/0.49  # Clauses deleted for lack of memory   : 0
% 0.19/0.49  # Backward-subsumed                    : 0
% 0.19/0.49  # Backward-rewritten                   : 2
% 0.19/0.49  # Generated clauses                    : 60
% 0.19/0.49  # ...of the previous two non-redundant : 49
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 0
% 0.19/0.49  # Paramodulations                      : 52
% 0.19/0.49  # Factorizations                       : 0
% 0.19/0.49  # NegExts                              : 0
% 0.19/0.49  # Equation resolutions                 : 11
% 0.19/0.49  # Disequality decompositions           : 0
% 0.19/0.49  # Total rewrite steps                  : 10
% 0.19/0.49  # ...of those cached                   : 1
% 0.19/0.49  # Propositional unsat checks           : 0
% 0.19/0.49  #    Propositional check models        : 0
% 0.19/0.49  #    Propositional check unsatisfiable : 0
% 0.19/0.49  #    Propositional clauses             : 0
% 0.19/0.49  #    Propositional clauses after purity: 0
% 0.19/0.49  #    Propositional unsat core size     : 0
% 0.19/0.49  #    Propositional preprocessing time  : 0.000
% 0.19/0.49  #    Propositional encoding time       : 0.000
% 0.19/0.49  #    Propositional solver time         : 0.000
% 0.19/0.49  #    Success case prop preproc time    : 0.000
% 0.19/0.49  #    Success case prop encoding time   : 0.000
% 0.19/0.49  #    Success case prop solver time     : 0.000
% 0.19/0.49  # Current number of processed clauses  : 28
% 0.19/0.49  #    Positive orientable unit clauses  : 8
% 0.19/0.49  #    Positive unorientable unit clauses: 2
% 0.19/0.49  #    Negative unit clauses             : 7
% 0.19/0.49  #    Non-unit-clauses                  : 11
% 0.19/0.49  # Current number of unprocessed clauses: 26
% 0.19/0.49  # ...number of literals in the above   : 72
% 0.19/0.49  # Current number of archived formulas  : 0
% 0.19/0.49  # Current number of archived clauses   : 25
% 0.19/0.49  # Clause-clause subsumption calls (NU) : 153
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 138
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 2
% 0.19/0.49  # Unit Clause-clause subsumption calls : 17
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 22
% 0.19/0.49  # BW rewrite match successes           : 18
% 0.19/0.49  # Condensation attempts                : 0
% 0.19/0.49  # Condensation successes               : 0
% 0.19/0.49  # Termbank termtop insertions          : 1959
% 0.19/0.49  # Search garbage collected termcells   : 478
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.008 s
% 0.19/0.49  # System time              : 0.002 s
% 0.19/0.49  # Total time               : 0.010 s
% 0.19/0.49  # Maximum resident set size: 1696 pages
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.008 s
% 0.19/0.49  # System time              : 0.005 s
% 0.19/0.49  # Total time               : 0.013 s
% 0.19/0.49  # Maximum resident set size: 1696 pages
% 0.19/0.49  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------