TSTP Solution File: SET930+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 03:00:27 EDT 2024

% Result   : Theorem 136.30s 136.65s
% Output   : CNFRefutation 136.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  12 unt;   0 def)
%            Number of atoms       :   99 (  51 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  116 (  54   ~;  34   |;  21   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   68 (   2 sgn  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(l39_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    <=> ( ~ in(X1,X3)
        & ( in(X2,X3)
          | X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).

fof(t72_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
    <=> ( ~ in(X1,X3)
        & ~ in(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).

fof(antisymmetry_r2_hidden,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(t74_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
        & set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
        & set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
        & set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).

fof(t73_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = empty_set
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_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(c_0_6,plain,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    <=> ( ~ in(X1,X3)
        & ( in(X2,X3)
          | X1 = X2 ) ) ),
    inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).

fof(c_0_7,plain,
    ! [X15,X16,X17] :
      ( ( ~ in(X15,X17)
        | set_difference(unordered_pair(X15,X16),X17) != singleton(X15) )
      & ( in(X16,X17)
        | X15 = X16
        | set_difference(unordered_pair(X15,X16),X17) != singleton(X15) )
      & ( ~ in(X16,X17)
        | in(X15,X17)
        | set_difference(unordered_pair(X15,X16),X17) = singleton(X15) )
      & ( X15 != X16
        | in(X15,X17)
        | set_difference(unordered_pair(X15,X16),X17) = singleton(X15) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_8,plain,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
    <=> ( ~ in(X1,X3)
        & ~ in(X2,X3) ) ),
    inference(fof_simplification,[status(thm)],[t72_zfmisc_1]) ).

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

cnf(c_0_10,plain,
    ( in(X1,X3)
    | set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X9,X10,X11] :
      ( ( ~ in(X9,X11)
        | set_difference(unordered_pair(X9,X10),X11) != unordered_pair(X9,X10) )
      & ( ~ in(X10,X11)
        | set_difference(unordered_pair(X9,X10),X11) != unordered_pair(X9,X10) )
      & ( in(X9,X11)
        | in(X10,X11)
        | set_difference(unordered_pair(X9,X10),X11) = unordered_pair(X9,X10) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

fof(c_0_12,plain,
    ! [X18,X19] :
      ( ~ in(X18,X19)
      | ~ in(X19,X18) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_13,plain,
    ( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
    | in(X1,X2) ),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( in(X1,X2)
    | in(X3,X2)
    | set_difference(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
          & set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
          & set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
          & set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t74_zfmisc_1])]) ).

cnf(c_0_16,plain,
    ( ~ in(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( unordered_pair(X1,X1) = singleton(X1)
    | in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

fof(c_0_18,negated_conjecture,
    ( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set
    & set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0)
    & set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk2_0)
    & set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != unordered_pair(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_15])])])]) ).

fof(c_0_19,plain,
    ! [X12,X13,X14] :
      ( ( in(X12,X14)
        | set_difference(unordered_pair(X12,X13),X14) != empty_set )
      & ( in(X13,X14)
        | set_difference(unordered_pair(X12,X13),X14) != empty_set )
      & ( ~ in(X12,X14)
        | ~ in(X13,X14)
        | set_difference(unordered_pair(X12,X13),X14) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t73_zfmisc_1])])])]) ).

cnf(c_0_20,plain,
    ( unordered_pair(X1,X1) = singleton(X1)
    | ~ in(X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,plain,
    ( set_difference(unordered_pair(X1,X3),X2) = empty_set
    | ~ in(X1,X2)
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    ( unordered_pair(X1,X1) = singleton(X1)
    | unordered_pair(X2,X2) = singleton(X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

fof(c_0_24,plain,
    ! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_25,negated_conjecture,
    set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( in(X3,X2)
    | set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ in(esk2_0,esk3_0)
    | ~ in(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_29,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(ef,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != unordered_pair(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_32,negated_conjecture,
    ~ in(esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != unordered_pair(esk2_0,esk2_0),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
    | in(X2,X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    in(esk1_0,esk3_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_35])]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n024.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 11:25:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.52  Running first-order model finding
% 0.21/0.52  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/benchmark/theBenchmark.p
% 136.30/136.65  # Version: 3.1.0
% 136.30/136.65  # Preprocessing class: FSMSSMSSSSSNFFN.
% 136.30/136.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.30/136.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 136.30/136.65  # Starting new_bool_3 with 300s (1) cores
% 136.30/136.65  # Starting new_bool_1 with 300s (1) cores
% 136.30/136.65  # Starting sh5l with 300s (1) cores
% 136.30/136.65  # new_bool_1 with pid 29546 completed with status 0
% 136.30/136.65  # Result found by new_bool_1
% 136.30/136.65  # Preprocessing class: FSMSSMSSSSSNFFN.
% 136.30/136.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.30/136.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 136.30/136.65  # Starting new_bool_3 with 300s (1) cores
% 136.30/136.65  # Starting new_bool_1 with 300s (1) cores
% 136.30/136.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 136.30/136.65  # Search class: FGHSF-FFSF21-SFFFFFNN
% 136.30/136.65  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 136.30/136.65  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 136.30/136.65  # SAT001_MinMin_p005000_rr_RG with pid 29549 completed with status 0
% 136.30/136.65  # Result found by SAT001_MinMin_p005000_rr_RG
% 136.30/136.65  # Preprocessing class: FSMSSMSSSSSNFFN.
% 136.30/136.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 136.30/136.65  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 136.30/136.65  # Starting new_bool_3 with 300s (1) cores
% 136.30/136.65  # Starting new_bool_1 with 300s (1) cores
% 136.30/136.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 136.30/136.65  # Search class: FGHSF-FFSF21-SFFFFFNN
% 136.30/136.65  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 136.30/136.65  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 136.30/136.65  # Preprocessing time       : 0.001 s
% 136.30/136.65  # Presaturation interreduction done
% 136.30/136.65  
% 136.30/136.65  # Proof found!
% 136.30/136.65  # SZS status Theorem
% 136.30/136.65  # SZS output start CNFRefutation
% See solution above
% 136.30/136.65  # Parsed axioms                        : 9
% 136.30/136.65  # Removed by relevancy pruning/SinE    : 0
% 136.30/136.65  # Initial clauses                      : 19
% 136.30/136.65  # Removed in clause preprocessing      : 0
% 136.30/136.65  # Initial clauses in saturation        : 19
% 136.30/136.65  # Processed clauses                    : 149
% 136.30/136.65  # ...of these trivial                  : 3
% 136.30/136.65  # ...subsumed                          : 65
% 136.30/136.65  # ...remaining for further processing  : 81
% 136.30/136.65  # Other redundant clauses eliminated   : 1
% 136.30/136.65  # Clauses deleted for lack of memory   : 0
% 136.30/136.65  # Backward-subsumed                    : 14
% 136.30/136.65  # Backward-rewritten                   : 6
% 136.30/136.65  # Generated clauses                    : 266
% 136.30/136.65  # ...of the previous two non-redundant : 222
% 136.30/136.65  # ...aggressively subsumed             : 0
% 136.30/136.65  # Contextual simplify-reflections      : 4
% 136.30/136.65  # Paramodulations                      : 256
% 136.30/136.65  # Factorizations                       : 4
% 136.30/136.65  # NegExts                              : 0
% 136.30/136.65  # Equation resolutions                 : 6
% 136.30/136.65  # Disequality decompositions           : 0
% 136.30/136.65  # Total rewrite steps                  : 34
% 136.30/136.65  # ...of those cached                   : 28
% 136.30/136.65  # Propositional unsat checks           : 0
% 136.30/136.65  #    Propositional check models        : 0
% 136.30/136.65  #    Propositional check unsatisfiable : 0
% 136.30/136.65  #    Propositional clauses             : 0
% 136.30/136.65  #    Propositional clauses after purity: 0
% 136.30/136.65  #    Propositional unsat core size     : 0
% 136.30/136.65  #    Propositional preprocessing time  : 0.000
% 136.30/136.65  #    Propositional encoding time       : 0.000
% 136.30/136.65  #    Propositional solver time         : 0.000
% 136.30/136.65  #    Success case prop preproc time    : 0.000
% 136.30/136.65  #    Success case prop encoding time   : 0.000
% 136.30/136.65  #    Success case prop solver time     : 0.000
% 136.30/136.65  # Current number of processed clauses  : 41
% 136.30/136.65  #    Positive orientable unit clauses  : 3
% 136.30/136.65  #    Positive unorientable unit clauses: 2
% 136.30/136.65  #    Negative unit clauses             : 11
% 136.30/136.65  #    Non-unit-clauses                  : 25
% 136.30/136.65  # Current number of unprocessed clauses: 98
% 136.30/136.65  # ...number of literals in the above   : 298
% 136.30/136.65  # Current number of archived formulas  : 0
% 136.30/136.65  # Current number of archived clauses   : 39
% 136.30/136.65  # Clause-clause subsumption calls (NU) : 175
% 136.30/136.65  # Rec. Clause-clause subsumption calls : 160
% 136.30/136.65  # Non-unit clause-clause subsumptions  : 51
% 136.30/136.65  # Unit Clause-clause subsumption calls : 35
% 136.30/136.65  # Rewrite failures with RHS unbound    : 0
% 136.30/136.65  # BW rewrite match attempts            : 22
% 136.30/136.65  # BW rewrite match successes           : 14
% 136.30/136.65  # Condensation attempts                : 0
% 136.30/136.65  # Condensation successes               : 0
% 136.30/136.65  # Termbank termtop insertions          : 3254
% 136.30/136.65  # Search garbage collected termcells   : 176
% 136.30/136.65  
% 136.30/136.65  # -------------------------------------------------
% 136.30/136.65  # User time                : 0.011 s
% 136.30/136.65  # System time              : 0.001 s
% 136.30/136.65  # Total time               : 0.012 s
% 136.30/136.65  # Maximum resident set size: 1740 pages
% 136.30/136.65  
% 136.30/136.65  # -------------------------------------------------
% 136.30/136.65  # User time                : 0.011 s
% 136.30/136.65  # System time              : 0.004 s
% 136.30/136.65  # Total time               : 0.015 s
% 136.30/136.65  # Maximum resident set size: 1696 pages
% 136.30/136.65  % E---3.1 exiting
%------------------------------------------------------------------------------