TSTP Solution File: SEU215+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU215+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 03:25:59 EDT 2024

% Result   : Theorem 0.20s 0.54s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (   9 unt;   0 def)
%            Number of atoms       :  171 (  29 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  222 (  84   ~;  85   |;  29   &)
%                                         (   5 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   56 (   0 sgn  35   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t23_funct_1,conjecture,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(X2))
           => apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).

fof(d4_funct_1,axiom,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

fof(t21_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(relation_composition(X3,X2)))
          <=> ( in(X1,relation_dom(X3))
              & in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

fof(t22_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ! [X3] :
          ( ( relation(X3)
            & function(X3) )
         => ( in(X1,relation_dom(relation_composition(X3,X2)))
           => apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).

fof(fc1_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & function(X1)
        & relation(X2)
        & function(X2) )
     => ( relation(relation_composition(X1,X2))
        & function(relation_composition(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

fof(dt_k5_relat_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & relation(X2) )
     => relation(relation_composition(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => ! [X3] :
            ( ( relation(X3)
              & function(X3) )
           => ( in(X1,relation_dom(X2))
             => apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
    inference(assume_negation,[status(cth)],[t23_funct_1]) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2,X3] :
          ( ( in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> in(ordered_pair(X2,X3),X1) ) )
          & ( ~ in(X2,relation_dom(X1))
           => ( X3 = apply(X1,X2)
            <=> X3 = empty_set ) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_funct_1]) ).

fof(c_0_8,plain,
    ! [X40,X41,X42] :
      ( ( in(X40,relation_dom(X42))
        | ~ in(X40,relation_dom(relation_composition(X42,X41)))
        | ~ relation(X42)
        | ~ function(X42)
        | ~ relation(X41)
        | ~ function(X41) )
      & ( in(apply(X42,X40),relation_dom(X41))
        | ~ in(X40,relation_dom(relation_composition(X42,X41)))
        | ~ relation(X42)
        | ~ function(X42)
        | ~ relation(X41)
        | ~ function(X41) )
      & ( ~ in(X40,relation_dom(X42))
        | ~ in(apply(X42,X40),relation_dom(X41))
        | in(X40,relation_dom(relation_composition(X42,X41)))
        | ~ relation(X42)
        | ~ function(X42)
        | ~ relation(X41)
        | ~ function(X41) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])])]) ).

fof(c_0_9,negated_conjecture,
    ( relation(esk9_0)
    & function(esk9_0)
    & relation(esk10_0)
    & function(esk10_0)
    & in(esk8_0,relation_dom(esk9_0))
    & apply(relation_composition(esk9_0,esk10_0),esk8_0) != apply(esk10_0,apply(esk9_0,esk8_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_10,plain,
    ! [X10,X11,X12] :
      ( ( X12 != apply(X10,X11)
        | in(ordered_pair(X11,X12),X10)
        | ~ in(X11,relation_dom(X10))
        | ~ relation(X10)
        | ~ function(X10) )
      & ( ~ in(ordered_pair(X11,X12),X10)
        | X12 = apply(X10,X11)
        | ~ in(X11,relation_dom(X10))
        | ~ relation(X10)
        | ~ function(X10) )
      & ( X12 != apply(X10,X11)
        | X12 = empty_set
        | in(X11,relation_dom(X10))
        | ~ relation(X10)
        | ~ function(X10) )
      & ( X12 != empty_set
        | X12 = apply(X10,X11)
        | in(X11,relation_dom(X10))
        | ~ relation(X10)
        | ~ function(X10) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

cnf(c_0_11,plain,
    ( in(X1,relation_dom(relation_composition(X2,X3)))
    | ~ in(X1,relation_dom(X2))
    | ~ in(apply(X2,X1),relation_dom(X3))
    | ~ relation(X2)
    | ~ function(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    in(esk8_0,relation_dom(esk9_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    relation(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    function(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( X1 = empty_set
    | in(X3,relation_dom(X2))
    | X1 != apply(X2,X3)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X43,X44,X45] :
      ( ~ relation(X44)
      | ~ function(X44)
      | ~ relation(X45)
      | ~ function(X45)
      | ~ in(X43,relation_dom(relation_composition(X45,X44)))
      | apply(relation_composition(X45,X44),X43) = apply(X44,apply(X45,X43)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( in(esk8_0,relation_dom(relation_composition(esk9_0,X1)))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ in(apply(esk9_0,esk8_0),relation_dom(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).

cnf(c_0_18,plain,
    ( apply(X1,X2) = empty_set
    | in(X2,relation_dom(X1))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(er,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2)
    | ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( apply(X1,apply(esk9_0,esk8_0)) = empty_set
    | in(esk8_0,relation_dom(relation_composition(esk9_0,X1)))
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_21,plain,
    ! [X21,X22] :
      ( ( relation(relation_composition(X21,X22))
        | ~ relation(X21)
        | ~ function(X21)
        | ~ relation(X22)
        | ~ function(X22) )
      & ( function(relation_composition(X21,X22))
        | ~ relation(X21)
        | ~ function(X21)
        | ~ relation(X22)
        | ~ function(X22) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])])]) ).

fof(c_0_22,plain,
    ! [X15,X16] :
      ( ~ relation(X15)
      | ~ relation(X16)
      | relation(relation_composition(X15,X16)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).

cnf(c_0_23,negated_conjecture,
    apply(relation_composition(esk9_0,esk10_0),esk8_0) != apply(esk10_0,apply(esk9_0,esk8_0)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_24,negated_conjecture,
    ( apply(X1,apply(esk9_0,esk8_0)) = apply(relation_composition(esk9_0,X1),esk8_0)
    | apply(X1,apply(esk9_0,esk8_0)) = empty_set
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]),c_0_14])]) ).

cnf(c_0_25,negated_conjecture,
    relation(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,negated_conjecture,
    function(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_27,plain,
    ( function(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ function(X1)
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,plain,
    ( relation(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    apply(esk10_0,apply(esk9_0,esk8_0)) = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_30,plain,
    ( apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3)
    | apply(relation_composition(X2,X1),X3) = empty_set
    | ~ relation(X2)
    | ~ relation(X1)
    | ~ function(X2)
    | ~ function(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_27]),c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    apply(relation_composition(esk9_0,esk10_0),esk8_0) != empty_set,
    inference(rw,[status(thm)],[c_0_23,c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_13]),c_0_25]),c_0_14]),c_0_26])]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU215+1 : TPTP v8.2.0. Released v3.3.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 17:55:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 0.20/0.54  # Version: 3.1.0
% 0.20/0.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54  # Starting sh5l with 300s (1) cores
% 0.20/0.54  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 30307 completed with status 0
% 0.20/0.54  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.54  # No SInE strategy applied
% 0.20/0.54  # Search class: FGHSS-FFMM21-SFFFFFNN
% 0.20/0.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 811s (1) cores
% 0.20/0.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.54  # Starting new_bool_3 with 136s (1) cores
% 0.20/0.54  # Starting new_bool_1 with 136s (1) cores
% 0.20/0.54  # Starting sh5l with 136s (1) cores
% 0.20/0.54  # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 30311 completed with status 0
% 0.20/0.54  # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.20/0.54  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.54  # No SInE strategy applied
% 0.20/0.54  # Search class: FGHSS-FFMM21-SFFFFFNN
% 0.20/0.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.54  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 811s (1) cores
% 0.20/0.54  # Preprocessing time       : 0.002 s
% 0.20/0.54  # Presaturation interreduction done
% 0.20/0.54  
% 0.20/0.54  # Proof found!
% 0.20/0.54  # SZS status Theorem
% 0.20/0.54  # SZS output start CNFRefutation
% See solution above
% 0.20/0.54  # Parsed axioms                        : 40
% 0.20/0.54  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.54  # Initial clauses                      : 61
% 0.20/0.54  # Removed in clause preprocessing      : 8
% 0.20/0.54  # Initial clauses in saturation        : 53
% 0.20/0.54  # Processed clauses                    : 556
% 0.20/0.54  # ...of these trivial                  : 3
% 0.20/0.54  # ...subsumed                          : 365
% 0.20/0.54  # ...remaining for further processing  : 188
% 0.20/0.54  # Other redundant clauses eliminated   : 26
% 0.20/0.54  # Clauses deleted for lack of memory   : 0
% 0.20/0.54  # Backward-subsumed                    : 12
% 0.20/0.54  # Backward-rewritten                   : 9
% 0.20/0.54  # Generated clauses                    : 1256
% 0.20/0.54  # ...of the previous two non-redundant : 1180
% 0.20/0.54  # ...aggressively subsumed             : 0
% 0.20/0.54  # Contextual simplify-reflections      : 12
% 0.20/0.54  # Paramodulations                      : 1229
% 0.20/0.54  # Factorizations                       : 1
% 0.20/0.54  # NegExts                              : 0
% 0.20/0.54  # Equation resolutions                 : 26
% 0.20/0.54  # Disequality decompositions           : 0
% 0.20/0.54  # Total rewrite steps                  : 219
% 0.20/0.54  # ...of those cached                   : 202
% 0.20/0.54  # Propositional unsat checks           : 0
% 0.20/0.54  #    Propositional check models        : 0
% 0.20/0.54  #    Propositional check unsatisfiable : 0
% 0.20/0.54  #    Propositional clauses             : 0
% 0.20/0.54  #    Propositional clauses after purity: 0
% 0.20/0.54  #    Propositional unsat core size     : 0
% 0.20/0.54  #    Propositional preprocessing time  : 0.000
% 0.20/0.54  #    Propositional encoding time       : 0.000
% 0.20/0.54  #    Propositional solver time         : 0.000
% 0.20/0.54  #    Success case prop preproc time    : 0.000
% 0.20/0.54  #    Success case prop encoding time   : 0.000
% 0.20/0.54  #    Success case prop solver time     : 0.000
% 0.20/0.54  # Current number of processed clauses  : 117
% 0.20/0.54  #    Positive orientable unit clauses  : 20
% 0.20/0.54  #    Positive unorientable unit clauses: 1
% 0.20/0.54  #    Negative unit clauses             : 12
% 0.20/0.54  #    Non-unit-clauses                  : 84
% 0.20/0.54  # Current number of unprocessed clauses: 712
% 0.20/0.54  # ...number of literals in the above   : 4469
% 0.20/0.54  # Current number of archived formulas  : 0
% 0.20/0.54  # Current number of archived clauses   : 69
% 0.20/0.54  # Clause-clause subsumption calls (NU) : 3900
% 0.20/0.54  # Rec. Clause-clause subsumption calls : 1340
% 0.20/0.54  # Non-unit clause-clause subsumptions  : 202
% 0.20/0.54  # Unit Clause-clause subsumption calls : 86
% 0.20/0.54  # Rewrite failures with RHS unbound    : 0
% 0.20/0.54  # BW rewrite match attempts            : 7
% 0.20/0.54  # BW rewrite match successes           : 7
% 0.20/0.54  # Condensation attempts                : 0
% 0.20/0.54  # Condensation successes               : 0
% 0.20/0.54  # Termbank termtop insertions          : 20726
% 0.20/0.54  # Search garbage collected termcells   : 541
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.041 s
% 0.20/0.54  # System time              : 0.004 s
% 0.20/0.54  # Total time               : 0.045 s
% 0.20/0.54  # Maximum resident set size: 1852 pages
% 0.20/0.54  
% 0.20/0.54  # -------------------------------------------------
% 0.20/0.54  # User time                : 0.173 s
% 0.20/0.54  # System time              : 0.009 s
% 0.20/0.54  # Total time               : 0.182 s
% 0.20/0.54  # Maximum resident set size: 1720 pages
% 0.20/0.54  % E---3.1 exiting
% 0.63/0.54  % E exiting
%------------------------------------------------------------------------------