TSTP Solution File: SEU182+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n005.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 : Thu Aug 31 16:23:08 EDT 2023

% Result   : Theorem 157.83s 158.05s
% Output   : CNFRefutation 157.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   70 (  10 unt;  28 typ;   0 def)
%            Number of atoms       :  196 (  38 equ)
%            Maximal formula atoms :   38 (   4 avg)
%            Number of connectives :  270 ( 116   ~; 125   |;  14   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   43 (  22   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   6 con; 0-5 aty)
%            Number of variables   :  133 (   5 sgn;  48   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    in: ( $i * $i ) > $o ).

tff(decl_23,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_24,type,
    subset: ( $i * $i ) > $o ).

tff(decl_25,type,
    relation: $i > $o ).

tff(decl_26,type,
    relation_dom: $i > $i ).

tff(decl_27,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_28,type,
    singleton: $i > $i ).

tff(decl_29,type,
    relation_composition: ( $i * $i ) > $i ).

tff(decl_30,type,
    element: ( $i * $i ) > $o ).

tff(decl_31,type,
    powerset: $i > $i ).

tff(decl_32,type,
    empty: $i > $o ).

tff(decl_33,type,
    empty_set: $i ).

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk5_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk9_1: $i > $i ).

tff(decl_43,type,
    esk10_0: $i ).

tff(decl_44,type,
    esk11_1: $i > $i ).

tff(decl_45,type,
    esk12_0: $i ).

tff(decl_46,type,
    esk13_1: $i > $i ).

tff(decl_47,type,
    esk14_0: $i ).

tff(decl_48,type,
    esk15_0: $i ).

tff(decl_49,type,
    esk16_0: $i ).

fof(d4_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( X2 = relation_dom(X1)
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(d8_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => ! [X3] :
              ( relation(X3)
             => ( X3 = relation_composition(X1,X2)
              <=> ! [X4,X5] :
                    ( in(ordered_pair(X4,X5),X3)
                  <=> ? [X6] :
                        ( in(ordered_pair(X4,X6),X1)
                        & in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(dt_k5_relat_1,axiom,
    ! [X1,X2] :
      ( ( relation(X1)
        & relation(X2) )
     => relation(relation_composition(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t44_relat_1,conjecture,
    ! [X1] :
      ( relation(X1)
     => ! [X2] :
          ( relation(X2)
         => subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).

fof(c_0_7,plain,
    ! [X17,X18,X19,X21,X22,X23,X25] :
      ( ( ~ in(X19,X18)
        | in(ordered_pair(X19,esk2_3(X17,X18,X19)),X17)
        | X18 != relation_dom(X17)
        | ~ relation(X17) )
      & ( ~ in(ordered_pair(X21,X22),X17)
        | in(X21,X18)
        | X18 != relation_dom(X17)
        | ~ relation(X17) )
      & ( ~ in(esk3_2(X17,X23),X23)
        | ~ in(ordered_pair(esk3_2(X17,X23),X25),X17)
        | X23 = relation_dom(X17)
        | ~ relation(X17) )
      & ( in(esk3_2(X17,X23),X23)
        | in(ordered_pair(esk3_2(X17,X23),esk4_2(X17,X23)),X17)
        | X23 = relation_dom(X17)
        | ~ relation(X17) ) ),
    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)],[d4_relat_1])])])])])]) ).

fof(c_0_8,plain,
    ! [X27,X28] : ordered_pair(X27,X28) = unordered_pair(unordered_pair(X27,X28),singleton(X27)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_9,plain,
    ! [X29,X30,X31,X32,X33,X35,X36,X37,X40] :
      ( ( in(ordered_pair(X32,esk5_5(X29,X30,X31,X32,X33)),X29)
        | ~ in(ordered_pair(X32,X33),X31)
        | X31 != relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) )
      & ( in(ordered_pair(esk5_5(X29,X30,X31,X32,X33),X33),X30)
        | ~ in(ordered_pair(X32,X33),X31)
        | X31 != relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) )
      & ( ~ in(ordered_pair(X35,X37),X29)
        | ~ in(ordered_pair(X37,X36),X30)
        | in(ordered_pair(X35,X36),X31)
        | X31 != relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) )
      & ( ~ in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
        | ~ in(ordered_pair(esk6_3(X29,X30,X31),X40),X29)
        | ~ in(ordered_pair(X40,esk7_3(X29,X30,X31)),X30)
        | X31 = relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) )
      & ( in(ordered_pair(esk6_3(X29,X30,X31),esk8_3(X29,X30,X31)),X29)
        | in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
        | X31 = relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) )
      & ( in(ordered_pair(esk8_3(X29,X30,X31),esk7_3(X29,X30,X31)),X30)
        | in(ordered_pair(esk6_3(X29,X30,X31),esk7_3(X29,X30,X31)),X31)
        | X31 = relation_composition(X29,X30)
        | ~ relation(X31)
        | ~ relation(X30)
        | ~ relation(X29) ) ),
    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)],[d8_relat_1])])])])])]) ).

cnf(c_0_10,plain,
    ( in(X1,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

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

fof(c_0_12,plain,
    ! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_13,plain,
    ( in(ordered_pair(X1,esk5_5(X2,X3,X4,X1,X5)),X2)
    | ~ in(ordered_pair(X1,X5),X4)
    | X4 != relation_composition(X2,X3)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( in(X1,X4)
    | X4 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

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

cnf(c_0_16,plain,
    ( in(unordered_pair(unordered_pair(X1,esk5_5(X2,X3,X4,X1,X5)),singleton(X1)),X2)
    | X4 != relation_composition(X2,X3)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).

cnf(c_0_17,plain,
    ( in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_5(X2,X3,X4,X1,X5))),X2)
    | X4 != relation_composition(X2,X3)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
    inference(rw,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_19,plain,
    ( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
    | ~ in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,plain,
    ( in(X1,X2)
    | X3 != relation_composition(X4,X5)
    | X2 != relation_dom(X4)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X5)
    | ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X3) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_19,c_0_11]) ).

cnf(c_0_22,plain,
    ( in(X1,X2)
    | X3 != relation_composition(X4,X5)
    | X2 != relation_dom(X4)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X5)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

cnf(c_0_23,plain,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,X3,X1))),X2)
    | X3 != relation_dom(X2)
    | ~ relation(X2)
    | ~ in(X1,X3) ),
    inference(rw,[status(thm)],[c_0_21,c_0_15]) ).

fof(c_0_24,plain,
    ! [X42,X43] :
      ( ~ relation(X42)
      | ~ relation(X43)
      | relation(relation_composition(X42,X43)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).

cnf(c_0_25,plain,
    ( in(X1,X2)
    | X3 != relation_composition(X4,X5)
    | X2 != relation_dom(X4)
    | X6 != relation_dom(X3)
    | ~ relation(X4)
    | ~ relation(X3)
    | ~ relation(X5)
    | ~ in(X1,X6) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,plain,
    ( relation(relation_composition(X1,X2))
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_27,plain,
    ( in(X1,X2)
    | X3 != relation_dom(relation_composition(X4,X5))
    | X2 != relation_dom(X4)
    | ~ relation(X4)
    | ~ relation(X5)
    | ~ in(X1,X3) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).

fof(c_0_28,plain,
    ! [X11,X12,X13,X14,X15] :
      ( ( ~ subset(X11,X12)
        | ~ in(X13,X11)
        | in(X13,X12) )
      & ( in(esk1_2(X14,X15),X14)
        | subset(X14,X15) )
      & ( ~ in(esk1_2(X14,X15),X15)
        | subset(X14,X15) ) ),
    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_29,plain,
    ( in(X1,X2)
    | X2 != relation_dom(X3)
    | ~ relation(X3)
    | ~ relation(X4)
    | ~ in(X1,relation_dom(relation_composition(X3,X4))) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_30,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_31,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ! [X2] :
            ( relation(X2)
           => subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
    inference(assume_negation,[status(cth)],[t44_relat_1]) ).

cnf(c_0_32,plain,
    ( subset(relation_dom(relation_composition(X1,X2)),X3)
    | in(esk1_2(relation_dom(relation_composition(X1,X2)),X3),X4)
    | X4 != relation_dom(X1)
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

fof(c_0_33,negated_conjecture,
    ( relation(esk15_0)
    & relation(esk16_0)
    & ~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).

cnf(c_0_34,plain,
    ( subset(relation_dom(relation_composition(X1,X2)),X3)
    | in(esk1_2(relation_dom(relation_composition(X1,X2)),X3),relation_dom(X1))
    | ~ relation(X1)
    | ~ relation(X2) ),
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    relation(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ( subset(relation_dom(relation_composition(esk15_0,X1)),X2)
    | in(esk1_2(relation_dom(relation_composition(esk15_0,X1)),X2),relation_dom(esk15_0))
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    relation(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_38,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_39,negated_conjecture,
    ( subset(relation_dom(relation_composition(esk15_0,esk16_0)),X1)
    | in(esk1_2(relation_dom(relation_composition(esk15_0,esk16_0)),X1),relation_dom(esk15_0)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    ~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Wed Aug 23 15:10:39 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.61  start to proof: theBenchmark
% 157.83/158.05  % Version  : CSE_E---1.5
% 157.83/158.05  % Problem  : theBenchmark.p
% 157.83/158.05  % Proof found
% 157.83/158.05  % SZS status Theorem for theBenchmark.p
% 157.83/158.05  % SZS output start Proof
% See solution above
% 157.83/158.06  % Total time : 157.458000 s
% 157.83/158.06  % SZS output end Proof
% 157.83/158.06  % Total time : 157.468000 s
%------------------------------------------------------------------------------