TSTP Solution File: SEU251+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% 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 : Thu Aug 31 16:23:48 EDT 2023

% Result   : Theorem 192.10s 192.73s
% Output   : CNFRefutation 192.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   69 (  16 unt;  27 typ;   0 def)
%            Number of atoms       :  130 (  30 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  153 (  65   ~;  66   |;  12   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  18   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   9 con; 0-3 aty)
%            Number of variables   :   90 (   2 sgn;  43   !;   0   ?;   0   :)

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

tff(decl_23,type,
    empty: $i > $o ).

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

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

tff(decl_26,type,
    one_to_one: $i > $o ).

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

tff(decl_28,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

tff(decl_31,type,
    subset: ( $i * $i ) > $o ).

tff(decl_32,type,
    singleton: $i > $i ).

tff(decl_33,type,
    relation_restriction: ( $i * $i ) > $i ).

tff(decl_34,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

tff(decl_36,type,
    empty_set: $i ).

tff(decl_37,type,
    powerset: $i > $i ).

tff(decl_38,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk3_1: $i > $i ).

tff(decl_41,type,
    esk4_0: $i ).

tff(decl_42,type,
    esk5_0: $i ).

tff(decl_43,type,
    esk6_0: $i ).

tff(decl_44,type,
    esk7_0: $i ).

tff(decl_45,type,
    esk8_0: $i ).

tff(decl_46,type,
    esk9_0: $i ).

tff(decl_47,type,
    esk10_0: $i ).

tff(decl_48,type,
    esk11_0: $i ).

fof(d1_wellord1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2,X3] :
          ( X3 = fiber(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ( X4 != X2
                & in(ordered_pair(X4,X2),X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord1) ).

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

fof(t21_wellord1,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).

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

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(dt_k2_wellord1,axiom,
    ! [X1,X2] :
      ( relation(X1)
     => relation(relation_restriction(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).

fof(t16_wellord1,axiom,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(X1,relation_restriction(X3,X2))
      <=> ( in(X1,X3)
          & in(X1,cartesian_product2(X2,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).

fof(c_0_7,plain,
    ! [X13,X14,X15,X16,X17,X18,X19] :
      ( ( X16 != X14
        | ~ in(X16,X15)
        | X15 != fiber(X13,X14)
        | ~ relation(X13) )
      & ( in(ordered_pair(X16,X14),X13)
        | ~ in(X16,X15)
        | X15 != fiber(X13,X14)
        | ~ relation(X13) )
      & ( X17 = X14
        | ~ in(ordered_pair(X17,X14),X13)
        | in(X17,X15)
        | X15 != fiber(X13,X14)
        | ~ relation(X13) )
      & ( ~ in(esk1_3(X13,X18,X19),X19)
        | esk1_3(X13,X18,X19) = X18
        | ~ in(ordered_pair(esk1_3(X13,X18,X19),X18),X13)
        | X19 = fiber(X13,X18)
        | ~ relation(X13) )
      & ( esk1_3(X13,X18,X19) != X18
        | in(esk1_3(X13,X18,X19),X19)
        | X19 = fiber(X13,X18)
        | ~ relation(X13) )
      & ( in(ordered_pair(esk1_3(X13,X18,X19),X18),X13)
        | in(esk1_3(X13,X18,X19),X19)
        | X19 = fiber(X13,X18)
        | ~ relation(X13) ) ),
    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)],[d1_wellord1])])])])])]) ).

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,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => subset(fiber(relation_restriction(X3,X1),X2),fiber(X3,X2)) ),
    inference(assume_negation,[status(cth)],[t21_wellord1]) ).

cnf(c_0_10,plain,
    ( in(ordered_pair(X1,X2),X3)
    | ~ in(X1,X4)
    | X4 != fiber(X3,X2)
    | ~ 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,negated_conjecture,
    ( relation(esk11_0)
    & ~ subset(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_13,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ( ~ subset(X21,X22)
        | ~ in(X23,X21)
        | in(X23,X22) )
      & ( in(esk2_2(X24,X25),X24)
        | subset(X24,X25) )
      & ( ~ in(esk2_2(X24,X25),X25)
        | subset(X24,X25) ) ),
    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_14,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
    | X4 != fiber(X3,X2)
    | ~ relation(X3)
    | ~ in(X1,X4) ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    ~ subset(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_17,plain,
    ! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_18,plain,
    ( X1 = X2
    | in(X1,X4)
    | ~ in(ordered_pair(X1,X2),X3)
    | X4 != fiber(X3,X2)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
    | ~ relation(X3)
    | ~ in(X1,fiber(X3,X2)) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    in(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),fiber(relation_restriction(esk11_0,esk9_0),esk10_0)),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_22,plain,
    ! [X31,X32] :
      ( ~ relation(X31)
      | relation(relation_restriction(X31,X32)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | in(X1,X4)
    | X4 != fiber(X3,X2)
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(rw,[status(thm)],[c_0_18,c_0_11]) ).

fof(c_0_24,plain,
    ! [X44,X45,X46] :
      ( ( in(X44,X46)
        | ~ in(X44,relation_restriction(X46,X45))
        | ~ relation(X46) )
      & ( in(X44,cartesian_product2(X45,X45))
        | ~ in(X44,relation_restriction(X46,X45))
        | ~ relation(X46) )
      & ( ~ in(X44,X46)
        | ~ in(X44,cartesian_product2(X45,X45))
        | in(X44,relation_restriction(X46,X45))
        | ~ relation(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).

cnf(c_0_25,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),relation_restriction(esk11_0,esk9_0))
    | ~ relation(relation_restriction(esk11_0,esk9_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_26,plain,
    ( relation(relation_restriction(X1,X2))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    relation(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | in(X1,fiber(X3,X2))
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    ( in(X1,X2)
    | ~ in(X1,relation_restriction(X2,X3))
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),relation_restriction(esk11_0,esk9_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_31,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_32,plain,
    ( X1 != X2
    | ~ in(X1,X3)
    | X3 != fiber(X4,X2)
    | ~ relation(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_33,plain,
    ( X1 = X2
    | in(X1,fiber(X3,X2))
    | ~ relation(X3)
    | ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X1)),X3) ),
    inference(spm,[status(thm)],[c_0_28,c_0_21]) ).

cnf(c_0_34,negated_conjecture,
    in(unordered_pair(unordered_pair(esk10_0,esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0))),singleton(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)))),esk11_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).

cnf(c_0_35,negated_conjecture,
    ~ in(esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)),fiber(esk11_0,esk10_0)),
    inference(spm,[status(thm)],[c_0_15,c_0_31]) ).

cnf(c_0_36,plain,
    ( X1 != fiber(X2,X3)
    | ~ relation(X2)
    | ~ in(X3,X1) ),
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    esk2_2(fiber(relation_restriction(esk11_0,esk9_0),esk10_0),fiber(esk11_0,esk10_0)) = esk10_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27])]),c_0_35]) ).

cnf(c_0_38,plain,
    ( ~ relation(X1)
    | ~ in(X2,fiber(X1,X2)) ),
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    in(esk10_0,fiber(relation_restriction(esk11_0,esk9_0),esk10_0)),
    inference(rw,[status(thm)],[c_0_20,c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    ~ relation(relation_restriction(esk11_0,esk9_0)),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_26]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 20:49:23 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 192.10/192.73  % Version  : CSE_E---1.5
% 192.10/192.73  % Problem  : theBenchmark.p
% 192.10/192.73  % Proof found
% 192.10/192.73  % SZS status Theorem for theBenchmark.p
% 192.10/192.73  % SZS output start Proof
% See solution above
% 192.10/192.74  % Total time : 191.606000 s
% 192.10/192.74  % SZS output end Proof
% 192.10/192.74  % Total time : 191.618000 s
%------------------------------------------------------------------------------