TSTP Solution File: SEU353+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU353+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 : n020.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 16:24:42 EDT 2023

% Result   : Theorem 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  110 (  16 unt;  45 typ;   0 def)
%            Number of atoms       :  200 (  22 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  212 (  77   ~;  70   |;  43   &)
%                                         (   1 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   61 (  37   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-3 aty)
%            Number of functors    :   26 (  26 usr;   8 con; 0-4 aty)
%            Number of variables   :   98 (   2 sgn;  62   !;   0   ?;   0   :)

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

tff(decl_23,type,
    relation_of2: ( $i * $i * $i ) > $o ).

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

tff(decl_25,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

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

tff(decl_27,type,
    relation: $i > $o ).

tff(decl_28,type,
    symmetric: $i > $o ).

tff(decl_29,type,
    transitive: $i > $o ).

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

tff(decl_31,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

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

tff(decl_37,type,
    empty: $i > $o ).

tff(decl_38,type,
    one_sorted_str: $i > $o ).

tff(decl_39,type,
    identity_on_carrier: $i > $i ).

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

tff(decl_41,type,
    identity_as_relation_of: $i > $i ).

tff(decl_42,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

tff(decl_43,type,
    identity_relation: $i > $i ).

tff(decl_44,type,
    apply_as_element: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    empty_carrier: $i > $o ).

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

tff(decl_47,type,
    antisymmetric: $i > $o ).

tff(decl_48,type,
    apply: ( $i * $i ) > $i ).

tff(decl_49,type,
    subset: ( $i * $i ) > $o ).

tff(decl_50,type,
    esk1_0: $i ).

tff(decl_51,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk3_1: $i > $i ).

tff(decl_53,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk6_0: $i ).

tff(decl_56,type,
    esk7_1: $i > $i ).

tff(decl_57,type,
    esk8_0: $i ).

tff(decl_58,type,
    esk9_1: $i > $i ).

tff(decl_59,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk11_1: $i > $i ).

tff(decl_61,type,
    esk12_0: $i ).

tff(decl_62,type,
    esk13_1: $i > $i ).

tff(decl_63,type,
    esk14_0: $i ).

tff(decl_64,type,
    esk15_1: $i > $i ).

tff(decl_65,type,
    esk16_0: $i ).

tff(decl_66,type,
    esk17_0: $i ).

fof(cc5_funct_2,axiom,
    ! [X1,X2] :
      ( ~ empty(X2)
     => ! [X3] :
          ( relation_of2(X3,X1,X2)
         => ( ( function(X3)
              & quasi_total(X3,X1,X2) )
           => ( function(X3)
              & v1_partfun1(X3,X1,X2)
              & quasi_total(X3,X1,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).

fof(redefinition_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
    <=> relation_of2(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(dt_k7_grcat_1,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => ( function(identity_on_carrier(X1))
        & quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
        & relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).

fof(t91_tmap_1,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).

fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(redefinition_k8_funct_2,axiom,
    ! [X1,X2,X3,X4] :
      ( ( ~ empty(X1)
        & function(X3)
        & quasi_total(X3,X1,X2)
        & relation_of2(X3,X1,X2)
        & element(X4,X1) )
     => apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).

fof(cc1_funct_2,axiom,
    ! [X1,X2,X3] :
      ( relation_of2(X3,X1,X2)
     => ( ( function(X3)
          & v1_partfun1(X3,X1,X2) )
       => ( function(X3)
          & quasi_total(X3,X1,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).

fof(fc2_partfun1,axiom,
    ! [X1] :
      ( relation(identity_relation(X1))
      & function(identity_relation(X1))
      & reflexive(identity_relation(X1))
      & symmetric(identity_relation(X1))
      & antisymmetric(identity_relation(X1))
      & transitive(identity_relation(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).

fof(redefinition_k6_partfun1,axiom,
    ! [X1] : identity_as_relation_of(X1) = identity_relation(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).

fof(dt_k6_partfun1,axiom,
    ! [X1] :
      ( v1_partfun1(identity_as_relation_of(X1),X1,X1)
      & relation_of2_as_subset(identity_as_relation_of(X1),X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).

fof(t35_funct_1,axiom,
    ! [X1,X2] :
      ( in(X2,X1)
     => apply(identity_relation(X1),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).

fof(d11_grcat_1,axiom,
    ! [X1] :
      ( one_sorted_str(X1)
     => identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(c_0_14,plain,
    ! [X1,X2] :
      ( ~ empty(X2)
     => ! [X3] :
          ( relation_of2(X3,X1,X2)
         => ( ( function(X3)
              & quasi_total(X3,X1,X2) )
           => ( function(X3)
              & v1_partfun1(X3,X1,X2)
              & quasi_total(X3,X1,X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cc5_funct_2]) ).

fof(c_0_15,plain,
    ! [X78,X79,X80] :
      ( ( ~ relation_of2_as_subset(X80,X78,X79)
        | relation_of2(X80,X78,X79) )
      & ( ~ relation_of2(X80,X78,X79)
        | relation_of2_as_subset(X80,X78,X79) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).

fof(c_0_16,plain,
    ! [X31] :
      ( ( function(identity_on_carrier(X31))
        | ~ one_sorted_str(X31) )
      & ( quasi_total(identity_on_carrier(X31),the_carrier(X31),the_carrier(X31))
        | ~ one_sorted_str(X31) )
      & ( relation_of2_as_subset(identity_on_carrier(X31),the_carrier(X31),the_carrier(X31))
        | ~ one_sorted_str(X31) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_grcat_1])])]) ).

fof(c_0_17,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(X1))
           => apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t91_tmap_1])]) ).

fof(c_0_18,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ~ empty(the_carrier(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).

fof(c_0_19,plain,
    ! [X22,X23,X24] :
      ( ( function(X24)
        | ~ function(X24)
        | ~ quasi_total(X24,X22,X23)
        | ~ relation_of2(X24,X22,X23)
        | empty(X23) )
      & ( v1_partfun1(X24,X22,X23)
        | ~ function(X24)
        | ~ quasi_total(X24,X22,X23)
        | ~ relation_of2(X24,X22,X23)
        | empty(X23) )
      & ( quasi_total(X24,X22,X23)
        | ~ function(X24)
        | ~ quasi_total(X24,X22,X23)
        | ~ relation_of2(X24,X22,X23)
        | empty(X23) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).

cnf(c_0_20,plain,
    ( relation_of2(X1,X2,X3)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_22,negated_conjecture,
    ( ~ empty_carrier(esk16_0)
    & one_sorted_str(esk16_0)
    & element(esk17_0,the_carrier(esk16_0))
    & apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_on_carrier(esk16_0),esk17_0) != esk17_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

fof(c_0_23,plain,
    ! [X48] :
      ( empty_carrier(X48)
      | ~ one_sorted_str(X48)
      | ~ empty(the_carrier(X48)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

cnf(c_0_24,plain,
    ( v1_partfun1(X1,X2,X3)
    | empty(X3)
    | ~ function(X1)
    | ~ quasi_total(X1,X2,X3)
    | ~ relation_of2(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    ( quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,plain,
    ( relation_of2(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    ( function(identity_on_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_28,negated_conjecture,
    ~ empty_carrier(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( empty_carrier(X1)
    | ~ one_sorted_str(X1)
    | ~ empty(the_carrier(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,negated_conjecture,
    one_sorted_str(esk16_0),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_31,plain,
    ! [X1,X2,X3,X4] :
      ( ( ~ empty(X1)
        & function(X3)
        & quasi_total(X3,X1,X2)
        & relation_of2(X3,X1,X2)
        & element(X4,X1) )
     => apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
    inference(fof_simplification,[status(thm)],[redefinition_k8_funct_2]) ).

fof(c_0_32,plain,
    ! [X7,X8,X9] :
      ( ( function(X9)
        | ~ function(X9)
        | ~ v1_partfun1(X9,X7,X8)
        | ~ relation_of2(X9,X7,X8) )
      & ( quasi_total(X9,X7,X8)
        | ~ function(X9)
        | ~ v1_partfun1(X9,X7,X8)
        | ~ relation_of2(X9,X7,X8) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])]) ).

cnf(c_0_33,plain,
    ( empty(the_carrier(X1))
    | v1_partfun1(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    ~ empty(the_carrier(esk16_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

fof(c_0_35,plain,
    ! [X74,X75,X76,X77] :
      ( empty(X74)
      | ~ function(X76)
      | ~ quasi_total(X76,X74,X75)
      | ~ relation_of2(X76,X74,X75)
      | ~ element(X77,X74)
      | apply_as_element(X74,X75,X76,X77) = apply(X76,X77) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).

cnf(c_0_36,plain,
    ( quasi_total(X1,X2,X3)
    | ~ function(X1)
    | ~ v1_partfun1(X1,X2,X3)
    | ~ relation_of2(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    v1_partfun1(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_34]) ).

fof(c_0_38,plain,
    ! [X50] :
      ( relation(identity_relation(X50))
      & function(identity_relation(X50))
      & reflexive(identity_relation(X50))
      & symmetric(identity_relation(X50))
      & antisymmetric(identity_relation(X50))
      & transitive(identity_relation(X50)) ),
    inference(variable_rename,[status(thm)],[fc2_partfun1]) ).

fof(c_0_39,plain,
    ! [X73] : identity_as_relation_of(X73) = identity_relation(X73),
    inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).

fof(c_0_40,plain,
    ! [X29] :
      ( v1_partfun1(identity_as_relation_of(X29),X29,X29)
      & relation_of2_as_subset(identity_as_relation_of(X29),X29,X29) ),
    inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).

fof(c_0_41,plain,
    ! [X86,X87] :
      ( ~ in(X87,X86)
      | apply(identity_relation(X86),X87) = X87 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_funct_1])]) ).

cnf(c_0_42,plain,
    ( empty(X1)
    | apply_as_element(X1,X3,X2,X4) = apply(X2,X4)
    | ~ function(X2)
    | ~ quasi_total(X2,X1,X3)
    | ~ relation_of2(X2,X1,X3)
    | ~ element(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    ( quasi_total(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0))
    | ~ function(identity_on_carrier(esk16_0))
    | ~ relation_of2(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_44,plain,
    ! [X28] :
      ( ~ one_sorted_str(X28)
      | identity_on_carrier(X28) = identity_as_relation_of(the_carrier(X28)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_grcat_1])]) ).

cnf(c_0_45,plain,
    function(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    identity_as_relation_of(X1) = identity_relation(X1),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_47,plain,
    relation_of2_as_subset(identity_as_relation_of(X1),X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_48,plain,
    ( apply(identity_relation(X2),X1) = X1
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_49,negated_conjecture,
    ( apply(identity_on_carrier(esk16_0),X1) = apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_on_carrier(esk16_0),X1)
    | ~ element(X1,the_carrier(esk16_0))
    | ~ function(identity_on_carrier(esk16_0))
    | ~ relation_of2(identity_on_carrier(esk16_0),the_carrier(esk16_0),the_carrier(esk16_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]) ).

cnf(c_0_50,plain,
    ( identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1))
    | ~ one_sorted_str(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_51,plain,
    function(identity_as_relation_of(X1)),
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_52,plain,
    relation_of2(identity_as_relation_of(X1),X1,X1),
    inference(spm,[status(thm)],[c_0_20,c_0_47]) ).

fof(c_0_53,plain,
    ! [X82,X83] :
      ( ~ in(X82,X83)
      | element(X82,X83) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

fof(c_0_54,plain,
    ! [X84,X85] :
      ( ~ element(X84,X85)
      | empty(X85)
      | in(X84,X85) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

cnf(c_0_55,negated_conjecture,
    apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_on_carrier(esk16_0),esk17_0) != esk17_0,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_56,plain,
    ( apply(identity_as_relation_of(X2),X1) = X1
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_48,c_0_46]) ).

cnf(c_0_57,negated_conjecture,
    ( apply(identity_as_relation_of(the_carrier(esk16_0)),X1) = apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_as_relation_of(the_carrier(esk16_0)),X1)
    | ~ element(X1,the_carrier(esk16_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_30])]) ).

cnf(c_0_58,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_59,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_60,negated_conjecture,
    element(esk17_0,the_carrier(esk16_0)),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_61,negated_conjecture,
    apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_as_relation_of(the_carrier(esk16_0)),esk17_0) != esk17_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_30])]) ).

cnf(c_0_62,negated_conjecture,
    ( apply_as_element(the_carrier(esk16_0),the_carrier(esk16_0),identity_as_relation_of(the_carrier(esk16_0)),X1) = X1
    | ~ in(X1,the_carrier(esk16_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).

cnf(c_0_63,negated_conjecture,
    in(esk17_0,the_carrier(esk16_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_34]) ).

cnf(c_0_64,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Thu Aug 24 01:01:31 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.027000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.030000 s
%------------------------------------------------------------------------------