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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SET648+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n016.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  5 05:08:14 PM UTC 2026

% Result   : Theorem 2.29s 2.02s
% Output   : CNFRefutation 2.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   66 (  11 unt;   0 def)
%            Number of atoms       :  265 (   0 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  334 ( 135   ~; 134   |;  20   &)
%                                         (   7 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-2 aty)
%            Number of variables   :  130 (   2 sgn  58   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( ( subset(X1,X2)
                  & subset(X2,X3) )
               => subset(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(p26,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).

fof(p3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( subset(X1,X2)
               => ( subset(cross_product(X1,X3),cross_product(X2,X3))
                  & subset(cross_product(X3,X1),cross_product(X3,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,binary_relation_type)
     => subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(prove_relset_1_10,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,binary_relation_type)
         => ( subset(range_of(X2),X1)
           => ilf_type(X2,relation_type(domain_of(X2),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_10) ).

fof(p24,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).

fof(p17,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => subset(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).

fof(p22,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(p12,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( subset(X1,X2)
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).

fof(p4,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X1,X2)))
               => ilf_type(X3,relation_type(X1,X2)) )
            & ! [X4] :
                ( ilf_type(X4,relation_type(X1,X2))
               => ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).

fof(p15,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,subset_type(X1))
          <=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).

fof(p20,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X1,power_set(X2))
          <=> ! [X3] :
                ( ilf_type(X3,set_type)
               => ( member(X3,X1)
                 => member(X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).

fof(c_0_12,plain,
    ! [X62,X63,X64] :
      ( ~ ilf_type(X62,set_type)
      | ~ ilf_type(X63,set_type)
      | ~ ilf_type(X64,set_type)
      | ~ subset(X62,X63)
      | ~ subset(X63,X64)
      | subset(X62,X64) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).

fof(c_0_13,plain,
    ! [X124] : ilf_type(X124,set_type),
    inference(variable_rename,[status(thm)],[p26]) ).

fof(c_0_14,plain,
    ! [X66,X67,X68] :
      ( ( subset(cross_product(X66,X68),cross_product(X67,X68))
        | ~ subset(X66,X67)
        | ~ ilf_type(X68,set_type)
        | ~ ilf_type(X67,set_type)
        | ~ ilf_type(X66,set_type) )
      & ( subset(cross_product(X68,X66),cross_product(X68,X67))
        | ~ subset(X66,X67)
        | ~ ilf_type(X68,set_type)
        | ~ ilf_type(X67,set_type)
        | ~ ilf_type(X66,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).

cnf(c_0_15,plain,
    ( subset(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( subset(cross_product(X1,X2),cross_product(X3,X2))
    | ~ subset(X1,X3)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( subset(cross_product(X1,X2),cross_product(X1,X3))
    | ~ subset(X2,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16])]) ).

cnf(c_0_20,plain,
    ( subset(cross_product(X1,X2),cross_product(X3,X2))
    | ~ subset(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_16]),c_0_16])]) ).

fof(c_0_21,plain,
    ! [X65] :
      ( ~ ilf_type(X65,binary_relation_type)
      | subset(X65,cross_product(domain_of(X65),range_of(X65))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])]) ).

cnf(c_0_22,plain,
    ( subset(cross_product(X1,X2),cross_product(X1,X3))
    | ~ subset(X2,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_16]),c_0_16]),c_0_16])]) ).

cnf(c_0_23,plain,
    ( subset(X1,cross_product(X2,X3))
    | ~ subset(X1,cross_product(X4,X3))
    | ~ subset(X4,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( subset(X1,cross_product(domain_of(X1),range_of(X1)))
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_25,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,binary_relation_type)
           => ( subset(range_of(X2),X1)
             => ilf_type(X2,relation_type(domain_of(X2),X1)) ) ) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_10]) ).

fof(c_0_26,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[p24]) ).

cnf(c_0_27,plain,
    ( subset(X1,cross_product(X2,X3))
    | ~ subset(X1,cross_product(X2,X4))
    | ~ subset(X4,X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_22]) ).

cnf(c_0_28,plain,
    ( subset(X1,cross_product(X2,range_of(X1)))
    | ~ subset(domain_of(X1),X2)
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

fof(c_0_29,negated_conjecture,
    ( ilf_type(esk13_0,set_type)
    & ilf_type(esk14_0,binary_relation_type)
    & subset(range_of(esk14_0),esk13_0)
    & ~ ilf_type(esk14_0,relation_type(domain_of(esk14_0),esk13_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).

fof(c_0_30,plain,
    ! [X100] :
      ( ~ ilf_type(X100,set_type)
      | subset(X100,X100) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])]) ).

fof(c_0_31,plain,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ( ~ empty(X2)
            & ilf_type(X2,set_type) )
         => ( ilf_type(X1,member_type(X2))
          <=> member(X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[p22]) ).

fof(c_0_32,plain,
    ! [X120,X121] :
      ( ( ~ empty(X120)
        | ~ ilf_type(X121,set_type)
        | ~ member(X121,X120)
        | ~ ilf_type(X120,set_type) )
      & ( ilf_type(esk12_1(X120),set_type)
        | empty(X120)
        | ~ ilf_type(X120,set_type) )
      & ( member(esk12_1(X120),X120)
        | empty(X120)
        | ~ ilf_type(X120,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).

fof(c_0_33,plain,
    ! [X88,X89,X90] :
      ( ( ~ subset(X88,X89)
        | ~ ilf_type(X90,set_type)
        | ~ member(X90,X88)
        | member(X90,X89)
        | ~ ilf_type(X89,set_type)
        | ~ ilf_type(X88,set_type) )
      & ( ilf_type(esk5_2(X88,X89),set_type)
        | subset(X88,X89)
        | ~ ilf_type(X89,set_type)
        | ~ ilf_type(X88,set_type) )
      & ( member(esk5_2(X88,X89),X88)
        | subset(X88,X89)
        | ~ ilf_type(X89,set_type)
        | ~ ilf_type(X88,set_type) )
      & ( ~ member(esk5_2(X88,X89),X89)
        | subset(X88,X89)
        | ~ ilf_type(X89,set_type)
        | ~ ilf_type(X88,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])])]) ).

cnf(c_0_34,plain,
    ( subset(X1,cross_product(X2,X3))
    | ~ subset(range_of(X1),X3)
    | ~ subset(domain_of(X1),X2)
    | ~ ilf_type(X1,binary_relation_type) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    subset(range_of(esk14_0),esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_36,negated_conjecture,
    ilf_type(esk14_0,binary_relation_type),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_37,plain,
    ( subset(X1,X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_38,plain,
    ! [X69,X70,X71,X72] :
      ( ( ~ ilf_type(X71,subset_type(cross_product(X69,X70)))
        | ilf_type(X71,relation_type(X69,X70))
        | ~ ilf_type(X70,set_type)
        | ~ ilf_type(X69,set_type) )
      & ( ~ ilf_type(X72,relation_type(X69,X70))
        | ilf_type(X72,subset_type(cross_product(X69,X70)))
        | ~ ilf_type(X70,set_type)
        | ~ ilf_type(X69,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).

fof(c_0_39,plain,
    ! [X96,X97] :
      ( ( ~ ilf_type(X97,subset_type(X96))
        | ilf_type(X97,member_type(power_set(X96)))
        | ~ ilf_type(X97,set_type)
        | ~ ilf_type(X96,set_type) )
      & ( ~ ilf_type(X97,member_type(power_set(X96)))
        | ilf_type(X97,subset_type(X96))
        | ~ ilf_type(X97,set_type)
        | ~ ilf_type(X96,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])]) ).

fof(c_0_40,plain,
    ! [X116,X117] :
      ( ( ~ ilf_type(X116,member_type(X117))
        | member(X116,X117)
        | empty(X117)
        | ~ ilf_type(X117,set_type)
        | ~ ilf_type(X116,set_type) )
      & ( ~ member(X116,X117)
        | ilf_type(X116,member_type(X117))
        | empty(X117)
        | ~ ilf_type(X117,set_type)
        | ~ ilf_type(X116,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).

cnf(c_0_41,plain,
    ( ~ empty(X1)
    | ~ ilf_type(X2,set_type)
    | ~ member(X2,X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_42,plain,
    ! [X111,X112,X113] :
      ( ( ~ member(X111,power_set(X112))
        | ~ ilf_type(X113,set_type)
        | ~ member(X113,X111)
        | member(X113,X112)
        | ~ ilf_type(X112,set_type)
        | ~ ilf_type(X111,set_type) )
      & ( ilf_type(esk10_2(X111,X112),set_type)
        | member(X111,power_set(X112))
        | ~ ilf_type(X112,set_type)
        | ~ ilf_type(X111,set_type) )
      & ( member(esk10_2(X111,X112),X111)
        | member(X111,power_set(X112))
        | ~ ilf_type(X112,set_type)
        | ~ ilf_type(X111,set_type) )
      & ( ~ member(esk10_2(X111,X112),X112)
        | member(X111,power_set(X112))
        | ~ ilf_type(X112,set_type)
        | ~ ilf_type(X111,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])])])]) ).

cnf(c_0_43,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ ilf_type(X3,set_type)
    | ~ member(X3,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_44,negated_conjecture,
    ( subset(esk14_0,cross_product(X1,esk13_0))
    | ~ subset(domain_of(esk14_0),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_45,plain,
    subset(X1,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_16])]) ).

cnf(c_0_46,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,member_type(power_set(X2)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,plain,
    ( ilf_type(X1,member_type(X2))
    | empty(X2)
    | ~ member(X1,X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_49,plain,
    ( ~ empty(X1)
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_16]),c_0_16])]) ).

cnf(c_0_50,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk10_2(X1,X2),X2)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_51,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_16]),c_0_16]),c_0_16])]) ).

cnf(c_0_52,negated_conjecture,
    subset(esk14_0,cross_product(domain_of(esk14_0),esk13_0)),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    ~ ilf_type(esk14_0,relation_type(domain_of(esk14_0),esk13_0)),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_54,plain,
    ( ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_16]),c_0_16])]) ).

cnf(c_0_55,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ ilf_type(X1,member_type(power_set(X2))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_16]),c_0_16])]) ).

cnf(c_0_56,plain,
    ( ilf_type(X1,member_type(X2))
    | ~ member(X1,X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_16]),c_0_16])]),c_0_49]) ).

cnf(c_0_57,plain,
    ( member(X1,power_set(X2))
    | ~ member(esk10_2(X1,X2),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_16]),c_0_16])]) ).

cnf(c_0_58,negated_conjecture,
    ( member(X1,cross_product(domain_of(esk14_0),esk13_0))
    | ~ member(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_59,plain,
    ( member(esk10_2(X1,X2),X1)
    | member(X1,power_set(X2))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_60,negated_conjecture,
    ~ ilf_type(esk14_0,subset_type(cross_product(domain_of(esk14_0),esk13_0))),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,plain,
    ( ilf_type(X1,subset_type(X2))
    | ~ member(X1,power_set(X2)) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,negated_conjecture,
    ( member(X1,power_set(cross_product(domain_of(esk14_0),esk13_0)))
    | ~ member(esk10_2(X1,cross_product(domain_of(esk14_0),esk13_0)),esk14_0) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_63,plain,
    ( member(esk10_2(X1,X2),X1)
    | member(X1,power_set(X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_16]),c_0_16])]) ).

cnf(c_0_64,negated_conjecture,
    ~ member(esk14_0,power_set(cross_product(domain_of(esk14_0),esk13_0))),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET648+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n016.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 02:31:51 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 2.29/2.02  % Version  : CSE_E---1.7
% 2.29/2.02  % Problem  : theBenchmark.p
% 2.29/2.02  % SZS status Theorem for theBenchmark.p
% 2.29/2.02  % SZS output start CNFRefutation
% See solution above
% 2.41/2.03  % Total time : 1.371s
%------------------------------------------------------------------------------