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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : SET648+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:43:43 PM UTC 2026

% Result   : Theorem 22.52s 8.72s
% Output   : Proof 22.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   81 (  14 unt;   0 def)
%            Number of atoms       :  302 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  370 ( 149   ~; 152   |;  33   &)
%                                         (   4 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-2 aty)
%            Number of variables   :  152 (   2 sgn  73   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( subset(B,C)
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).

fof(f11_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ( ? [D] :
                  ( ~ member(D,C)
                  & member(D,B)
                  & ilf_type(D,set_type) )
              | subset(B,C) )
            & ( ! [D] :
                  ( member(D,C)
                  | ~ member(D,B)
                  | ~ ilf_type(D,set_type) )
              | ~ subset(B,C) ) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ! [B,C,D] :
      ( ( ( ( ~ member(sk4(B,C),C)
            & member(sk4(B,C),B)
            & ilf_type(sk4(B,C),set_type) )
          | subset(B,C) )
        & ( member(D,C)
          | ~ member(D,B)
          | ~ ilf_type(D,set_type)
          | ~ subset(B,C) ) )
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f11_nnf]) ).

cnf(c19,plain,
    ( member(X2,X1)
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | ~ subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

fof(f25,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).

fof(f25_nnf,plain,
    ! [B] : ilf_type(B,set_type),
    inference(nnf_transformation,[status(thm)],[f25]) ).

fof(f25_sk,plain,
    ! [B] : ilf_type(B,set_type),
    inference(skolemisation,[status(esa)],[f25_nnf]) ).

cnf(c49,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f25_sk]) ).

cnf(p108,plain,
    ( member(X2,X0)
    | ~ member(X2,X1)
    | ~ ilf_type(X2,set_type)
    | ~ subset(X1,X0)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c19,c49]) ).

cnf(p305,plain,
    ( member(X2,X1)
    | ~ member(X2,X0)
    | ~ ilf_type(X2,set_type)
    | ~ subset(X0,X1) ),
    inference(resolution,[status(thm)],[p108,c49]) ).

fof(f2,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ( subset(B,C)
               => ( subset(cross_product(D,B),cross_product(D,C))
                  & subset(cross_product(B,D),cross_product(C,D)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

fof(f2_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ! [D] :
              ( ( subset(cross_product(D,B),cross_product(D,C))
                & subset(cross_product(B,D),cross_product(C,D)) )
              | ~ subset(B,C)
              | ~ ilf_type(D,set_type) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ! [B,C,D] :
      ( ( subset(cross_product(D,B),cross_product(D,C))
        & subset(cross_product(B,D),cross_product(C,D)) )
      | ~ subset(B,C)
      | ~ ilf_type(D,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c3,plain,
    ( subset(cross_product(X2,X0),cross_product(X2,X1))
    | ~ subset(X0,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p65,plain,
    ( subset(cross_product(X1,X2),cross_product(X1,X0))
    | ~ subset(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c3,c49]) ).

cnf(p237,plain,
    ( subset(cross_product(X0,X1),cross_product(X0,X2))
    | ~ subset(X1,X2)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p65,c49]) ).

cnf(p349,plain,
    ( subset(cross_product(X2,X0),cross_product(X2,X1))
    | ~ subset(X0,X1) ),
    inference(resolution,[status(thm)],[p237,c49]) ).

fof(f26,conjecture,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,binary_relation_type)
         => ( subset(range_of(C),B)
           => ilf_type(C,relation_type(domain_of(C),B)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_10) ).

fof(f26_neg,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,binary_relation_type)
           => ( subset(range_of(C),B)
             => ilf_type(C,relation_type(domain_of(C),B)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f26]) ).

fof(f26_nnf,plain,
    ? [B] :
      ( ? [C] :
          ( ~ ilf_type(C,relation_type(domain_of(C),B))
          & subset(range_of(C),B)
          & ilf_type(C,binary_relation_type) )
      & ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f26_neg]) ).

fof(f26_sk,plain,
    ( ~ ilf_type(sk13,relation_type(domain_of(sk13),sk12))
    & subset(range_of(sk13),sk12)
    & ilf_type(sk13,binary_relation_type)
    & ilf_type(sk12,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f26_nnf]) ).

cnf(c52,plain,
    subset(range_of(sk13),sk12),
    inference(cnf_transformation,[status(esa)],[f26_sk]) ).

cnf(p350,plain,
    subset(cross_product(X0,range_of(sk13)),cross_product(X0,sk12)),
    inference(resolution,[status(thm)],[p349,c52]) ).

fof(f0,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ( ( subset(C,D)
                  & subset(B,C) )
               => subset(B,D) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f0_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ! [D] :
              ( subset(B,D)
              | ~ subset(C,D)
              | ~ subset(B,C)
              | ~ ilf_type(D,set_type) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [B,C,D] :
      ( subset(B,D)
      | ~ subset(C,D)
      | ~ subset(B,C)
      | ~ ilf_type(D,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f0_nnf]) ).

cnf(c0,plain,
    ( subset(X0,X2)
    | ~ subset(X1,X2)
    | ~ subset(X0,X1)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(p54,plain,
    ( subset(X2,X1)
    | ~ subset(X0,X1)
    | ~ subset(X2,X0)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c0,c49]) ).

cnf(p208,plain,
    ( subset(X1,X0)
    | ~ subset(X2,X0)
    | ~ subset(X1,X2)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p54,c49]) ).

cnf(p306,plain,
    ( subset(X0,X2)
    | ~ subset(X1,X2)
    | ~ subset(X0,X1) ),
    inference(resolution,[status(thm)],[p208,c49]) ).

fof(f1,axiom,
    ! [B] :
      ( ilf_type(B,binary_relation_type)
     => subset(B,cross_product(domain_of(B),range_of(B))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f1_nnf,plain,
    ! [B] :
      ( subset(B,cross_product(domain_of(B),range_of(B)))
      | ~ ilf_type(B,binary_relation_type) ),
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [B] :
      ( subset(B,cross_product(domain_of(B),range_of(B)))
      | ~ ilf_type(B,binary_relation_type) ),
    inference(skolemisation,[status(esa)],[f1_nnf]) ).

cnf(c1,plain,
    ( subset(X0,cross_product(domain_of(X0),range_of(X0)))
    | ~ ilf_type(X0,binary_relation_type) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(c51,plain,
    ilf_type(sk13,binary_relation_type),
    inference(cnf_transformation,[status(esa)],[f26_sk]) ).

cnf(p57,plain,
    subset(sk13,cross_product(domain_of(sk13),range_of(sk13))),
    inference(resolution,[status(thm)],[c1,c51]) ).

cnf(p309,plain,
    ( subset(sk13,X0)
    | ~ subset(cross_product(domain_of(sk13),range_of(sk13)),X0) ),
    inference(resolution,[status(thm)],[p306,p57]) ).

cnf(p363,plain,
    subset(sk13,cross_product(domain_of(sk13),sk12)),
    inference(resolution,[status(thm)],[p350,p309]) ).

cnf(p531,plain,
    ( member(X0,cross_product(domain_of(sk13),sk12))
    | ~ member(X0,sk13)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p305,p363]) ).

cnf(p600,plain,
    ( member(X0,cross_product(domain_of(sk13),sk12))
    | ~ member(X0,sk13) ),
    inference(resolution,[status(thm)],[p531,c49]) ).

fof(f19,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( member(B,power_set(C))
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

fof(f19_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ( ? [D] :
                  ( ~ member(D,C)
                  & member(D,B)
                  & ilf_type(D,set_type) )
              | member(B,power_set(C)) )
            & ( ! [D] :
                  ( member(D,C)
                  | ~ member(D,B)
                  | ~ ilf_type(D,set_type) )
              | ~ member(B,power_set(C)) ) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f19]) ).

fof(f19_sk,plain,
    ! [B,C,D] :
      ( ( ( ( ~ member(sk9(B,C),C)
            & member(sk9(B,C),B)
            & ilf_type(sk9(B,C),set_type) )
          | member(B,power_set(C)) )
        & ( member(D,C)
          | ~ member(D,B)
          | ~ ilf_type(D,set_type)
          | ~ member(B,power_set(C)) ) )
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f19_nnf]) ).

cnf(c38,plain,
    ( member(sk9(X0,X1),X0)
    | member(X0,power_set(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f19_sk]) ).

cnf(p157,plain,
    ( member(sk9(X1,X0),X1)
    | member(X1,power_set(X0))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c38,c49]) ).

cnf(p162,plain,
    ( member(sk9(X0,X1),X0)
    | member(X0,power_set(X1)) ),
    inference(resolution,[status(thm)],[p157,c49]) ).

cnf(p609,plain,
    ( member(sk13,power_set(X0))
    | member(sk9(sk13,X0),cross_product(domain_of(sk13),sk12)) ),
    inference(resolution,[status(thm)],[p600,p162]) ).

cnf(c39,plain,
    ( ~ member(sk9(X0,X1),X1)
    | member(X0,power_set(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f19_sk]) ).

cnf(p177,plain,
    ( ~ member(sk9(X1,X0),X0)
    | member(X1,power_set(X0))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c39,c49]) ).

cnf(p178,plain,
    ( ~ member(sk9(X0,X1),X1)
    | member(X0,power_set(X1)) ),
    inference(resolution,[status(thm)],[p177,c49]) ).

cnf(p621,plain,
    ( member(sk13,power_set(cross_product(domain_of(sk13),sk12)))
    | member(sk13,power_set(cross_product(domain_of(sk13),sk12))) ),
    inference(resolution,[status(thm)],[p609,p178]) ).

cnf(p849,plain,
    member(sk13,power_set(cross_product(domain_of(sk13),sk12))),
    inference(factoring,[status(thm)],[p621]) ).

fof(f21,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ( ilf_type(C,set_type)
            & ~ empty(C) )
         => ( ilf_type(B,member_type(C))
          <=> member(B,C) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).

fof(f21_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ( ~ member(B,C)
              | ilf_type(B,member_type(C)) )
            & ( member(B,C)
              | ~ ilf_type(B,member_type(C)) ) )
          | ~ ilf_type(C,set_type)
          | empty(C) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f21]) ).

fof(f21_sk,plain,
    ! [B,C] :
      ( ( ( ~ member(B,C)
          | ilf_type(B,member_type(C)) )
        & ( member(B,C)
          | ~ ilf_type(B,member_type(C)) ) )
      | ~ ilf_type(C,set_type)
      | empty(C)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f21_nnf]) ).

cnf(c43,plain,
    ( ~ member(X0,X1)
    | ilf_type(X0,member_type(X1))
    | ~ ilf_type(X1,set_type)
    | empty(X1)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f21_sk]) ).

cnf(p189,plain,
    ( ~ member(X1,X0)
    | ilf_type(X1,member_type(X0))
    | ~ ilf_type(X0,set_type)
    | empty(X0) ),
    inference(resolution,[status(thm)],[c43,c49]) ).

cnf(p194,plain,
    ( ~ member(X1,X0)
    | ilf_type(X1,member_type(X0))
    | empty(X0) ),
    inference(resolution,[status(thm)],[p189,c49]) ).

cnf(p850,plain,
    ( ilf_type(sk13,member_type(power_set(cross_product(domain_of(sk13),sk12))))
    | empty(power_set(cross_product(domain_of(sk13),sk12))) ),
    inference(resolution,[status(thm)],[p849,p194]) ).

fof(f14,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ilf_type(C,subset_type(B))
          <=> ilf_type(C,member_type(power_set(B))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).

fof(f14_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ( ~ ilf_type(C,member_type(power_set(B)))
              | ilf_type(C,subset_type(B)) )
            & ( ilf_type(C,member_type(power_set(B)))
              | ~ ilf_type(C,subset_type(B)) ) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f14]) ).

fof(f14_sk,plain,
    ! [B,C] :
      ( ( ( ~ ilf_type(C,member_type(power_set(B)))
          | ilf_type(C,subset_type(B)) )
        & ( ilf_type(C,member_type(power_set(B)))
          | ~ ilf_type(C,subset_type(B)) ) )
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f14_nnf]) ).

cnf(c26,plain,
    ( ~ ilf_type(X1,member_type(power_set(X0)))
    | ilf_type(X1,subset_type(X0))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f14_sk]) ).

cnf(p130,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ilf_type(X0,subset_type(X1))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c26,c49]) ).

cnf(p144,plain,
    ( ~ ilf_type(X0,member_type(power_set(X1)))
    | ilf_type(X0,subset_type(X1)) ),
    inference(resolution,[status(thm)],[p130,c49]) ).

cnf(p871,plain,
    ( ilf_type(sk13,subset_type(cross_product(domain_of(sk13),sk12)))
    | empty(power_set(cross_product(domain_of(sk13),sk12))) ),
    inference(resolution,[status(thm)],[p850,p144]) ).

fof(f3,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ! [E] :
                ( ilf_type(E,relation_type(B,C))
               => ilf_type(E,subset_type(cross_product(B,C))) )
            & ! [D] :
                ( ilf_type(D,subset_type(cross_product(B,C)))
               => ilf_type(D,relation_type(B,C)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

fof(f3_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ! [E] :
                ( ilf_type(E,subset_type(cross_product(B,C)))
                | ~ ilf_type(E,relation_type(B,C)) )
            & ! [D] :
                ( ilf_type(D,relation_type(B,C))
                | ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f3]) ).

fof(f3_sk,plain,
    ! [B,C,D,E] :
      ( ( ( ilf_type(E,subset_type(cross_product(B,C)))
          | ~ ilf_type(E,relation_type(B,C)) )
        & ( ilf_type(D,relation_type(B,C))
          | ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f3_nnf]) ).

cnf(c4,plain,
    ( ilf_type(X2,relation_type(X0,X1))
    | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f3_sk]) ).

cnf(p70,plain,
    ( ilf_type(X1,relation_type(X2,X0))
    | ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c4,c49]) ).

cnf(p88,plain,
    ( ilf_type(X0,relation_type(X1,X2))
    | ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(resolution,[status(thm)],[p70,c49]) ).

cnf(p872,plain,
    ( ilf_type(sk13,relation_type(domain_of(sk13),sk12))
    | empty(power_set(cross_product(domain_of(sk13),sk12))) ),
    inference(resolution,[status(thm)],[p871,p88]) ).

fof(f20,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(power_set(B),set_type)
        & ~ empty(power_set(B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).

fof(f20_nnf,plain,
    ! [B] :
      ( ( ilf_type(power_set(B),set_type)
        & ~ empty(power_set(B)) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f20]) ).

fof(f20_sk,plain,
    ! [B] :
      ( ( ilf_type(power_set(B),set_type)
        & ~ empty(power_set(B)) )
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f20_nnf]) ).

cnf(c40,plain,
    ( ~ empty(power_set(X0))
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f20_sk]) ).

cnf(p58,plain,
    ~ empty(power_set(X0)),
    inference(resolution,[status(thm)],[c40,c49]) ).

cnf(p873,plain,
    ilf_type(sk13,relation_type(domain_of(sk13),sk12)),
    inference(resolution,[status(thm)],[p872,p58]) ).

cnf(c53,plain,
    ~ ilf_type(sk13,relation_type(domain_of(sk13),sk12)),
    inference(cnf_transformation,[status(esa)],[f26_sk]) ).

cnf(p875,plain,
    $false,
    inference(resolution,[status(thm)],[p873,c53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET648+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38  % Computer : n011.cluster.edu
% 0.11/5.38  % Model    : x86_64 x86_64
% 0.11/5.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38  % Memory   : 8046.5625MB
% 0.11/5.38  % OS       : Linux 6.8.0-71-generic
% 0.11/5.39  % CPULimit : 300
% 0.11/5.39  % WCLimit  : 300
% 0.11/5.39  % DateTime : Thu Sep 24 11:33:33 UTC 2026
% 0.11/5.39  % CPUTime  : 
% 0.11/5.39  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.52/8.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.52/8.72  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------