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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : SET681+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 : n001.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 02:43:47 PM UTC 2026

% Result   : Theorem 20.94s 3.51s
% Output   : Proof 20.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   78 (  17 unt;   0 def)
%            Number of atoms       :  300 (   7 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  373 ( 151   ~; 145   |;  43   &)
%                                         (   5 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :  152 (   4 sgn  75   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f30,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).

fof(f30_nnf,plain,
    ! [B] : ilf_type(B,set_type),
    inference(nnf_transformation,[status(thm)],[f30]) ).

fof(f30_sk,plain,
    ! [B] : ilf_type(B,set_type),
    inference(skolemisation,[status(esa)],[f30_nnf]) ).

cnf(c57,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f30_sk]) ).

fof(f28,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => range(B,C,D) = range_of(D) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).

fof(f28_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ! [D] :
              ( range(B,C,D) = range_of(D)
              | ~ ilf_type(D,relation_type(B,C)) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f28]) ).

fof(f28_sk,plain,
    ! [B,C,D] :
      ( range(B,C,D) = range_of(D)
      | ~ ilf_type(D,relation_type(B,C))
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f28_nnf]) ).

cnf(c55,plain,
    ( range(X0,X1,X2) = range_of(X2)
    | ~ ilf_type(X2,relation_type(X0,X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f28_sk]) ).

cnf(p406,plain,
    ( range(X2,X0,X1) = range_of(X1)
    | ~ ilf_type(X1,relation_type(X2,X0))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c57,c55]) ).

cnf(p745,plain,
    ( range(X1,X2,X0) = range_of(X0)
    | ~ ilf_type(X0,relation_type(X1,X2)) ),
    inference(resolution,[status(thm)],[p406,c57]) ).

fof(f31,conjecture,
    ! [B] :
      ( ( ilf_type(B,set_type)
        & ~ empty(B) )
     => ! [C] :
          ( ( ilf_type(C,set_type)
            & ~ empty(C) )
         => ! [D] :
              ( ilf_type(D,relation_type(C,B))
             => ! [E] :
                  ( ilf_type(E,member_type(B))
                 => ( member(E,range(C,B,D))
                  <=> ? [F] :
                        ( member(ordered_pair(F,E),D)
                        & ilf_type(F,member_type(C)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_48) ).

fof(f31_neg,negated_conjecture,
    ~ ! [B] :
        ( ( ilf_type(B,set_type)
          & ~ empty(B) )
       => ! [C] :
            ( ( ilf_type(C,set_type)
              & ~ empty(C) )
           => ! [D] :
                ( ilf_type(D,relation_type(C,B))
               => ! [E] :
                    ( ilf_type(E,member_type(B))
                   => ( member(E,range(C,B,D))
                    <=> ? [F] :
                          ( member(ordered_pair(F,E),D)
                          & ilf_type(F,member_type(C)) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f31]) ).

fof(f31_nnf,plain,
    ? [B] :
      ( ? [C] :
          ( ? [D] :
              ( ? [E] :
                  ( ( ( ? [F] :
                          ( member(ordered_pair(F,E),D)
                          & ilf_type(F,member_type(C)) )
                      & ~ member(E,range(C,B,D)) )
                    | ( ! [F] :
                          ( ~ member(ordered_pair(F,E),D)
                          | ~ ilf_type(F,member_type(C)) )
                      & member(E,range(C,B,D)) ) )
                  & ilf_type(E,member_type(B)) )
              & ilf_type(D,relation_type(C,B)) )
          & ilf_type(C,set_type)
          & ~ empty(C) )
      & ilf_type(B,set_type)
      & ~ empty(B) ),
    inference(nnf_transformation,[status(thm)],[f31_neg]) ).

fof(f31_sk,plain,
    ! [F] :
      ( ( ( member(ordered_pair(sk15,sk14),sk13)
          & ilf_type(sk15,member_type(sk12))
          & ~ member(sk14,range(sk12,sk11,sk13)) )
        | ( ( ~ member(ordered_pair(F,sk14),sk13)
            | ~ ilf_type(F,member_type(sk12)) )
          & member(sk14,range(sk12,sk11,sk13)) ) )
      & ilf_type(sk14,member_type(sk11))
      & ilf_type(sk13,relation_type(sk12,sk11))
      & ilf_type(sk12,set_type)
      & ~ empty(sk12)
      & ilf_type(sk11,set_type)
      & ~ empty(sk11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14,sk15])],[f31_nnf]) ).

cnf(c62,plain,
    ilf_type(sk13,relation_type(sk12,sk11)),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p1299,plain,
    range(sk12,sk11,sk13) = range_of(sk13),
    inference(resolution,[status(thm)],[p745,c62]) ).

cnf(c67,plain,
    ( ~ member(sk14,range(sk12,sk11,sk13))
    | ~ member(ordered_pair(X4,sk14),sk13)
    | ~ ilf_type(X4,member_type(sk12)) ),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p1302,plain,
    ( ~ member(sk14,range_of(sk13))
    | ~ member(ordered_pair(X0,sk14),sk13)
    | ~ ilf_type(X0,member_type(sk12)) ),
    inference(demodulation,[status(thm)],[p1299,c67]) ).

cnf(c66,plain,
    ( member(ordered_pair(sk15,sk14),sk13)
    | member(sk14,range(sk12,sk11,sk13)) ),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p1301,plain,
    ( member(ordered_pair(sk15,sk14),sk13)
    | member(sk14,range_of(sk13)) ),
    inference(demodulation,[status(thm)],[p1299,c66]) ).

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

fof(f0_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ( ( ! [D] :
                  ( ~ member(ordered_pair(D,B),C)
                  | ~ ilf_type(D,set_type) )
              | member(B,range_of(C)) )
            & ( ? [D] :
                  ( member(ordered_pair(D,B),C)
                  & ilf_type(D,set_type) )
              | ~ member(B,range_of(C)) ) )
          | ~ ilf_type(C,binary_relation_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [B,C,D] :
      ( ( ( ~ member(ordered_pair(D,B),C)
          | ~ ilf_type(D,set_type)
          | member(B,range_of(C)) )
        & ( ( member(ordered_pair(sk0(B,C),B),C)
            & ilf_type(sk0(B,C),set_type) )
          | ~ member(B,range_of(C)) ) )
      | ~ ilf_type(C,binary_relation_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).

cnf(c2,plain,
    ( ~ member(ordered_pair(X2,X0),X1)
    | ~ ilf_type(X2,set_type)
    | member(X0,range_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(p355,plain,
    ( ~ member(ordered_pair(X2,X1),X0)
    | ~ ilf_type(X2,set_type)
    | member(X1,range_of(X0))
    | ~ ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[c57,c2]) ).

fof(f16,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( ilf_type(B,set_type)
          & relation_like(B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).

fof(f16_nnf,plain,
    ! [B] :
      ( ( ( ~ ilf_type(B,set_type)
          | ~ relation_like(B)
          | ilf_type(B,binary_relation_type) )
        & ( ( ilf_type(B,set_type)
            & relation_like(B) )
          | ~ ilf_type(B,binary_relation_type) ) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f16]) ).

fof(f16_sk,plain,
    ! [B] :
      ( ( ( ~ ilf_type(B,set_type)
          | ~ relation_like(B)
          | ilf_type(B,binary_relation_type) )
        & ( ( ilf_type(B,set_type)
            & relation_like(B) )
          | ~ ilf_type(B,binary_relation_type) ) )
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f16_nnf]) ).

cnf(c27,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f16_sk]) ).

cnf(p208,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type)
    | ~ ilf_type(X0,set_type) ),
    inference(factoring,[status(thm)],[c27]) ).

cnf(p488,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[p208,c57]) ).

fof(f25,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,subset_type(cross_product(B,C)))
             => relation_like(D) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).

fof(f25_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ! [D] :
              ( relation_like(D)
              | ~ ilf_type(D,subset_type(cross_product(B,C))) )
          | ~ ilf_type(C,set_type) )
      | ~ ilf_type(B,set_type) ),
    inference(nnf_transformation,[status(thm)],[f25]) ).

fof(f25_sk,plain,
    ! [B,C,D] :
      ( relation_like(D)
      | ~ ilf_type(D,subset_type(cross_product(B,C)))
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f25_nnf]) ).

cnf(c52,plain,
    ( relation_like(X2)
    | ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f25_sk]) ).

cnf(c61,plain,
    ilf_type(sk12,set_type),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p325,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,subset_type(cross_product(sk12,X0)))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c52,c61]) ).

cnf(c59,plain,
    ilf_type(sk11,set_type),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p337,plain,
    ( relation_like(X0)
    | ~ ilf_type(X0,subset_type(cross_product(sk12,sk11))) ),
    inference(resolution,[status(thm)],[p325,c59]) ).

fof(f5,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',p6) ).

fof(f5_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)],[f5]) ).

fof(f5_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)],[f5_nnf]) ).

cnf(c11,plain,
    ( ilf_type(X3,subset_type(cross_product(X0,X1)))
    | ~ ilf_type(X3,relation_type(X0,X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f5_sk]) ).

cnf(p144,plain,
    ( ilf_type(X1,subset_type(cross_product(sk12,X0)))
    | ~ ilf_type(X1,relation_type(sk12,X0))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c11,c61]) ).

cnf(p184,plain,
    ( ilf_type(X0,subset_type(cross_product(sk12,sk11)))
    | ~ ilf_type(X0,relation_type(sk12,sk11)) ),
    inference(resolution,[status(thm)],[p144,c59]) ).

cnf(p186,plain,
    ilf_type(sk13,subset_type(cross_product(sk12,sk11))),
    inference(resolution,[status(thm)],[p184,c62]) ).

cnf(p339,plain,
    relation_like(sk13),
    inference(resolution,[status(thm)],[p337,p186]) ).

cnf(p528,plain,
    ilf_type(sk13,binary_relation_type),
    inference(resolution,[status(thm)],[p488,p339]) ).

cnf(p543,plain,
    ( ~ member(ordered_pair(X1,X0),sk13)
    | ~ ilf_type(X1,set_type)
    | member(X0,range_of(sk13)) ),
    inference(resolution,[status(thm)],[p355,p528]) ).

cnf(p601,plain,
    ( ~ member(ordered_pair(X1,X0),sk13)
    | member(X0,range_of(sk13)) ),
    inference(resolution,[status(thm)],[p543,c57]) ).

cnf(p1320,plain,
    ( member(sk14,range_of(sk13))
    | member(sk14,range_of(sk13)) ),
    inference(resolution,[status(thm)],[p1301,p601]) ).

cnf(p1360,plain,
    member(sk14,range_of(sk13)),
    inference(factoring,[status(thm)],[p1320]) ).

cnf(c1,plain,
    ( member(ordered_pair(sk0(X0,X1),X0),X1)
    | ~ member(X0,range_of(X1))
    | ~ ilf_type(X1,binary_relation_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(p354,plain,
    ( member(ordered_pair(sk0(X1,X0),X1),X0)
    | ~ member(X1,range_of(X0))
    | ~ ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[c57,c1]) ).

cnf(p541,plain,
    ( member(ordered_pair(sk0(X0,sk13),X0),sk13)
    | ~ member(X0,range_of(sk13)) ),
    inference(resolution,[status(thm)],[p528,p354]) ).

cnf(p1361,plain,
    member(ordered_pair(sk0(sk14,sk13),sk14),sk13),
    inference(resolution,[status(thm)],[p1360,p541]) ).

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

fof(f2_nnf,plain,
    ! [B] :
      ( ! [C] :
          ( ! [D] :
              ( ! [E] :
                  ( ! [F] :
                      ( ( member(E,C)
                        & member(D,B) )
                      | ~ member(ordered_pair(D,E),F)
                      | ~ ilf_type(F,relation_type(B,C)) )
                  | ~ ilf_type(E,set_type) )
              | ~ 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,E,F] :
      ( ( member(E,C)
        & member(D,B) )
      | ~ member(ordered_pair(D,E),F)
      | ~ ilf_type(F,relation_type(B,C))
      | ~ ilf_type(E,set_type)
      | ~ ilf_type(D,set_type)
      | ~ ilf_type(C,set_type)
      | ~ ilf_type(B,set_type) ),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c5,plain,
    ( member(X2,X0)
    | ~ member(ordered_pair(X2,X3),X4)
    | ~ ilf_type(X4,relation_type(X0,X1))
    | ~ ilf_type(X3,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(p93,plain,
    ( member(X1,sk12)
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ ilf_type(X3,relation_type(sk12,X0))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c5,c61]) ).

cnf(p125,plain,
    ( member(X0,sk12)
    | ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(sk12,sk11))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p93,c59]) ).

cnf(p462,plain,
    ( member(X2,sk12)
    | ~ member(ordered_pair(X2,X0),X1)
    | ~ ilf_type(X1,relation_type(sk12,sk11))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p125,c57]) ).

cnf(p490,plain,
    ( member(X1,sk12)
    | ~ member(ordered_pair(X1,X2),X0)
    | ~ ilf_type(X0,relation_type(sk12,sk11)) ),
    inference(resolution,[status(thm)],[p462,c57]) ).

cnf(p492,plain,
    ( member(X0,sk12)
    | ~ member(ordered_pair(X0,X1),sk13) ),
    inference(resolution,[status(thm)],[p490,c62]) ).

cnf(p1363,plain,
    member(sk0(sk14,sk13),sk12),
    inference(resolution,[status(thm)],[p1361,p492]) ).

fof(f7,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',p8) ).

fof(f7_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)],[f7]) ).

fof(f7_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)],[f7_nnf]) ).

cnf(c14,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)],[f7_sk]) ).

cnf(p368,plain,
    ( ~ member(X1,X0)
    | ilf_type(X1,member_type(X0))
    | ~ ilf_type(X0,set_type)
    | empty(X0) ),
    inference(resolution,[status(thm)],[c57,c14]) ).

cnf(p616,plain,
    ( ~ member(X1,X0)
    | ilf_type(X1,member_type(X0))
    | empty(X0) ),
    inference(resolution,[status(thm)],[p368,c57]) ).

cnf(p1368,plain,
    ( ilf_type(sk0(sk14,sk13),member_type(sk12))
    | empty(sk12) ),
    inference(resolution,[status(thm)],[p1363,p616]) ).

cnf(p1483,plain,
    ( empty(sk12)
    | ~ member(sk14,range_of(sk13))
    | ~ member(ordered_pair(sk0(sk14,sk13),sk14),sk13) ),
    inference(resolution,[status(thm)],[p1302,p1368]) ).

cnf(p1522,plain,
    ( empty(sk12)
    | ~ member(sk14,range_of(sk13)) ),
    inference(resolution,[status(thm)],[p1483,p1361]) ).

cnf(p1556,plain,
    empty(sk12),
    inference(resolution,[status(thm)],[p1522,p1360]) ).

cnf(c60,plain,
    ~ empty(sk12),
    inference(cnf_transformation,[status(esa)],[f31_sk]) ).

cnf(p1557,plain,
    $false,
    inference(resolution,[status(thm)],[p1556,c60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36  % Computer : n001.cluster.edu
% 0.08/0.36  % Model    : x86_64 x86_64
% 0.08/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36  % Memory   : 8046.5625MB
% 0.08/0.36  % OS       : Linux 6.8.0-71-generic
% 0.08/0.36  % CPULimit : 300
% 0.08/0.37  % WCLimit  : 300
% 0.08/0.37  % DateTime : Thu Sep 24 11:45:07 UTC 2026
% 0.08/0.37  % CPUTime  : 
% 0.08/0.37  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.94/3.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.94/3.51  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------