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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n020.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 29.24s 4.86s
% Output   : Proof 29.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   77 (  12 unt;   0 def)
%            Number of atoms       :  303 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  381 ( 155   ~; 159   |;  35   &)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :  183 (  16 sgn  73   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox/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(c7,plain,
    ( member(X3,X1)
    | ~ 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]) ).

fof(f25,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox/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(c53,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f25_sk]) ).

cnf(p87,plain,
    ( member(X2,X0)
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ ilf_type(X3,relation_type(X4,X0))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c7,c53]) ).

cnf(p356,plain,
    ( member(X1,X4)
    | ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p87,c53]) ).

cnf(p1673,plain,
    ( member(X0,X3)
    | ~ member(ordered_pair(X4,X0),X1)
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p356,c53]) ).

cnf(p3871,plain,
    ( member(X4,X2)
    | ~ member(ordered_pair(X3,X4),X0)
    | ~ ilf_type(X0,relation_type(X1,X2)) ),
    inference(resolution,[status(thm)],[p1673,c53]) ).

fof(f26,conjecture,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( subset(range_of(D),C)
                & subset(domain_of(D),B) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).

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

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

fof(f26_sk,plain,
    ( ( ~ subset(range_of(sk16),sk15)
      | ~ subset(domain_of(sk16),sk14) )
    & ilf_type(sk16,relation_type(sk14,sk15))
    & ilf_type(sk15,set_type)
    & ilf_type(sk14,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f26_nnf]) ).

cnf(c56,plain,
    ilf_type(sk16,relation_type(sk14,sk15)),
    inference(cnf_transformation,[status(esa)],[f26_sk]) ).

cnf(p3872,plain,
    ( member(X1,sk15)
    | ~ member(ordered_pair(X0,X1),sk16) ),
    inference(resolution,[status(thm)],[p3871,c56]) ).

fof(f22,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/sandbox/benchmark/theBenchmark.p',p23) ).

fof(f22_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)],[f22]) ).

fof(f22_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)],[f22_nnf]) ).

cnf(c48,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)],[f22_sk]) ).

cnf(p128,plain,
    ( relation_like(X1)
    | ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c48,c53]) ).

cnf(p131,plain,
    ( relation_like(X0)
    | ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
    inference(resolution,[status(thm)],[p128,c53]) ).

fof(f7,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/sandbox/benchmark/theBenchmark.p',p8) ).

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

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

cnf(c17,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)],[f7_sk]) ).

cnf(p112,plain,
    ( ilf_type(X1,subset_type(cross_product(X2,X0)))
    | ~ ilf_type(X1,relation_type(X2,X0))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c17,c53]) ).

cnf(p113,plain,
    ( ilf_type(X0,subset_type(cross_product(X1,X2)))
    | ~ ilf_type(X0,relation_type(X1,X2)) ),
    inference(resolution,[status(thm)],[p112,c53]) ).

cnf(p114,plain,
    ilf_type(sk16,subset_type(cross_product(sk14,sk15))),
    inference(resolution,[status(thm)],[p113,c56]) ).

cnf(p133,plain,
    relation_like(sk16),
    inference(resolution,[status(thm)],[p131,p114]) ).

fof(f12,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( ilf_type(B,set_type)
          & relation_like(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).

fof(f12_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)],[f12]) ).

fof(f12_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)],[f12_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)],[f12_sk]) ).

cnf(p79,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type)
    | ~ ilf_type(X0,set_type) ),
    inference(factoring,[status(thm)],[c27]) ).

cnf(p80,plain,
    ( ~ relation_like(X0)
    | ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[p79,c53]) ).

cnf(p135,plain,
    ilf_type(sk16,binary_relation_type),
    inference(resolution,[status(thm)],[p133,p80]) ).

fof(f1,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/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f1_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)],[f1]) ).

fof(f1_sk,plain,
    ! [B,C,D] :
      ( ( ( ~ member(ordered_pair(D,B),C)
          | ~ ilf_type(D,set_type)
          | member(B,range_of(C)) )
        & ( ( member(ordered_pair(sk1(B,C),B),C)
            & ilf_type(sk1(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,[sk1])],[f1_nnf]) ).

cnf(c4,plain,
    ( member(ordered_pair(sk1(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)],[f1_sk]) ).

cnf(p66,plain,
    ( member(ordered_pair(sk1(X1,X0),X1),X0)
    | ~ member(X1,range_of(X0))
    | ~ ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[c4,c53]) ).

cnf(p138,plain,
    ( member(ordered_pair(sk1(X0,sk16),X0),sk16)
    | ~ member(X0,range_of(sk16)) ),
    inference(resolution,[status(thm)],[p135,p66]) ).

fof(f9,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/sandbox/benchmark/theBenchmark.p',p10) ).

fof(f9_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)],[f9]) ).

fof(f9_sk,plain,
    ! [B,C,D] :
      ( ( ( ( ~ member(sk5(B,C),C)
            & member(sk5(B,C),B)
            & ilf_type(sk5(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,[sk5])],[f9_nnf]) ).

cnf(c21,plain,
    ( member(sk5(X0,X1),X0)
    | subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f9_sk]) ).

cnf(p119,plain,
    ( member(sk5(X1,X0),X1)
    | subset(X1,X0)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c21,c53]) ).

cnf(p120,plain,
    ( member(sk5(X0,X1),X0)
    | subset(X0,X1) ),
    inference(resolution,[status(thm)],[p119,c53]) ).

cnf(p161,plain,
    ( subset(range_of(sk16),X0)
    | member(ordered_pair(sk1(sk5(range_of(sk16),X0),sk16),sk5(range_of(sk16),X0)),sk16) ),
    inference(resolution,[status(thm)],[p138,p120]) ).

cnf(p3896,plain,
    ( subset(range_of(sk16),X0)
    | member(sk5(range_of(sk16),X0),sk15) ),
    inference(resolution,[status(thm)],[p3872,p161]) ).

cnf(c22,plain,
    ( ~ member(sk5(X0,X1),X1)
    | subset(X0,X1)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[status(esa)],[f9_sk]) ).

cnf(p121,plain,
    ( ~ member(sk5(X1,X0),X0)
    | subset(X1,X0)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c22,c53]) ).

cnf(p126,plain,
    ( ~ member(sk5(X0,X1),X1)
    | subset(X0,X1) ),
    inference(resolution,[status(thm)],[p121,c53]) ).

cnf(p3979,plain,
    ( subset(range_of(sk16),sk15)
    | subset(range_of(sk16),sk15) ),
    inference(resolution,[status(thm)],[p3896,p126]) ).

cnf(p3981,plain,
    subset(range_of(sk16),sk15),
    inference(factoring,[status(thm)],[p3979]) ).

cnf(c6,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(p78,plain,
    ( member(X1,X4)
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ ilf_type(X3,relation_type(X4,X0))
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[c6,c53]) ).

cnf(p308,plain,
    ( member(X0,X3)
    | ~ member(ordered_pair(X0,X1),X2)
    | ~ ilf_type(X2,relation_type(X3,X4))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p78,c53]) ).

cnf(p1521,plain,
    ( member(X4,X2)
    | ~ member(ordered_pair(X4,X0),X1)
    | ~ ilf_type(X1,relation_type(X2,X3))
    | ~ ilf_type(X0,set_type) ),
    inference(resolution,[status(thm)],[p308,c53]) ).

cnf(p2620,plain,
    ( member(X3,X1)
    | ~ member(ordered_pair(X3,X4),X0)
    | ~ ilf_type(X0,relation_type(X1,X2)) ),
    inference(resolution,[status(thm)],[p1521,c53]) ).

cnf(p2621,plain,
    ( member(X0,sk14)
    | ~ member(ordered_pair(X0,X1),sk16) ),
    inference(resolution,[status(thm)],[p2620,c56]) ).

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

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

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

cnf(p60,plain,
    ( member(ordered_pair(X1,sk0(X1,X0)),X0)
    | ~ member(X1,domain_of(X0))
    | ~ ilf_type(X0,binary_relation_type) ),
    inference(resolution,[status(thm)],[c1,c53]) ).

cnf(p136,plain,
    ( member(ordered_pair(X0,sk0(X0,sk16)),sk16)
    | ~ member(X0,domain_of(sk16)) ),
    inference(resolution,[status(thm)],[p135,p60]) ).

cnf(p158,plain,
    ( subset(domain_of(sk16),X0)
    | member(ordered_pair(sk5(domain_of(sk16),X0),sk0(sk5(domain_of(sk16),X0),sk16)),sk16) ),
    inference(resolution,[status(thm)],[p136,p120]) ).

cnf(p2639,plain,
    ( subset(domain_of(sk16),X0)
    | member(sk5(domain_of(sk16),X0),sk14) ),
    inference(resolution,[status(thm)],[p2621,p158]) ).

cnf(p2709,plain,
    ( subset(domain_of(sk16),sk14)
    | subset(domain_of(sk16),sk14) ),
    inference(resolution,[status(thm)],[p2639,p126]) ).

cnf(p2712,plain,
    subset(domain_of(sk16),sk14),
    inference(factoring,[status(thm)],[p2709]) ).

cnf(c57,plain,
    ( ~ subset(range_of(sk16),sk15)
    | ~ subset(domain_of(sk16),sk14) ),
    inference(cnf_transformation,[status(esa)],[f26_sk]) ).

cnf(p2713,plain,
    ~ subset(range_of(sk16),sk15),
    inference(resolution,[status(thm)],[p2712,c57]) ).

cnf(p3984,plain,
    $false,
    inference(resolution,[status(thm)],[p3981,p2713]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.56  % Computer : n020.cluster.edu
% 0.09/0.56  % Model    : x86_64 x86_64
% 0.09/0.56  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56  % Memory   : 8046.5625MB
% 0.09/0.56  % OS       : Linux 6.8.0-71-generic
% 0.09/0.56  % CPULimit : 300
% 0.09/0.57  % WCLimit  : 300
% 0.09/0.57  % DateTime : Thu Sep 24 11:34:49 UTC 2026
% 0.09/0.57  % CPUTime  : 
% 0.09/0.57  Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.24/4.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.24/4.86  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------