TSTP Solution File: SEU183+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU183+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 Apr 30 20:41:23 EDT 2024

% Result   : Theorem 2.95s 0.79s
% Output   : CNFRefutation 3.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (   5 unt;   0 def)
%            Number of atoms       :  219 (  19 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  288 ( 114   ~; 117   |;  37   &)
%                                         (  10 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-5 aty)
%            Number of variables   :  159 ( 137   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => ! [C] :
              ( relation(C)
             => ( C = relation_composition(A,B)
              <=> ! [D,E] :
                    ( in(ordered_pair(D,E),C)
                  <=> ? [F] :
                        ( in(ordered_pair(D,F),A)
                        & in(ordered_pair(F,E),B) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A,B] :
      ( ( relation(A)
        & relation(B) )
     => relation(relation_composition(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,conjecture,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ! [B] :
            ( relation(B)
           => subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
    inference(negated_conjecture,[status(cth)],[f30]) ).

fof(f40,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f41,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f40]) ).

fof(f42,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f41]) ).

fof(f43,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f42]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f47,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f48,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_rng(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
          & ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(sk0_1(C,B,A),C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ( ( ~ in(sk0_2(B,A),B)
                | ! [D] : ~ in(ordered_pair(D,sk0_2(B,A)),A) )
              & ( in(sk0_2(B,A),B)
                | in(ordered_pair(sk0_3(B,A),sk0_2(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | X1 != relation_rng(X0)
      | ~ in(X2,X1)
      | in(ordered_pair(sk0_1(X2,X1,X0),X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_rng(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f56,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( C = relation_composition(A,B)
              <=> ! [D,E] :
                    ( in(ordered_pair(D,E),C)
                  <=> ? [F] :
                        ( in(ordered_pair(D,F),A)
                        & in(ordered_pair(F,E),B) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f57,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ! [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ? [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ? [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ( in(ordered_pair(D,sk0_4(E,D,C,B,A)),A)
                          & in(ordered_pair(sk0_4(E,D,C,B,A),E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ( ( ~ in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
                      | ! [F] :
                          ( ~ in(ordered_pair(sk0_5(C,B,A),F),A)
                          | ~ in(ordered_pair(F,sk0_6(C,B,A)),B) ) )
                    & ( in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
                      | ( in(ordered_pair(sk0_5(C,B,A),sk0_7(C,B,A)),A)
                        & in(ordered_pair(sk0_7(C,B,A),sk0_6(C,B,A)),B) ) ) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(X2)
      | X2 != relation_composition(X0,X1)
      | ~ in(ordered_pair(X3,X4),X2)
      | in(ordered_pair(sk0_4(X4,X3,X2,X1,X0),X4),X1) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f66,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ relation(B)
      | relation(relation_composition(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | relation(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f99,plain,
    ? [A] :
      ( relation(A)
      & ? [B] :
          ( relation(B)
          & ~ subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f100,plain,
    ( relation(sk0_14)
    & relation(sk0_15)
    & ~ subset(relation_rng(relation_composition(sk0_14,sk0_15)),relation_rng(sk0_15)) ),
    inference(skolemization,[status(esa)],[f99]) ).

fof(f101,plain,
    relation(sk0_14),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f102,plain,
    relation(sk0_15),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f103,plain,
    ~ subset(relation_rng(relation_composition(sk0_14,sk0_15)),relation_rng(sk0_15)),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ in(X1,relation_rng(X0))
      | in(ordered_pair(sk0_1(X1,relation_rng(X0),X0),X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f51]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_rng(X0))
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f52]) ).

fof(f122,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(relation_composition(X0,X1))
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(sk0_4(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f61]) ).

fof(f125,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(sk0_4(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[f122,f67]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(sk0_15))
      | ~ in(ordered_pair(X1,X0),sk0_15) ),
    inference(resolution,[status(thm)],[f119,f102]) ).

fof(f168,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,relation_rng(relation_composition(X1,X2)))
      | in(ordered_pair(sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),X0),relation_composition(X1,X2))
      | ~ relation(X1)
      | ~ relation(X2) ),
    inference(resolution,[status(thm)],[f118,f67]) ).

fof(f239,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,relation_rng(relation_composition(X1,X2)))
      | ~ relation(X1)
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X2)
      | in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),relation_composition(X1,X2),X2,X1),X0),X2) ),
    inference(resolution,[status(thm)],[f168,f125]) ).

fof(f240,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,relation_rng(relation_composition(X1,X2)))
      | ~ relation(X1)
      | ~ relation(X2)
      | in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),relation_composition(X1,X2),X2,X1),X0),X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f239]) ).

fof(f421,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_rng(relation_composition(X1,sk0_15)))
      | ~ relation(X1)
      | in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,sk0_15)),relation_composition(X1,sk0_15)),relation_composition(X1,sk0_15),sk0_15,X1),X0),sk0_15) ),
    inference(resolution,[status(thm)],[f240,f102]) ).

fof(f572,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_rng(relation_composition(X1,sk0_15)))
      | ~ relation(X1)
      | in(X0,relation_rng(sk0_15)) ),
    inference(resolution,[status(thm)],[f421,f128]) ).

fof(f609,plain,
    ! [X0,X1] :
      ( ~ in(sk0_0(relation_rng(sk0_15),X0),relation_rng(relation_composition(X1,sk0_15)))
      | ~ relation(X1)
      | subset(X0,relation_rng(sk0_15)) ),
    inference(resolution,[status(thm)],[f572,f46]) ).

fof(f640,plain,
    ! [X0] :
      ( ~ relation(X0)
      | subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15))
      | subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15)) ),
    inference(resolution,[status(thm)],[f609,f45]) ).

fof(f641,plain,
    ! [X0] :
      ( ~ relation(X0)
      | subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15)) ),
    inference(duplicate_literals_removal,[status(esa)],[f640]) ).

fof(f642,plain,
    ~ relation(sk0_14),
    inference(resolution,[status(thm)],[f641,f103]) ).

fof(f643,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f642,f101]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU183+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 19:52:43 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 2.95/0.79  % Refutation found
% 2.95/0.79  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.95/0.79  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.46/0.81  % Elapsed time: 0.458387 seconds
% 3.46/0.81  % CPU time: 3.512090 seconds
% 3.46/0.81  % Total memory used: 103.160 MB
% 3.46/0.81  % Net memory used: 101.650 MB
%------------------------------------------------------------------------------