TSTP Solution File: NUN082+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:36:23 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   89 (  36 unt;   0 def)
%            Number of atoms       :  196 (  59 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  182 (  75   ~;  53   |;  50   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :   13 (  13 usr;   1 con; 0-2 aty)
%            Number of variables   :  198 ( 171   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( ~ r1(X19)
        & X19 != Y24 )
      | ( r1(X19)
        & X19 = Y24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & X12 != Y21 )
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( ( ~ r3(X13,X14,X15)
        & X15 != Y22 )
      | ( r3(X13,X14,X15)
        & X15 = Y22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X16,X17] :
    ? [Y23] :
    ! [X18] :
      ( ( ~ r4(X16,X17,X18)
        & X18 != Y23 )
      | ( r4(X16,X17,X18)
        & X18 = Y23 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X2,X9] :
    ? [Y2] :
      ( ? [Y3] :
          ( ? [Y14] :
              ( r2(X9,Y14)
              & r4(X2,Y14,Y3) )
          & Y3 = Y2 )
      & ? [Y6] :
          ( r3(Y6,X2,Y2)
          & r4(X2,X9,Y6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X4] :
    ? [Y9] :
      ( ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) )
      & Y9 = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X5] :
    ? [Y8] :
      ( ? [Y17] :
          ( r1(Y17)
          & r4(X5,Y17,Y8) )
      & ? [Y18] :
          ( r1(Y18)
          & Y8 = Y18 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ? [Y1,Y2] :
      ( ? [Y3] :
          ( r4(Y1,Y3,Y2)
          & ? [Y4] :
              ( r1(Y4)
              & r2(Y4,Y3) ) )
      & ? [Y5] :
          ( r1(Y5)
          & Y2 = Y5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ? [Y1,Y2] :
        ( ? [Y3] :
            ( r4(Y1,Y3,Y2)
            & ? [Y4] :
                ( r1(Y4)
                & r2(Y4,Y3) ) )
        & ? [Y5] :
            ( r1(Y5)
            & Y2 = Y5 ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [Y24,X19] :
      ( pd0_0(X19,Y24)
     => ( ~ r1(X19)
        & X19 != Y24 ) ),
    introduced(predicate_definition,[f1]) ).

fof(f15,plain,
    ? [Y24] :
    ! [X19] :
      ( pd0_0(X19,Y24)
      | ( r1(X19)
        & X19 = Y24 ) ),
    inference(formula_renaming,[status(thm)],[f1,f14]) ).

fof(f16,plain,
    ! [X19] :
      ( pd0_0(X19,sk0_0)
      | ( r1(X19)
        & X19 = sk0_0 ) ),
    inference(skolemization,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0] :
      ( pd0_0(X0,sk0_0)
      | X0 = sk0_0 ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X11,Y21,X12] :
      ( pd0_1(X12,Y21,X11)
     => ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    introduced(predicate_definition,[f2]) ).

fof(f20,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( pd0_1(X12,Y21,X11)
      | ( r2(X11,X12)
        & X12 = Y21 ) ),
    inference(formula_renaming,[status(thm)],[f2,f19]) ).

fof(f21,plain,
    ! [X11,X12] :
      ( pd0_1(X12,sk0_1(X11),X11)
      | ( r2(X11,X12)
        & X12 = sk0_1(X11) ) ),
    inference(skolemization,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | r2(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( pd0_1(X0,sk0_1(X1),X1)
      | X0 = sk0_1(X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f24,plain,
    ! [X13,X14,Y22,X15] :
      ( pd0_2(X15,Y22,X14,X13)
     => ( ~ r3(X13,X14,X15)
        & X15 != Y22 ) ),
    introduced(predicate_definition,[f3]) ).

fof(f25,plain,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( pd0_2(X15,Y22,X14,X13)
      | ( r3(X13,X14,X15)
        & X15 = Y22 ) ),
    inference(formula_renaming,[status(thm)],[f3,f24]) ).

fof(f26,plain,
    ! [X13,X14,X15] :
      ( pd0_2(X15,sk0_2(X14,X13),X14,X13)
      | ( r3(X13,X14,X15)
        & X15 = sk0_2(X14,X13) ) ),
    inference(skolemization,[status(esa)],[f25]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( pd0_2(X0,sk0_2(X1,X2),X1,X2)
      | X0 = sk0_2(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f29,plain,
    ! [X16,X17,Y23,X18] :
      ( pd0_3(X18,Y23,X17,X16)
     => ( ~ r4(X16,X17,X18)
        & X18 != Y23 ) ),
    introduced(predicate_definition,[f4]) ).

fof(f30,plain,
    ! [X16,X17] :
    ? [Y23] :
    ! [X18] :
      ( pd0_3(X18,Y23,X17,X16)
      | ( r4(X16,X17,X18)
        & X18 = Y23 ) ),
    inference(formula_renaming,[status(thm)],[f4,f29]) ).

fof(f31,plain,
    ! [X16,X17,X18] :
      ( pd0_3(X18,sk0_3(X17,X16),X17,X16)
      | ( r4(X16,X17,X18)
        & X18 = sk0_3(X17,X16) ) ),
    inference(skolemization,[status(esa)],[f30]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( pd0_3(X0,sk0_3(X1,X2),X1,X2)
      | X0 = sk0_3(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f40,plain,
    ! [X2,X9] :
      ( r2(X9,sk0_10(X9,X2))
      & r4(X2,sk0_10(X9,X2),sk0_9(X9,X2))
      & sk0_9(X9,X2) = sk0_8(X9,X2)
      & r3(sk0_11(X9,X2),X2,sk0_8(X9,X2))
      & r4(X2,X9,sk0_11(X9,X2)) ),
    inference(skolemization,[status(esa)],[f6]) ).

fof(f41,plain,
    ! [X0,X1] : r2(X0,sk0_10(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f42,plain,
    ! [X0,X1] : r4(X0,sk0_10(X1,X0),sk0_9(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f43,plain,
    ! [X0,X1] : sk0_9(X0,X1) = sk0_8(X0,X1),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f44,plain,
    ! [X0,X1] : r3(sk0_11(X0,X1),X1,sk0_8(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f45,plain,
    ! [X0,X1] : r4(X0,X1,sk0_11(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f47,plain,
    ! [X4] :
      ( r1(sk0_13(X4))
      & r3(X4,sk0_13(X4),sk0_12(X4))
      & sk0_12(X4) = X4 ),
    inference(skolemization,[status(esa)],[f8]) ).

fof(f48,plain,
    ! [X0] : r1(sk0_13(X0)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0] : r3(X0,sk0_13(X0),sk0_12(X0)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ! [X0] : sk0_12(X0) = X0,
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f51,plain,
    ! [X5] :
      ( r1(sk0_15(X5))
      & r4(X5,sk0_15(X5),sk0_14(X5))
      & r1(sk0_16(X5))
      & sk0_14(X5) = sk0_16(X5) ),
    inference(skolemization,[status(esa)],[f9]) ).

fof(f52,plain,
    ! [X0] : r1(sk0_15(X0)),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f53,plain,
    ! [X0] : r4(X0,sk0_15(X0),sk0_14(X0)),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f54,plain,
    ! [X0] : r1(sk0_16(X0)),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f55,plain,
    ! [X0] : sk0_14(X0) = sk0_16(X0),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f64,plain,
    ! [Y1,Y2] :
      ( ! [Y3] :
          ( ~ r4(Y1,Y3,Y2)
          | ! [Y4] :
              ( ~ r1(Y4)
              | ~ r2(Y4,Y3) ) )
      | ! [Y5] :
          ( ~ r1(Y5)
          | Y2 != Y5 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f65,plain,
    ! [Y2] :
      ( ! [Y3] :
          ( ! [Y1] : ~ r4(Y1,Y3,Y2)
          | ! [Y4] :
              ( ~ r1(Y4)
              | ~ r2(Y4,Y3) ) )
      | ! [Y5] :
          ( ~ r1(Y5)
          | Y2 != Y5 ) ),
    inference(miniscoping,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ r4(X0,X1,X2)
      | ~ r1(X3)
      | ~ r2(X3,X1)
      | ~ r1(X4)
      | X2 != X4 ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [Y24,X19] :
      ( ~ pd0_0(X19,Y24)
      | ( ~ r1(X19)
        & X19 != Y24 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ r1(X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f70,plain,
    ! [X11,Y21,X12] :
      ( ~ pd0_1(X12,Y21,X11)
      | ( ~ r2(X11,X12)
        & X12 != Y21 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | ~ r2(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_1(X0,X1,X2)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f73,plain,
    ! [X13,X14,Y22,X15] :
      ( ~ pd0_2(X15,Y22,X14,X13)
      | ( ~ r3(X13,X14,X15)
        & X15 != Y22 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_2(X0,X1,X2,X3)
      | ~ r3(X3,X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

fof(f76,plain,
    ! [X16,X17,Y23,X18] :
      ( ~ pd0_3(X18,Y23,X17,X16)
      | ( ~ r4(X16,X17,X18)
        & X18 != Y23 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f29]) ).

fof(f77,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_3(X0,X1,X2,X3)
      | ~ r4(X3,X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f84,plain,
    ! [X0,X1,X2,X3] :
      ( ~ r4(X0,X1,X2)
      | ~ r1(X3)
      | ~ r2(X3,X1)
      | ~ r1(X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f66]) ).

fof(f85,plain,
    ! [X0] : ~ pd0_0(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f69]) ).

fof(f86,plain,
    ! [X0,X1] : ~ pd0_1(X0,X0,X1),
    inference(destructive_equality_resolution,[status(esa)],[f72]) ).

fof(f89,plain,
    r1(sk0_0),
    inference(resolution,[status(thm)],[f17,f85]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ~ r4(X0,X1,X2)
      | ~ r2(sk0_0,X1)
      | ~ r1(X2) ),
    inference(resolution,[status(thm)],[f89,f84]) ).

fof(f100,plain,
    ! [X0] : r1(sk0_14(X0)),
    inference(backward_demodulation,[status(thm)],[f55,f54]) ).

fof(f111,plain,
    ! [X0] :
      ( X0 = sk0_0
      | ~ r1(X0) ),
    inference(resolution,[status(thm)],[f18,f68]) ).

fof(f112,plain,
    ! [X0] : sk0_14(X0) = sk0_0,
    inference(resolution,[status(thm)],[f111,f100]) ).

fof(f113,plain,
    ! [X0] : sk0_15(X0) = sk0_0,
    inference(resolution,[status(thm)],[f111,f52]) ).

fof(f114,plain,
    ! [X0] : sk0_13(X0) = sk0_0,
    inference(resolution,[status(thm)],[f111,f48]) ).

fof(f118,plain,
    ! [X0] : r2(X0,sk0_1(X0)),
    inference(resolution,[status(thm)],[f22,f86]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ r4(X0,sk0_1(sk0_0),X1)
      | ~ r1(X1) ),
    inference(resolution,[status(thm)],[f118,f91]) ).

fof(f141,plain,
    ! [X0] : r3(X0,sk0_0,sk0_12(X0)),
    inference(forward_demodulation,[status(thm)],[f114,f49]) ).

fof(f142,plain,
    ! [X0] : r3(X0,sk0_0,X0),
    inference(forward_demodulation,[status(thm)],[f50,f141]) ).

fof(f143,plain,
    ! [X0] : r4(X0,sk0_0,sk0_14(X0)),
    inference(forward_demodulation,[status(thm)],[f113,f53]) ).

fof(f144,plain,
    ! [X0] : r4(X0,sk0_0,sk0_0),
    inference(forward_demodulation,[status(thm)],[f112,f143]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | X1 = sk0_1(X0) ),
    inference(resolution,[status(thm)],[f71,f23]) ).

fof(f149,plain,
    ! [X0,X1] : sk0_10(X0,X1) = sk0_1(X0),
    inference(resolution,[status(thm)],[f145,f41]) ).

fof(f164,plain,
    ! [X0,X1] : r4(X0,sk0_1(X1),sk0_9(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f149,f42]) ).

fof(f165,plain,
    ! [X0,X1] : r4(X0,sk0_1(X1),sk0_8(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f43,f164]) ).

fof(f166,plain,
    ! [X0] : ~ r1(sk0_8(sk0_0,X0)),
    inference(resolution,[status(thm)],[f165,f132]) ).

fof(f235,plain,
    ! [X0,X1,X2] :
      ( ~ r3(X0,X1,X2)
      | X2 = sk0_2(X1,X0) ),
    inference(resolution,[status(thm)],[f74,f28]) ).

fof(f238,plain,
    ! [X0] : X0 = sk0_2(sk0_0,X0),
    inference(resolution,[status(thm)],[f235,f142]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( pd0_2(X0,X1,sk0_0,X1)
      | X0 = sk0_2(sk0_0,X1) ),
    inference(paramodulation,[status(thm)],[f238,f28]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( pd0_2(X0,X1,sk0_0,X1)
      | X0 = X1 ),
    inference(forward_demodulation,[status(thm)],[f238,f241]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ r3(X1,sk0_0,X0) ),
    inference(resolution,[status(thm)],[f242,f74]) ).

fof(f249,plain,
    ! [X0] : sk0_8(X0,sk0_0) = sk0_11(X0,sk0_0),
    inference(resolution,[status(thm)],[f248,f44]) ).

fof(f276,plain,
    ! [X0] : r4(sk0_0,X0,sk0_8(X0,sk0_0)),
    inference(paramodulation,[status(thm)],[f249,f45]) ).

fof(f277,plain,
    ! [X0,X1,X2] :
      ( ~ r4(X0,X1,X2)
      | X2 = sk0_3(X1,X0) ),
    inference(resolution,[status(thm)],[f77,f33]) ).

fof(f733,plain,
    ! [X0] : sk0_8(X0,sk0_0) = sk0_3(X0,sk0_0),
    inference(resolution,[status(thm)],[f277,f276]) ).

fof(f735,plain,
    ! [X0] : sk0_0 = sk0_3(sk0_0,X0),
    inference(resolution,[status(thm)],[f277,f144]) ).

fof(f747,plain,
    ~ r1(sk0_3(sk0_0,sk0_0)),
    inference(paramodulation,[status(thm)],[f733,f166]) ).

fof(f748,plain,
    ~ r1(sk0_0),
    inference(forward_demodulation,[status(thm)],[f735,f747]) ).

fof(f749,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f748,f89]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUN082+2 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:34:56 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.13/0.38  % Refutation found
% 0.13/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.029599 seconds
% 0.13/0.38  % CPU time: 0.105418 seconds
% 0.13/0.38  % Total memory used: 21.519 MB
% 0.13/0.38  % Net memory used: 21.386 MB
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