TSTP Solution File: NUN086+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 : Thu Aug 31 12:49:24 EDT 2023

% Result   : Theorem 3.44s 1.20s
% Output   : CNFRefutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  128 (  54 unt;   0 def)
%            Number of atoms       :  373 ( 121 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  362 ( 117   ~;  88   |; 140   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   1 con; 0-2 aty)
%            Number of variables   :  323 (  10 sgn; 148   !;  87   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( X0 = X1
        & r1(X1) )
      | ( X0 != X1
        & ~ r1(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( X3 = X4
        & r2(X2,X4) )
      | ( X3 != X4
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f3,axiom,
    ! [X5,X6] :
    ? [X7] :
    ! [X8] :
      ( ( X7 = X8
        & r3(X5,X6,X8) )
      | ( X7 != X8
        & ~ r3(X5,X6,X8) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

fof(f4,axiom,
    ! [X9,X10] :
    ? [X11] :
    ! [X12] :
      ( ( X11 = X12
        & r4(X9,X10,X12) )
      | ( X11 != X12
        & ~ r4(X9,X10,X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

fof(f5,axiom,
    ! [X13,X14] :
    ? [X15] :
      ( ? [X18] :
          ( r3(X13,X14,X18)
          & r2(X18,X15) )
      & ? [X16] :
          ( X15 = X16
          & ? [X17] :
              ( r3(X13,X17,X16)
              & r2(X14,X17) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).

fof(f6,axiom,
    ! [X19,X20] :
    ? [X21] :
      ( ? [X24] :
          ( r4(X19,X20,X24)
          & r3(X24,X19,X21) )
      & ? [X22] :
          ( X21 = X22
          & ? [X23] :
              ( r4(X19,X23,X22)
              & r2(X20,X23) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2a) ).

fof(f7,axiom,
    ! [X25,X26] :
      ( X25 = X26
      | ! [X27] :
          ( ~ r2(X26,X27)
          | ! [X28] :
              ( X27 != X28
              | ~ r2(X25,X28) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).

fof(f8,axiom,
    ! [X29] :
    ? [X30] :
      ( X29 = X30
      & ? [X31] :
          ( r3(X29,X31,X30)
          & r1(X31) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).

fof(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X35] :
          ( X33 = X35
          & r1(X35) )
      & ? [X34] :
          ( r4(X32,X34,X33)
          & r1(X34) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).

fof(f12,conjecture,
    ? [X38] :
      ( ? [X16] :
          ( X16 = X38
          & r1(X16) )
      & ? [X21] :
          ( ? [X15] :
              ( r4(X15,X21,X38)
              & r1(X15) )
          & ? [X22] :
              ( r2(X22,X21)
              & r1(X22) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimesoneeqzero) ).

fof(f13,negated_conjecture,
    ~ ? [X38] :
        ( ? [X16] :
            ( X16 = X38
            & r1(X16) )
        & ? [X21] :
            ( ? [X15] :
                ( r4(X15,X21,X38)
                & r1(X15) )
            & ? [X22] :
                ( r2(X22,X21)
                & r1(X22) ) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f14,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 = X2
        & r2(X0,X2) )
      | ( X1 != X2
        & ~ r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r3(X0,X1,X3) )
      | ( X2 != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(rectify,[],[f3]) ).

fof(f16,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r4(X0,X1,X3) )
      | ( X2 != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(rectify,[],[f4]) ).

fof(f17,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f18,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,X2) )
      & ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( X2 != X3
              | ~ r2(X0,X3) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f20,plain,
    ! [X0] :
    ? [X1] :
      ( X0 = X1
      & ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) ) ),
    inference(rectify,[],[f8]) ).

fof(f21,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( X1 = X2
          & r1(X2) )
      & ? [X3] :
          ( r4(X0,X3,X1)
          & r1(X3) ) ),
    inference(rectify,[],[f9]) ).

fof(f24,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( X0 = X1
            & r1(X1) )
        & ? [X2] :
            ( ? [X3] :
                ( r4(X3,X2,X0)
                & r1(X3) )
            & ? [X4] :
                ( r2(X4,X2)
                & r1(X4) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f25,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 != X1
          | ~ r1(X1) )
      | ! [X2] :
          ( ! [X3] :
              ( ~ r4(X3,X2,X0)
              | ~ r1(X3) )
          | ! [X4] :
              ( ~ r2(X4,X2)
              | ~ r1(X4) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f26,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK0 = X1
          & r1(X1) )
        | ( sK0 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X1] :
      ( ( sK0 = X1
        & r1(X1) )
      | ( sK0 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK1(X0) = X2
            & r2(X0,X2) )
          | ( sK1(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X2] :
      ( ( sK1(X0) = X2
        & r2(X0,X2) )
      | ( sK1(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f28]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r3(X0,X1,X3) )
          | ( X2 != X3
            & ~ r3(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK2(X0,X1) = X3
            & r3(X0,X1,X3) )
          | ( sK2(X0,X1) != X3
            & ~ r3(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1,X3] :
      ( ( sK2(X0,X1) = X3
        & r3(X0,X1,X3) )
      | ( sK2(X0,X1) != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r4(X0,X1,X3) )
          | ( X2 != X3
            & ~ r4(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK3(X0,X1) = X3
            & r4(X0,X1,X3) )
          | ( sK3(X0,X1) != X3
            & ~ r4(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1,X3] :
      ( ( sK3(X0,X1) = X3
        & r4(X0,X1,X3) )
      | ( sK3(X0,X1) != X3
        & ~ r4(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f32]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) ) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK4(X0,X1)) )
        & ? [X4] :
            ( sK4(X0,X1) = X4
            & ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK4(X0,X1)) )
     => ( r3(X0,X1,sK5(X0,X1))
        & r2(sK5(X0,X1),sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK4(X0,X1) = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK4(X0,X1) = sK6(X0,X1)
        & ? [X5] :
            ( r3(X0,X5,sK6(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK6(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK7(X0,X1),sK6(X0,X1))
        & r2(X1,sK7(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK5(X0,X1))
      & r2(sK5(X0,X1),sK4(X0,X1))
      & sK4(X0,X1) = sK6(X0,X1)
      & r3(X0,sK7(X0,X1),sK6(X0,X1))
      & r2(X1,sK7(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f17,f37,f36,f35,f34]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r4(X0,X1,X3)
              & r3(X3,X0,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r4(X0,X5,X4)
                  & r2(X1,X5) ) ) )
     => ( ? [X3] :
            ( r4(X0,X1,X3)
            & r3(X3,X0,sK8(X0,X1)) )
        & ? [X4] :
            ( sK8(X0,X1) = X4
            & ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,sK8(X0,X1)) )
     => ( r4(X0,X1,sK9(X0,X1))
        & r3(sK9(X0,X1),X0,sK8(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK8(X0,X1) = X4
          & ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK8(X0,X1) = sK10(X0,X1)
        & ? [X5] :
            ( r4(X0,X5,sK10(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK10(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK11(X0,X1),sK10(X0,X1))
        & r2(X1,sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( r4(X0,X1,sK9(X0,X1))
      & r3(sK9(X0,X1),X0,sK8(X0,X1))
      & sK8(X0,X1) = sK10(X0,X1)
      & r4(X0,sK11(X0,X1),sK10(X0,X1))
      & r2(X1,sK11(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f18,f42,f41,f40,f39]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 = X1
          & ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) ) )
     => ( sK12(X0) = X0
        & ? [X2] :
            ( r3(X0,X2,sK12(X0))
            & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK12(X0))
          & r1(X2) )
     => ( r3(X0,sK13(X0),sK12(X0))
        & r1(sK13(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0] :
      ( sK12(X0) = X0
      & r3(X0,sK13(X0),sK12(X0))
      & r1(sK13(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f20,f45,f44]) ).

fof(f47,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( X1 = X2
              & r1(X2) )
          & ? [X3] :
              ( r4(X0,X3,X1)
              & r1(X3) ) )
     => ( ? [X2] :
            ( sK14(X0) = X2
            & r1(X2) )
        & ? [X3] :
            ( r4(X0,X3,sK14(X0))
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X2] :
          ( sK14(X0) = X2
          & r1(X2) )
     => ( sK14(X0) = sK15(X0)
        & r1(sK15(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0] :
      ( ? [X3] :
          ( r4(X0,X3,sK14(X0))
          & r1(X3) )
     => ( r4(X0,sK16(X0),sK14(X0))
        & r1(sK16(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ! [X0] :
      ( sK14(X0) = sK15(X0)
      & r1(sK15(X0))
      & r4(X0,sK16(X0),sK14(X0))
      & r1(sK16(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f21,f49,f48,f47]) ).

fof(f55,plain,
    ! [X1] :
      ( r1(X1)
      | sK0 != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f56,plain,
    ! [X1] :
      ( sK0 = X1
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f59,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK1(X0) != X2 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f60,plain,
    ! [X2,X0] :
      ( sK1(X0) = X2
      | ~ r2(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f64,plain,
    ! [X3,X0,X1] :
      ( sK2(X0,X1) = X3
      | ~ r3(X0,X1,X3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f68,plain,
    ! [X3,X0,X1] :
      ( sK3(X0,X1) = X3
      | ~ r4(X0,X1,X3) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f72,plain,
    ! [X0,X1] : sK4(X0,X1) = sK6(X0,X1),
    inference(cnf_transformation,[],[f38]) ).

fof(f73,plain,
    ! [X0,X1] : r2(sK5(X0,X1),sK4(X0,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f74,plain,
    ! [X0,X1] : r3(X0,X1,sK5(X0,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f75,plain,
    ! [X0,X1] : r2(X1,sK11(X0,X1)),
    inference(cnf_transformation,[],[f43]) ).

fof(f76,plain,
    ! [X0,X1] : r4(X0,sK11(X0,X1),sK10(X0,X1)),
    inference(cnf_transformation,[],[f43]) ).

fof(f77,plain,
    ! [X0,X1] : sK8(X0,X1) = sK10(X0,X1),
    inference(cnf_transformation,[],[f43]) ).

fof(f78,plain,
    ! [X0,X1] : r3(sK9(X0,X1),X0,sK8(X0,X1)),
    inference(cnf_transformation,[],[f43]) ).

fof(f79,plain,
    ! [X0,X1] : r4(X0,X1,sK9(X0,X1)),
    inference(cnf_transformation,[],[f43]) ).

fof(f80,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X2)
      | X2 != X3
      | ~ r2(X0,X3) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f81,plain,
    ! [X0] : r1(sK13(X0)),
    inference(cnf_transformation,[],[f46]) ).

fof(f82,plain,
    ! [X0] : r3(X0,sK13(X0),sK12(X0)),
    inference(cnf_transformation,[],[f46]) ).

fof(f83,plain,
    ! [X0] : sK12(X0) = X0,
    inference(cnf_transformation,[],[f46]) ).

fof(f84,plain,
    ! [X0] : r1(sK16(X0)),
    inference(cnf_transformation,[],[f50]) ).

fof(f85,plain,
    ! [X0] : r4(X0,sK16(X0),sK14(X0)),
    inference(cnf_transformation,[],[f50]) ).

fof(f86,plain,
    ! [X0] : r1(sK15(X0)),
    inference(cnf_transformation,[],[f50]) ).

fof(f87,plain,
    ! [X0] : sK14(X0) = sK15(X0),
    inference(cnf_transformation,[],[f50]) ).

fof(f93,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X0 != X1
      | ~ r1(X1)
      | ~ r4(X3,X2,X0)
      | ~ r1(X3)
      | ~ r2(X4,X2)
      | ~ r1(X4) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f94,plain,
    ! [X0,X1] : r2(sK5(X0,X1),sK6(X0,X1)),
    inference(definition_unfolding,[],[f73,f72]) ).

fof(f95,plain,
    ! [X0,X1] : r3(sK9(X0,X1),X0,sK10(X0,X1)),
    inference(definition_unfolding,[],[f78,f77]) ).

fof(f96,plain,
    ! [X0] : r4(X0,sK16(X0),sK15(X0)),
    inference(definition_unfolding,[],[f85,f87]) ).

fof(f98,plain,
    r1(sK0),
    inference(equality_resolution,[],[f55]) ).

fof(f100,plain,
    ! [X0] : r2(X0,sK1(X0)),
    inference(equality_resolution,[],[f59]) ).

fof(f105,plain,
    ! [X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X3)
      | ~ r2(X0,X3) ),
    inference(equality_resolution,[],[f80]) ).

fof(f107,plain,
    ! [X2,X3,X1,X4] :
      ( ~ r1(X1)
      | ~ r4(X3,X2,X1)
      | ~ r1(X3)
      | ~ r2(X4,X2)
      | ~ r1(X4) ),
    inference(equality_resolution,[],[f93]) ).

cnf(c_49,plain,
    ( ~ r1(X0)
    | X0 = sK0 ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_50,plain,
    r1(sK0),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_51,plain,
    ( ~ r2(X0,X1)
    | sK1(X0) = X1 ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_52,plain,
    r2(X0,sK1(X0)),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_53,plain,
    ( ~ r3(X0,X1,X2)
    | sK2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_55,plain,
    ( ~ r4(X0,X1,X2)
    | sK3(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_57,plain,
    r3(X0,X1,sK5(X0,X1)),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_58,plain,
    r2(sK5(X0,X1),sK6(X0,X1)),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_61,plain,
    r4(X0,X1,sK9(X0,X1)),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_62,plain,
    r3(sK9(X0,X1),X0,sK10(X0,X1)),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_63,plain,
    r4(X0,sK11(X0,X1),sK10(X0,X1)),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_64,plain,
    r2(X0,sK11(X1,X0)),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_65,plain,
    ( ~ r2(X0,X1)
    | ~ r2(X2,X1)
    | X0 = X2 ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_66,plain,
    sK12(X0) = X0,
    inference(cnf_transformation,[],[f83]) ).

cnf(c_67,plain,
    r3(X0,sK13(X0),sK12(X0)),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_68,plain,
    r1(sK13(X0)),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_69,plain,
    r1(sK15(X0)),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_70,plain,
    r4(X0,sK16(X0),sK15(X0)),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_71,plain,
    r1(sK16(X0)),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_77,negated_conjecture,
    ( ~ r4(X0,X1,X2)
    | ~ r2(X3,X1)
    | ~ r1(X0)
    | ~ r1(X2)
    | ~ r1(X3) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_81,plain,
    r2(sK0,sK1(sK0)),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_193,plain,
    r3(X0,sK13(X0),X0),
    inference(light_normalisation,[status(thm)],[c_67,c_66]) ).

cnf(c_254,plain,
    ( sK5(X1,X3) != X4
    | X0 != X1
    | X2 != X3
    | sK2(X0,X2) = X4 ),
    inference(resolution_lifted,[status(thm)],[c_53,c_57]) ).

cnf(c_255,plain,
    sK2(X0,X1) = sK5(X0,X1),
    inference(unflattening,[status(thm)],[c_254]) ).

cnf(c_266,plain,
    ( sK9(X0,X1) != X2
    | sK10(X0,X1) != X4
    | X0 != X3
    | sK2(X2,X3) = X4 ),
    inference(resolution_lifted,[status(thm)],[c_53,c_62]) ).

cnf(c_267,plain,
    sK2(sK9(X0,X1),X0) = sK10(X0,X1),
    inference(unflattening,[status(thm)],[c_266]) ).

cnf(c_272,plain,
    ( sK13(X1) != X2
    | X0 != X1
    | X1 != X3
    | sK2(X0,X2) = X3 ),
    inference(resolution_lifted,[status(thm)],[c_53,c_193]) ).

cnf(c_273,plain,
    sK2(X0,sK13(X0)) = X0,
    inference(unflattening,[status(thm)],[c_272]) ).

cnf(c_467,plain,
    r2(sK2(X0,X1),sK6(X0,X1)),
    inference(demodulation,[status(thm)],[c_58,c_255]) ).

cnf(c_609,plain,
    ( X0 != X1
    | ~ r1(X1)
    | r1(X0) ),
    theory(equality) ).

cnf(c_879,plain,
    sK13(X0) = sK0,
    inference(superposition,[status(thm)],[c_68,c_49]) ).

cnf(c_880,plain,
    sK15(X0) = sK0,
    inference(superposition,[status(thm)],[c_69,c_49]) ).

cnf(c_881,plain,
    sK16(X0) = sK0,
    inference(superposition,[status(thm)],[c_71,c_49]) ).

cnf(c_883,plain,
    r4(X0,sK16(X0),sK0),
    inference(demodulation,[status(thm)],[c_70,c_880]) ).

cnf(c_913,plain,
    r4(X0,sK0,sK0),
    inference(light_normalisation,[status(thm)],[c_883,c_881]) ).

cnf(c_927,plain,
    ( ~ r2(X0,sK11(X1,X2))
    | ~ r1(sK10(X1,X2))
    | ~ r1(X0)
    | ~ r1(X1) ),
    inference(superposition,[status(thm)],[c_63,c_77]) ).

cnf(c_953,plain,
    sK11(X0,X1) = sK1(X1),
    inference(superposition,[status(thm)],[c_64,c_51]) ).

cnf(c_968,plain,
    sK2(X0,sK0) = X0,
    inference(light_normalisation,[status(thm)],[c_273,c_879]) ).

cnf(c_969,plain,
    r2(X0,sK6(X0,sK0)),
    inference(superposition,[status(thm)],[c_968,c_467]) ).

cnf(c_970,plain,
    r2(sK0,sK6(sK0,sK0)),
    inference(instantiation,[status(thm)],[c_969]) ).

cnf(c_979,plain,
    ( ~ r1(sK10(X0,X1))
    | ~ r2(X2,sK1(X1))
    | ~ r1(X0)
    | ~ r1(X2) ),
    inference(demodulation,[status(thm)],[c_927,c_953]) ).

cnf(c_1062,plain,
    sK3(X0,X1) = sK9(X0,X1),
    inference(superposition,[status(thm)],[c_61,c_55]) ).

cnf(c_1063,plain,
    sK3(X0,sK0) = sK0,
    inference(superposition,[status(thm)],[c_913,c_55]) ).

cnf(c_1083,plain,
    ( ~ r2(X0,sK6(X1,X2))
    | sK2(X1,X2) = X0 ),
    inference(superposition,[status(thm)],[c_467,c_65]) ).

cnf(c_1094,plain,
    ( ~ r2(sK0,sK6(sK0,sK0))
    | sK2(sK0,sK0) = sK0 ),
    inference(instantiation,[status(thm)],[c_1083]) ).

cnf(c_1340,plain,
    sK2(sK3(X0,X1),X0) = sK10(X0,X1),
    inference(light_normalisation,[status(thm)],[c_267,c_1062]) ).

cnf(c_1343,plain,
    sK2(sK0,X0) = sK10(X0,sK0),
    inference(superposition,[status(thm)],[c_1063,c_1340]) ).

cnf(c_1515,plain,
    ( sK2(X0,X1) != X2
    | ~ r1(X2)
    | r1(sK2(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_609]) ).

cnf(c_1516,plain,
    ( sK2(sK0,sK0) != sK0
    | ~ r1(sK0)
    | r1(sK2(sK0,sK0)) ),
    inference(instantiation,[status(thm)],[c_1515]) ).

cnf(c_1651,plain,
    ( ~ r1(sK2(sK0,X0))
    | ~ r2(X1,sK1(sK0))
    | ~ r1(X0)
    | ~ r1(X1) ),
    inference(superposition,[status(thm)],[c_1343,c_979]) ).

cnf(c_1657,plain,
    ( ~ r1(sK2(sK0,sK0))
    | ~ r2(sK0,sK1(sK0))
    | ~ r1(sK0) ),
    inference(instantiation,[status(thm)],[c_1651]) ).

cnf(c_1658,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1657,c_1516,c_1094,c_970,c_81,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUN086+2 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun Aug 27 09:52:09 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.44/1.20  % SZS status Started for theBenchmark.p
% 3.44/1.20  % SZS status Theorem for theBenchmark.p
% 3.44/1.20  
% 3.44/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.44/1.20  
% 3.44/1.20  ------  iProver source info
% 3.44/1.20  
% 3.44/1.20  git: date: 2023-05-31 18:12:56 +0000
% 3.44/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.44/1.20  git: non_committed_changes: false
% 3.44/1.20  git: last_make_outside_of_git: false
% 3.44/1.20  
% 3.44/1.20  ------ Parsing...
% 3.44/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.44/1.20  
% 3.44/1.20  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 1  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 3.44/1.20  
% 3.44/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.44/1.20  
% 3.44/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.44/1.20  ------ Proving...
% 3.44/1.20  ------ Problem Properties 
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  clauses                                 27
% 3.44/1.20  conjectures                             1
% 3.44/1.20  EPR                                     5
% 3.44/1.20  Horn                                    23
% 3.44/1.20  unary                                   17
% 3.44/1.20  binary                                  8
% 3.44/1.20  lits                                    41
% 3.44/1.20  lits eq                                 13
% 3.44/1.20  fd_pure                                 0
% 3.44/1.20  fd_pseudo                               0
% 3.44/1.20  fd_cond                                 1
% 3.44/1.20  fd_pseudo_cond                          3
% 3.44/1.20  AC symbols                              0
% 3.44/1.20  
% 3.44/1.20  ------ Schedule dynamic 5 is on 
% 3.44/1.20  
% 3.44/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  ------ 
% 3.44/1.20  Current options:
% 3.44/1.20  ------ 
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  ------ Proving...
% 3.44/1.20  
% 3.44/1.20  
% 3.44/1.20  % SZS status Theorem for theBenchmark.p
% 3.44/1.20  
% 3.44/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.44/1.20  
% 3.44/1.20  
%------------------------------------------------------------------------------