TSTP Solution File: SET955+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 : Mon Jun 24 14:36:41 EDT 2024

% Result   : Theorem 3.89s 1.12s
% Output   : CNFRefutation 3.89s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(f4,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f8,conjecture,
    ! [X0,X1,X2,X3] :
      ( ! [X4,X5] :
          ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
        <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
     => cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ! [X4,X5] :
            ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
          <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
       => cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f12,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      & ! [X4,X5] :
          ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
        <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X1)
                  & in(X6,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X1)
                  & in(X11,X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(rectify,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X1)
                & in(X6,X0) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
              | ~ in(X5,X1)
              | ~ in(X4,X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
              & in(X7,X1)
              & in(X6,X0) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
          & in(X7,X1)
          & in(X6,X0) )
     => ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
        & in(sK2(X0,X1,X2),X1)
        & in(sK1(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X1)
          & in(X11,X0) )
     => ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
        & in(sK4(X0,X1,X8),X1)
        & in(sK3(X0,X1,X8),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
              & in(sK2(X0,X1,X2),X1)
              & in(sK1(X0,X1,X2),X0) )
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
                & in(sK4(X0,X1,X8),X1)
                & in(sK3(X0,X1,X8),X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f15,f18,f17,f16]) ).

fof(f24,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      & ! [X4,X5] :
          ( ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
          & ( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f25,plain,
    ( ? [X0,X1,X2,X3] :
        ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
        & ! [X4,X5] :
            ( ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
              | ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
            & ( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
              | ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) ) )
   => ( cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10)
      & ! [X5,X4] :
          ( ( in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) )
          & ( in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ( cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10)
    & ! [X4,X5] :
        ( ( in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
          | ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) )
        & ( in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
          | ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f24,f25]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK11(X0,X1),X1)
          | ~ in(sK11(X0,X1),X0) )
        & ( in(sK11(X0,X1),X1)
          | in(sK11(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK11(X0,X1),X1)
          | ~ in(sK11(X0,X1),X0) )
        & ( in(sK11(X0,X1),X1)
          | in(sK11(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f28]) ).

fof(f31,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f32,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f33,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f34,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f35,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | ordered_pair(X9,X10) != X8
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f40,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f44,plain,
    ! [X4,X5] :
      ( in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10))
      | ~ in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f45,plain,
    ! [X4,X5] :
      ( in(ordered_pair(X4,X5),cartesian_product2(sK7,sK8))
      | ~ in(ordered_pair(X4,X5),cartesian_product2(sK9,sK10)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f46,plain,
    cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
    inference(cnf_transformation,[],[f26]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | in(sK11(X0,X1),X1)
      | in(sK11(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ in(sK11(X0,X1),X1)
      | ~ in(sK11(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f51,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f35,f40]) ).

fof(f52,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f34,f40]) ).

fof(f54,plain,
    ! [X4,X5] :
      ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK7,sK8))
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK9,sK10)) ),
    inference(definition_unfolding,[],[f45,f40,f40]) ).

fof(f55,plain,
    ! [X4,X5] :
      ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK9,sK10))
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK7,sK8)) ),
    inference(definition_unfolding,[],[f44,f40,f40]) ).

fof(f56,plain,
    ! [X2,X10,X0,X1,X9] :
      ( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
      | ~ in(X10,X1)
      | ~ in(X9,X0)
      | cartesian_product2(X0,X1) != X2 ),
    inference(equality_resolution,[],[f51]) ).

fof(f57,plain,
    ! [X10,X0,X1,X9] :
      ( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
      | ~ in(X10,X1)
      | ~ in(X9,X0) ),
    inference(equality_resolution,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f52]) ).

fof(f59,plain,
    ! [X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f33]) ).

fof(f60,plain,
    ! [X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f32]) ).

cnf(c_50,plain,
    unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_55,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X3)
    | in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3)) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_56,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_57,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | in(sK4(X1,X2,X0),X2) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_58,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | in(sK3(X1,X2,X0),X1) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_62,negated_conjecture,
    cartesian_product2(sK7,sK8) != cartesian_product2(sK9,sK10),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_63,negated_conjecture,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8)) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_64,negated_conjecture,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8))
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10)) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_65,plain,
    ( ~ in(sK11(X0,X1),X0)
    | ~ in(sK11(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_66,plain,
    ( X0 = X1
    | in(sK11(X0,X1),X0)
    | in(sK11(X0,X1),X1) ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_80,plain,
    ( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8))
    | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10)) ),
    inference(prop_impl_just,[status(thm)],[c_63]) ).

cnf(c_81,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10))
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8)) ),
    inference(renaming,[status(thm)],[c_80]) ).

cnf(c_82,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK7,sK8))
    | in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(sK9,sK10)) ),
    inference(prop_impl_just,[status(thm)],[c_64]) ).

cnf(c_88,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_56]) ).

cnf(c_237,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X3)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),cartesian_product2(X1,X3)) ),
    inference(demodulation,[status(thm)],[c_55,c_50]) ).

cnf(c_259,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK7,sK8))
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK9,sK10)) ),
    inference(demodulation,[status(thm)],[c_82,c_50]) ).

cnf(c_266,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK9,sK10))
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK7,sK8)) ),
    inference(demodulation,[status(thm)],[c_81,c_50]) ).

cnf(c_273,plain,
    ( ~ in(X0,cartesian_product2(X1,X2))
    | unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 ),
    inference(demodulation,[status(thm)],[c_88,c_50]) ).

cnf(c_330,plain,
    cartesian_product2(sK7,sK8) = sP0_iProver_def,
    definition ).

cnf(c_331,plain,
    cartesian_product2(sK9,sK10) = sP1_iProver_def,
    definition ).

cnf(c_332,negated_conjecture,
    sP0_iProver_def != sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_62,c_331,c_330]) ).

cnf(c_333,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_335,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_747,plain,
    ( ~ in(X0,sK9)
    | ~ in(X1,sK10)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_331,c_237]) ).

cnf(c_893,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_259,c_330,c_331]) ).

cnf(c_959,plain,
    ( ~ in(X0,sP0_iProver_def)
    | unordered_pair(singleton(sK3(sK7,sK8,X0)),unordered_pair(sK3(sK7,sK8,X0),sK4(sK7,sK8,X0))) = X0 ),
    inference(superposition,[status(thm)],[c_330,c_273]) ).

cnf(c_960,plain,
    ( ~ in(X0,sP1_iProver_def)
    | unordered_pair(singleton(sK3(sK9,sK10,X0)),unordered_pair(sK3(sK9,sK10,X0),sK4(sK9,sK10,X0))) = X0 ),
    inference(superposition,[status(thm)],[c_331,c_273]) ).

cnf(c_1000,plain,
    ( sP0_iProver_def != X0
    | sP1_iProver_def != X0
    | sP0_iProver_def = sP1_iProver_def ),
    inference(instantiation,[status(thm)],[c_335]) ).

cnf(c_1061,plain,
    ( sP0_iProver_def != sP0_iProver_def
    | sP1_iProver_def != sP0_iProver_def
    | sP0_iProver_def = sP1_iProver_def ),
    inference(instantiation,[status(thm)],[c_1000]) ).

cnf(c_1062,plain,
    sP0_iProver_def = sP0_iProver_def,
    inference(instantiation,[status(thm)],[c_333]) ).

cnf(c_1349,plain,
    ( sP1_iProver_def = sP0_iProver_def
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_1350,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | sP1_iProver_def = sP0_iProver_def ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_1517,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP1_iProver_def)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_266,c_330,c_331]) ).

cnf(c_1525,plain,
    ( ~ in(X0,sK9)
    | ~ in(X1,sK10)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_747,c_1517]) ).

cnf(c_2175,plain,
    ( unordered_pair(singleton(sK3(sK7,sK8,sK11(X0,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(X0,sP0_iProver_def)),sK4(sK7,sK8,sK11(X0,sP0_iProver_def)))) = sK11(X0,sP0_iProver_def)
    | X0 = sP0_iProver_def
    | in(sK11(X0,sP0_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_66,c_959]) ).

cnf(c_2485,plain,
    ( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | unordered_pair(singleton(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | sP0_iProver_def = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_2175,c_960]) ).

cnf(c_2489,plain,
    ( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | unordered_pair(singleton(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2485,c_332]) ).

cnf(c_2588,plain,
    ( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
    | ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_2489,c_1525]) ).

cnf(c_2596,plain,
    ( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
    | ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_2489,c_747]) ).

cnf(c_4464,plain,
    ( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
    | ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9) ),
    inference(global_subsumption_just,[status(thm)],[c_2588,c_332,c_1061,c_1062,c_1350,c_2596,c_2588]) ).

cnf(c_4465,plain,
    ( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
    | ~ in(sK4(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK10)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(renaming,[status(thm)],[c_4464]) ).

cnf(c_4472,plain,
    ( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
    | ~ in(sK11(sP1_iProver_def,sP0_iProver_def),cartesian_product2(sK9,sK10))
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_57,c_4465]) ).

cnf(c_4473,plain,
    ( ~ in(sK3(sK9,sK10,sK11(sP1_iProver_def,sP0_iProver_def)),sK9)
    | ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_4472,c_331]) ).

cnf(c_5616,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),cartesian_product2(sK9,sK10))
    | ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_58,c_4473]) ).

cnf(c_5617,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_5616,c_331]) ).

cnf(c_5627,plain,
    ( unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def)
    | sP0_iProver_def = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_2175,c_5617]) ).

cnf(c_5628,plain,
    unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))) = sK11(sP1_iProver_def,sP0_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_5627,c_332]) ).

cnf(c_5656,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | in(unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_5628,c_1517]) ).

cnf(c_5661,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | in(unordered_pair(singleton(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def))),unordered_pair(sK3(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)),sK4(sK7,sK8,sK11(sP1_iProver_def,sP0_iProver_def)))),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_5628,c_893]) ).

cnf(c_5701,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def)
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_5661,c_5628]) ).

cnf(c_5704,plain,
    ( ~ in(sK11(sP1_iProver_def,sP0_iProver_def),sP1_iProver_def)
    | in(sK11(sP1_iProver_def,sP0_iProver_def),sP0_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_5656,c_5628]) ).

cnf(c_5894,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5701,c_5704,c_1349,c_1350,c_1062,c_1061,c_332]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n021.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun Jun 23 15:59:39 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.89/1.12  % SZS status Started for theBenchmark.p
% 3.89/1.12  % SZS status Theorem for theBenchmark.p
% 3.89/1.12  
% 3.89/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.89/1.12  
% 3.89/1.12  ------  iProver source info
% 3.89/1.12  
% 3.89/1.12  git: date: 2024-06-12 09:56:46 +0000
% 3.89/1.12  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.89/1.12  git: non_committed_changes: false
% 3.89/1.12  
% 3.89/1.12  ------ Parsing...
% 3.89/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.89/1.12  
% 3.89/1.12  ------ Preprocessing... sup_sim: 7  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.89/1.12  
% 3.89/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.89/1.12  
% 3.89/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.89/1.12  ------ Proving...
% 3.89/1.12  ------ Problem Properties 
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  clauses                                 20
% 3.89/1.12  conjectures                             1
% 3.89/1.12  EPR                                     4
% 3.89/1.12  Horn                                    16
% 3.89/1.12  unary                                   7
% 3.89/1.12  binary                                  6
% 3.89/1.12  lits                                    42
% 3.89/1.12  lits eq                                 13
% 3.89/1.12  fd_pure                                 0
% 3.89/1.12  fd_pseudo                               0
% 3.89/1.12  fd_cond                                 0
% 3.89/1.12  fd_pseudo_cond                          6
% 3.89/1.12  AC symbols                              0
% 3.89/1.12  
% 3.89/1.12  ------ Schedule dynamic 5 is on 
% 3.89/1.12  
% 3.89/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  ------ 
% 3.89/1.12  Current options:
% 3.89/1.12  ------ 
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  ------ Proving...
% 3.89/1.12  
% 3.89/1.12  
% 3.89/1.12  % SZS status Theorem for theBenchmark.p
% 3.89/1.12  
% 3.89/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.89/1.12  
% 3.89/1.12  
%------------------------------------------------------------------------------