TSTP Solution File: SET943+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET943+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n032.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 14:36:40 EDT 2024

% Result   : Theorem 55.87s 8.17s
% Output   : CNFRefutation 55.87s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

fof(f16,conjecture,
    ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).

fof(f17,negated_conjecture,
    ~ ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    inference(negated_conjecture,[],[f16]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f27,plain,
    ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1)),
    inference(ennf_transformation,[],[f17]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK0(X0,X1,X2),X1)
            & ~ in(sK0(X0,X1,X2),X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( in(sK0(X0,X1,X2),X1)
          | in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f32,f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f35]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f36,f37]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) ) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | ~ in(X2,X1) ) )
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( in(X4,X0)
                  & in(X2,X4) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ? [X7] :
                  ( in(X7,X0)
                  & in(X5,X7) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(rectify,[],[f39]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(X2,X3) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( in(X4,X0)
                & in(X2,X4) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ in(X3,X0)
              | ~ in(sK2(X0,X1),X3) )
          | ~ in(sK2(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK2(X0,X1),X4) )
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK2(X0,X1),X4) )
     => ( in(sK3(X0,X1),X0)
        & in(sK2(X0,X1),sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK4(X0,X5),X0)
        & in(X5,sK4(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK2(X0,X1),X3) )
            | ~ in(sK2(X0,X1),X1) )
          & ( ( in(sK3(X0,X1),X0)
              & in(sK2(X0,X1),sK3(X0,X1)) )
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK4(X0,X5),X0)
                & in(X5,sK4(X0,X5)) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f40,f43,f42,f41]) ).

fof(f49,plain,
    ( ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1))
   => union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f27,f49]) ).

fof(f56,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f57,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f58,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f62,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f65,plain,
    ! [X0,X1,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f66,plain,
    ! [X0,X1,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f67,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(X6,X0)
      | ~ in(X5,X6)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( union(X0) = X1
      | in(sK2(X0,X1),sK3(X0,X1))
      | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( union(X0) = X1
      | in(sK3(X0,X1),X0)
      | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f70,plain,
    ! [X3,X0,X1] :
      ( union(X0) = X1
      | ~ in(X3,X0)
      | ~ in(sK2(X0,X1),X3)
      | ~ in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f80,plain,
    union(set_union2(sK7,sK8)) != set_union2(union(sK7),union(sK8)),
    inference(cnf_transformation,[],[f50]) ).

fof(f83,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f58]) ).

fof(f84,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f57]) ).

fof(f85,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f56]) ).

fof(f86,plain,
    ! [X0,X6,X5] :
      ( in(X5,union(X0))
      | ~ in(X6,X0)
      | ~ in(X5,X6) ),
    inference(equality_resolution,[],[f67]) ).

fof(f87,plain,
    ! [X0,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f66]) ).

fof(f88,plain,
    ! [X0,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f65]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X2,X1)) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_58,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X1,X2)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_59,plain,
    ( ~ in(X0,set_union2(X1,X2))
    | in(X0,X1)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_60,plain,
    ( ~ in(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_61,plain,
    ( in(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_62,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_63,plain,
    ( ~ in(sK2(X0,X1),X1)
    | ~ in(sK2(X0,X1),X2)
    | ~ in(X2,X0)
    | union(X0) = X1 ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_64,plain,
    ( union(X0) = X1
    | in(sK2(X0,X1),X1)
    | in(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_65,plain,
    ( union(X0) = X1
    | in(sK2(X0,X1),sK3(X0,X1))
    | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_66,plain,
    ( ~ in(X0,X1)
    | ~ in(X1,X2)
    | in(X0,union(X2)) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_67,plain,
    ( ~ in(X0,union(X1))
    | in(sK4(X1,X0),X1) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_68,plain,
    ( ~ in(X0,union(X1))
    | in(X0,sK4(X1,X0)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_78,negated_conjecture,
    set_union2(union(sK7),union(sK8)) != union(set_union2(sK7,sK8)),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_573,plain,
    union(sK7) = sP0_iProver_def,
    definition ).

cnf(c_574,plain,
    union(sK8) = sP1_iProver_def,
    definition ).

cnf(c_575,plain,
    set_union2(sP0_iProver_def,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_576,plain,
    set_union2(sK7,sK8) = sP3_iProver_def,
    definition ).

cnf(c_577,plain,
    union(sP3_iProver_def) = sP4_iProver_def,
    definition ).

cnf(c_578,negated_conjecture,
    sP2_iProver_def != sP4_iProver_def,
    inference(demodulation,[status(thm)],[c_78,c_576,c_577,c_574,c_573,c_575]) ).

cnf(c_16379,plain,
    ( ~ in(X0,sK8)
    | in(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_576,c_57]) ).

cnf(c_16380,plain,
    ( ~ in(X0,sP1_iProver_def)
    | in(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_575,c_57]) ).

cnf(c_16505,plain,
    ( ~ in(X0,sK7)
    | in(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_576,c_58]) ).

cnf(c_16506,plain,
    ( ~ in(X0,sP0_iProver_def)
    | in(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_575,c_58]) ).

cnf(c_16582,plain,
    ( ~ in(X0,union(sK8))
    | in(sK4(sK8,X0),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_67,c_16379]) ).

cnf(c_16584,plain,
    ( ~ in(X0,union(sK7))
    | in(sK4(sK7,X0),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_67,c_16505]) ).

cnf(c_16588,plain,
    ( ~ in(X0,sP0_iProver_def)
    | in(sK4(sK7,X0),sP3_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_16584,c_573]) ).

cnf(c_16593,plain,
    ( ~ in(X0,sP1_iProver_def)
    | in(sK4(sK8,X0),sP3_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_16582,c_574]) ).

cnf(c_16734,plain,
    ( ~ subset(sK3(X0,X1),X2)
    | union(X0) = X1
    | in(sK2(X0,X1),X1)
    | in(sK2(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_65,c_62]) ).

cnf(c_16832,plain,
    ( ~ in(X0,sP3_iProver_def)
    | in(X0,sK7)
    | in(X0,sK8) ),
    inference(superposition,[status(thm)],[c_576,c_59]) ).

cnf(c_16833,plain,
    ( ~ in(X0,sP2_iProver_def)
    | in(X0,sP0_iProver_def)
    | in(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_575,c_59]) ).

cnf(c_16854,plain,
    ( ~ in(X0,X1)
    | in(sK1(X0,X2),union(X1))
    | subset(X0,X2) ),
    inference(superposition,[status(thm)],[c_61,c_66]) ).

cnf(c_17163,plain,
    ( ~ in(X0,X1)
    | subset(X0,union(X1)) ),
    inference(superposition,[status(thm)],[c_16854,c_60]) ).

cnf(c_17266,plain,
    ( ~ in(X0,sK7)
    | subset(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_573,c_17163]) ).

cnf(c_17267,plain,
    ( ~ in(X0,sK8)
    | subset(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_574,c_17163]) ).

cnf(c_28254,plain,
    ( union(sP3_iProver_def) = X0
    | in(sK2(sP3_iProver_def,X0),X0)
    | in(sK3(sP3_iProver_def,X0),sK7)
    | in(sK3(sP3_iProver_def,X0),sK8) ),
    inference(superposition,[status(thm)],[c_64,c_16832]) ).

cnf(c_28283,plain,
    ( X0 = sP4_iProver_def
    | in(sK2(sP3_iProver_def,X0),X0)
    | in(sK3(sP3_iProver_def,X0),sK7)
    | in(sK3(sP3_iProver_def,X0),sK8) ),
    inference(light_normalisation,[status(thm)],[c_28254,c_577]) ).

cnf(c_101977,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK8) ),
    inference(superposition,[status(thm)],[c_28283,c_16833]) ).

cnf(c_102101,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_101977,c_578]) ).

cnf(c_103638,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7)
    | subset(sK3(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_102101,c_17267]) ).

cnf(c_104097,plain,
    ( union(sP3_iProver_def) = sP2_iProver_def
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7) ),
    inference(superposition,[status(thm)],[c_103638,c_16734]) ).

cnf(c_104098,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7) ),
    inference(light_normalisation,[status(thm)],[c_104097,c_577]) ).

cnf(c_104099,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_104098,c_578]) ).

cnf(c_104113,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def)
    | in(sK3(sP3_iProver_def,sP2_iProver_def),sK7) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_104099,c_16380,c_16506]) ).

cnf(c_104124,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def)
    | subset(sK3(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_104113,c_17266]) ).

cnf(c_117619,plain,
    ( union(sP3_iProver_def) = sP2_iProver_def
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_104124,c_16734]) ).

cnf(c_117620,plain,
    ( sP2_iProver_def = sP4_iProver_def
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_117619,c_577]) ).

cnf(c_117621,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_117620,c_578]) ).

cnf(c_117639,plain,
    in(sK2(sP3_iProver_def,sP2_iProver_def),sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_117621,c_16506]) ).

cnf(c_117643,plain,
    ( ~ in(sK2(sP3_iProver_def,sP2_iProver_def),X0)
    | ~ in(X0,sP3_iProver_def)
    | union(sP3_iProver_def) = sP2_iProver_def ),
    inference(superposition,[status(thm)],[c_117639,c_63]) ).

cnf(c_117645,plain,
    ( in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def)
    | in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_117639,c_16833]) ).

cnf(c_117656,plain,
    ( ~ in(sK2(sP3_iProver_def,sP2_iProver_def),X0)
    | ~ in(X0,sP3_iProver_def)
    | sP2_iProver_def = sP4_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_117643,c_577]) ).

cnf(c_117657,plain,
    ( ~ in(sK2(sP3_iProver_def,sP2_iProver_def),X0)
    | ~ in(X0,sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_117656,c_578]) ).

cnf(c_117694,plain,
    ( ~ in(sK4(X0,sK2(sP3_iProver_def,sP2_iProver_def)),sP3_iProver_def)
    | ~ in(sK2(sP3_iProver_def,sP2_iProver_def),union(X0)) ),
    inference(superposition,[status(thm)],[c_68,c_117657]) ).

cnf(c_186498,plain,
    ( ~ in(sK2(sP3_iProver_def,sP2_iProver_def),union(sK8))
    | ~ in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_16593,c_117694]) ).

cnf(c_186499,plain,
    ( ~ in(sK2(sP3_iProver_def,sP2_iProver_def),union(sK7))
    | ~ in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_16588,c_117694]) ).

cnf(c_186514,plain,
    ~ in(sK2(sP3_iProver_def,sP2_iProver_def),sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_186499,c_573]) ).

cnf(c_186515,plain,
    ~ in(sK2(sP3_iProver_def,sP2_iProver_def),sP1_iProver_def),
    inference(light_normalisation,[status(thm)],[c_186498,c_574]) ).

cnf(c_186536,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_186514,c_186515,c_117645]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET943+1 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun Jun 23 14:54:24 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.18/0.42  Running first-order theorem proving
% 0.18/0.42  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
% 55.87/8.17  % SZS status Started for theBenchmark.p
% 55.87/8.17  % SZS status Theorem for theBenchmark.p
% 55.87/8.17  
% 55.87/8.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 55.87/8.17  
% 55.87/8.17  ------  iProver source info
% 55.87/8.17  
% 55.87/8.17  git: date: 2024-06-12 09:56:46 +0000
% 55.87/8.17  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 55.87/8.17  git: non_committed_changes: false
% 55.87/8.17  
% 55.87/8.17  ------ Parsing...
% 55.87/8.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 55.87/8.17  
% 55.87/8.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 55.87/8.17  
% 55.87/8.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 55.87/8.17  
% 55.87/8.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 55.87/8.17  ------ Proving...
% 55.87/8.17  ------ Problem Properties 
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  clauses                                 33
% 55.87/8.17  conjectures                             1
% 55.87/8.17  EPR                                     7
% 55.87/8.17  Horn                                    28
% 55.87/8.17  unary                                   12
% 55.87/8.17  binary                                  10
% 55.87/8.17  lits                                    67
% 55.87/8.17  lits eq                                 15
% 55.87/8.17  fd_pure                                 0
% 55.87/8.17  fd_pseudo                               0
% 55.87/8.17  fd_cond                                 0
% 55.87/8.17  fd_pseudo_cond                          7
% 55.87/8.17  AC symbols                              0
% 55.87/8.17  
% 55.87/8.17  ------ Schedule dynamic 5 is on 
% 55.87/8.17  
% 55.87/8.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  ------ 
% 55.87/8.17  Current options:
% 55.87/8.17  ------ 
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  ------ Proving...
% 55.87/8.17  
% 55.87/8.17  
% 55.87/8.17  % SZS status Theorem for theBenchmark.p
% 55.87/8.17  
% 55.87/8.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 55.87/8.17  
% 55.87/8.18  
%------------------------------------------------------------------------------