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FindProof---0.1.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 01:53:05 PM UTC 2026

% Result   : Unsatisfiable 7.90s 1.61s
% Output   : Proof 7.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  103 (  41 unt;   0 def)
%            Number of atoms       :  302 (  36 equ)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives :  316 ( 117   ~; 107   |;  70   &)
%                                         (  12 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   23 (  21 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   3 con; 0-4 aty)
%            Number of variables   :  157 (   3 sgn  83   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
     => ? [Y] :
          ( ca_Ax2(Y)
          & rs(X,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f3_nnf,plain,
    ! [X] :
      ( ? [Y] :
          ( ca_Ax2(Y)
          & rs(X,Y) )
      | ~ cUnsatisfiable(X) ),
    inference(nnf_transformation,[status(thm)],[f3]) ).

fof(f3_sk,plain,
    ! [X] :
      ( ( ca_Ax2(sk0(X))
        & rs(X,sk0(X)) )
      | ~ cUnsatisfiable(X) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).

cnf(c5,plain,
    ( rs(X0,sk0(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[status(esa)],[f3_sk]) ).

cnf(hi2,axiom,
    ifeq(cUnsatisfiable(X0),true,rs(X0,sk0(X0)),true) = true,
    inference(equality_encoding,[status(esa)],[c5]) ).

fof(f17,axiom,
    cUnsatisfiable(i2003_11_14_17_21_33997),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).

fof(f17_nnf,plain,
    cUnsatisfiable(i2003_11_14_17_21_33997),
    inference(nnf_transformation,[status(thm)],[f17]) ).

cnf(c60,plain,
    cUnsatisfiable(i2003_11_14_17_21_33997),
    inference(cnf_transformation,[status(esa)],[f17_nnf]) ).

cnf(hi57,axiom,
    cUnsatisfiable(i2003_11_14_17_21_33997) = true,
    inference(equality_encoding,[status(esa)],[c60]) ).

cnf(h1,plain,
    rs(i2003_11_14_17_21_33997,sk0(i2003_11_14_17_21_33997)) = true,
    inference(hyper_resolution,[status(thm)],[hi2,hi57]) ).

fof(f15,axiom,
    ! [X,Y] :
      ( rinvS(X,Y)
    <=> rs(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).

fof(f15_nnf,plain,
    ! [X,Y] :
      ( ( ~ rs(Y,X)
        | rinvS(X,Y) )
      & ( rs(Y,X)
        | ~ rinvS(X,Y) ) ),
    inference(nnf_transformation,[status(thm)],[f15]) ).

fof(f15_sk,plain,
    ! [X,Y] :
      ( ( ~ rs(Y,X)
        | rinvS(X,Y) )
      & ( rs(Y,X)
        | ~ rinvS(X,Y) ) ),
    inference(skolemisation,[status(esa)],[f15_nnf]) ).

cnf(c58,plain,
    ( ~ rs(X1,X0)
    | rinvS(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f15_sk]) ).

cnf(hi55,axiom,
    ifeq(rs(X0,X1),true,rinvS(X1,X0),true) = true,
    inference(equality_encoding,[status(esa)],[c58]) ).

cnf(h5,plain,
    rinvS(sk0(i2003_11_14_17_21_33997),i2003_11_14_17_21_33997) = true,
    inference(hyper_resolution,[status(thm)],[hi55,h1]) ).

cnf(c6,plain,
    ( ca_Ax2(sk0(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[status(esa)],[f3_sk]) ).

cnf(hi3,axiom,
    ifeq(cUnsatisfiable(X0),true,ca_Ax2(sk0(X0)),true) = true,
    inference(equality_encoding,[status(esa)],[c6]) ).

cnf(h0,plain,
    ca_Ax2(sk0(i2003_11_14_17_21_33997)) = true,
    inference(hyper_resolution,[status(thm)],[hi3,hi57]) ).

fof(f7,axiom,
    ! [X] :
      ( ca_Ax2(X)
    <=> ( ! [Y] :
            ( rp(X,Y)
           => ca_Vx4(Y) )
        & ? [Y] :
            ( cowlThing(Y)
            & rp(X,Y) )
        & ? [Y] :
            ( cowlThing(Y)
            & rr(X,Y) )
        & ! [Y] :
            ( rr(X,Y)
           => cc(Y) )
        & ! [Y] :
            ( rp(X,Y)
           => ca_Vx5(Y) )
        & ! [Y] :
            ( rp(X,Y)
           => ca_Vx3(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

fof(f7_nnf,plain,
    ! [X] :
      ( ( ? [Y] :
            ( ~ ca_Vx4(Y)
            & rp(X,Y) )
        | ! [Y] :
            ( ~ cowlThing(Y)
            | ~ rp(X,Y) )
        | ! [Y] :
            ( ~ cowlThing(Y)
            | ~ rr(X,Y) )
        | ? [Y] :
            ( ~ cc(Y)
            & rr(X,Y) )
        | ? [Y] :
            ( ~ ca_Vx5(Y)
            & rp(X,Y) )
        | ? [Y] :
            ( ~ ca_Vx3(Y)
            & rp(X,Y) )
        | ca_Ax2(X) )
      & ( ( ! [Y] :
              ( ca_Vx4(Y)
              | ~ rp(X,Y) )
          & ? [Y] :
              ( cowlThing(Y)
              & rp(X,Y) )
          & ? [Y] :
              ( cowlThing(Y)
              & rr(X,Y) )
          & ! [Y] :
              ( cc(Y)
              | ~ rr(X,Y) )
          & ! [Y] :
              ( ca_Vx5(Y)
              | ~ rp(X,Y) )
          & ! [Y] :
              ( ca_Vx3(Y)
              | ~ rp(X,Y) ) )
        | ~ ca_Ax2(X) ) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [X,Y] :
      ( ( ( ~ ca_Vx4(sk9(X))
          & rp(X,sk9(X)) )
        | ~ cowlThing(Y)
        | ~ rp(X,Y)
        | ~ cowlThing(Y)
        | ~ rr(X,Y)
        | ( ~ cc(sk8(X))
          & rr(X,sk8(X)) )
        | ( ~ ca_Vx5(sk7(X))
          & rp(X,sk7(X)) )
        | ( ~ ca_Vx3(sk6(X))
          & rp(X,sk6(X)) )
        | ca_Ax2(X) )
      & ( ( ( ca_Vx4(Y)
            | ~ rp(X,Y) )
          & cowlThing(sk5(X))
          & rp(X,sk5(X))
          & cowlThing(sk4(X))
          & rr(X,sk4(X))
          & ( cc(Y)
            | ~ rr(X,Y) )
          & ( ca_Vx5(Y)
            | ~ rp(X,Y) )
          & ( ca_Vx3(Y)
            | ~ rp(X,Y) ) )
        | ~ ca_Ax2(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7,sk8,sk9])],[f7_nnf]) ).

cnf(c19,plain,
    ( rp(X0,sk5(X0))
    | ~ ca_Ax2(X0) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(hi16,axiom,
    ifeq(ca_Ax2(X0),true,rp(X0,sk5(X0)),true) = true,
    inference(equality_encoding,[status(esa)],[c19]) ).

cnf(h3,plain,
    rp(sk0(i2003_11_14_17_21_33997),sk5(sk0(i2003_11_14_17_21_33997))) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h0]) ).

fof(f13,axiom,
    ! [X,Y] :
      ( rinvP(X,Y)
    <=> rp(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).

fof(f13_nnf,plain,
    ! [X,Y] :
      ( ( ~ rp(Y,X)
        | rinvP(X,Y) )
      & ( rp(Y,X)
        | ~ rinvP(X,Y) ) ),
    inference(nnf_transformation,[status(thm)],[f13]) ).

fof(f13_sk,plain,
    ! [X,Y] :
      ( ( ~ rp(Y,X)
        | rinvP(X,Y) )
      & ( rp(Y,X)
        | ~ rinvP(X,Y) ) ),
    inference(skolemisation,[status(esa)],[f13_nnf]) ).

cnf(c54,plain,
    ( ~ rp(X1,X0)
    | rinvP(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f13_sk]) ).

cnf(hi51,axiom,
    ifeq(rp(X0,X1),true,rinvP(X1,X0),true) = true,
    inference(equality_encoding,[status(esa)],[c54]) ).

cnf(h6,plain,
    rinvP(sk5(sk0(i2003_11_14_17_21_33997)),sk0(i2003_11_14_17_21_33997)) = true,
    inference(hyper_resolution,[status(thm)],[hi51,h3]) ).

cnf(c14,plain,
    ( ca_Vx3(X1)
    | ~ rp(X0,X1)
    | ~ ca_Ax2(X0) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(hi10,axiom,
    ifeq(ca_Ax2(X0),true,ifeq(rp(X0,X1),true,ca_Vx3(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c14]) ).

cnf(h9,plain,
    ca_Vx3(sk5(sk0(i2003_11_14_17_21_33997))) = true,
    inference(hyper_resolution,[status(thm)],[hi10,h0,h3]) ).

fof(f8,axiom,
    ! [X] :
      ( ca_Vx3(X)
    <=> ? [Y] :
          ( cowlThing(Y)
          & rr(X,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f8_nnf,plain,
    ! [X] :
      ( ( ! [Y] :
            ( ~ cowlThing(Y)
            | ~ rr(X,Y) )
        | ca_Vx3(X) )
      & ( ? [Y] :
            ( cowlThing(Y)
            & rr(X,Y) )
        | ~ ca_Vx3(X) ) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [X,Y] :
      ( ( ~ cowlThing(Y)
        | ~ rr(X,Y)
        | ca_Vx3(X) )
      & ( ( cowlThing(sk10(X))
          & rr(X,sk10(X)) )
        | ~ ca_Vx3(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f8_nnf]) ).

cnf(c38,plain,
    ( rr(X0,sk10(X0))
    | ~ ca_Vx3(X0) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(hi35,axiom,
    ifeq(ca_Vx3(X0),true,rr(X0,sk10(X0)),true) = true,
    inference(equality_encoding,[status(esa)],[c38]) ).

cnf(h11,plain,
    rr(sk5(sk0(i2003_11_14_17_21_33997)),sk10(sk5(sk0(i2003_11_14_17_21_33997)))) = true,
    inference(hyper_resolution,[status(thm)],[hi35,h9]) ).

fof(f14,axiom,
    ! [X,Y] :
      ( rinvR(X,Y)
    <=> rr(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).

fof(f14_nnf,plain,
    ! [X,Y] :
      ( ( ~ rr(Y,X)
        | rinvR(X,Y) )
      & ( rr(Y,X)
        | ~ rinvR(X,Y) ) ),
    inference(nnf_transformation,[status(thm)],[f14]) ).

fof(f14_sk,plain,
    ! [X,Y] :
      ( ( ~ rr(Y,X)
        | rinvR(X,Y) )
      & ( rr(Y,X)
        | ~ rinvR(X,Y) ) ),
    inference(skolemisation,[status(esa)],[f14_nnf]) ).

cnf(c56,plain,
    ( ~ rr(X1,X0)
    | rinvR(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f14_sk]) ).

cnf(hi53,axiom,
    ifeq(rr(X0,X1),true,rinvR(X1,X0),true) = true,
    inference(equality_encoding,[status(esa)],[c56]) ).

cnf(h23,plain,
    rinvR(sk10(sk5(sk0(i2003_11_14_17_21_33997))),sk5(sk0(i2003_11_14_17_21_33997))) = true,
    inference(hyper_resolution,[status(thm)],[hi53,h11]) ).

cnf(c15,plain,
    ( ca_Vx5(X1)
    | ~ rp(X0,X1)
    | ~ ca_Ax2(X0) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(hi11,axiom,
    ifeq(ca_Ax2(X0),true,ifeq(rp(X0,X1),true,ca_Vx5(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c15]) ).

cnf(h8,plain,
    ca_Vx5(sk5(sk0(i2003_11_14_17_21_33997))) = true,
    inference(hyper_resolution,[status(thm)],[hi11,h0,h3]) ).

fof(f10,axiom,
    ! [X] :
      ( ca_Vx5(X)
    <=> ! [Y] :
          ( rr(X,Y)
         => cc(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

fof(f10_nnf,plain,
    ! [X] :
      ( ( ? [Y] :
            ( ~ cc(Y)
            & rr(X,Y) )
        | ca_Vx5(X) )
      & ( ! [Y] :
            ( cc(Y)
            | ~ rr(X,Y) )
        | ~ ca_Vx5(X) ) ),
    inference(nnf_transformation,[status(thm)],[f10]) ).

fof(f10_sk,plain,
    ! [X,Y] :
      ( ( ( ~ cc(sk12(X))
          & rr(X,sk12(X)) )
        | ca_Vx5(X) )
      & ( cc(Y)
        | ~ rr(X,Y)
        | ~ ca_Vx5(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f10_nnf]) ).

cnf(c44,plain,
    ( cc(X1)
    | ~ rr(X0,X1)
    | ~ ca_Vx5(X0) ),
    inference(cnf_transformation,[status(esa)],[f10_sk]) ).

cnf(hi41,axiom,
    ifeq(ca_Vx5(X0),true,ifeq(rr(X0,X1),true,cc(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c44]) ).

cnf(h24,plain,
    cc(sk10(sk5(sk0(i2003_11_14_17_21_33997)))) = true,
    inference(hyper_resolution,[status(thm)],[hi41,h8,h11]) ).

fof(f6,axiom,
    ! [X] :
      ( cc(X)
    <=> ! [Y] :
          ( rinvR(X,Y)
         => ca_Vx7(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f6_nnf,plain,
    ! [X] :
      ( ( ? [Y] :
            ( ~ ca_Vx7(Y)
            & rinvR(X,Y) )
        | cc(X) )
      & ( ! [Y] :
            ( ca_Vx7(Y)
            | ~ rinvR(X,Y) )
        | ~ cc(X) ) ),
    inference(nnf_transformation,[status(thm)],[f6]) ).

fof(f6_sk,plain,
    ! [X,Y] :
      ( ( ( ~ ca_Vx7(sk3(X))
          & rinvR(X,sk3(X)) )
        | cc(X) )
      & ( ca_Vx7(Y)
        | ~ rinvR(X,Y)
        | ~ cc(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f6_nnf]) ).

cnf(c11,plain,
    ( ca_Vx7(X1)
    | ~ rinvR(X0,X1)
    | ~ cc(X0) ),
    inference(cnf_transformation,[status(esa)],[f6_sk]) ).

cnf(hi7,axiom,
    ifeq(cc(X0),true,ifeq(rinvR(X0,X1),true,ca_Vx7(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c11]) ).

cnf(h25,plain,
    ca_Vx7(sk5(sk0(i2003_11_14_17_21_33997))) = true,
    inference(hyper_resolution,[status(thm)],[hi7,h24,h23]) ).

fof(f12,axiom,
    ! [X] :
      ( ca_Vx7(X)
    <=> ! [Y] :
          ( rinvP(X,Y)
         => ca_Vx6(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).

fof(f12_nnf,plain,
    ! [X] :
      ( ( ? [Y] :
            ( ~ ca_Vx6(Y)
            & rinvP(X,Y) )
        | ca_Vx7(X) )
      & ( ! [Y] :
            ( ca_Vx6(Y)
            | ~ rinvP(X,Y) )
        | ~ ca_Vx7(X) ) ),
    inference(nnf_transformation,[status(thm)],[f12]) ).

fof(f12_sk,plain,
    ! [X,Y] :
      ( ( ( ~ ca_Vx6(sk14(X))
          & rinvP(X,sk14(X)) )
        | ca_Vx7(X) )
      & ( ca_Vx6(Y)
        | ~ rinvP(X,Y)
        | ~ ca_Vx7(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk14])],[f12_nnf]) ).

cnf(c50,plain,
    ( ca_Vx6(X1)
    | ~ rinvP(X0,X1)
    | ~ ca_Vx7(X0) ),
    inference(cnf_transformation,[status(esa)],[f12_sk]) ).

cnf(hi47,axiom,
    ifeq(ca_Vx7(X0),true,ifeq(rinvP(X0,X1),true,ca_Vx6(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c50]) ).

cnf(h26,plain,
    ca_Vx6(sk0(i2003_11_14_17_21_33997)) = true,
    inference(hyper_resolution,[status(thm)],[hi47,h25,h6]) ).

fof(f11,axiom,
    ! [X] :
      ( ca_Vx6(X)
    <=> ! [Y] :
          ( rinvS(X,Y)
         => caxcomp(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

fof(f11_nnf,plain,
    ! [X] :
      ( ( ? [Y] :
            ( ~ caxcomp(Y)
            & rinvS(X,Y) )
        | ca_Vx6(X) )
      & ( ! [Y] :
            ( caxcomp(Y)
            | ~ rinvS(X,Y) )
        | ~ ca_Vx6(X) ) ),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ! [X,Y] :
      ( ( ( ~ caxcomp(sk13(X))
          & rinvS(X,sk13(X)) )
        | ca_Vx6(X) )
      & ( caxcomp(Y)
        | ~ rinvS(X,Y)
        | ~ ca_Vx6(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f11_nnf]) ).

cnf(c47,plain,
    ( caxcomp(X1)
    | ~ rinvS(X0,X1)
    | ~ ca_Vx6(X0) ),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(hi44,axiom,
    ifeq(ca_Vx6(X0),true,ifeq(rinvS(X0,X1),true,caxcomp(X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c47]) ).

cnf(h27,plain,
    caxcomp(i2003_11_14_17_21_33997) = true,
    inference(hyper_resolution,[status(thm)],[hi44,h26,h5]) ).

fof(f5,axiom,
    ! [X] :
      ( caxcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f5_nnf,plain,
    ! [X] :
      ( ( ! [Y0] : ~ ra_Px1(X,Y0)
        | caxcomp(X) )
      & ( ? [Y0] : ra_Px1(X,Y0)
        | ~ caxcomp(X) ) ),
    inference(nnf_transformation,[status(thm)],[f5]) ).

fof(f5_sk,plain,
    ! [X,Y0] :
      ( ( ~ ra_Px1(X,Y0)
        | caxcomp(X) )
      & ( ra_Px1(X,sk2(X))
        | ~ caxcomp(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).

cnf(c9,plain,
    ( ra_Px1(X0,sk2(X0))
    | ~ caxcomp(X0) ),
    inference(cnf_transformation,[status(esa)],[f5_sk]) ).

cnf(hi5,axiom,
    ifeq(caxcomp(X0),true,ra_Px1(X0,sk2(X0)),true) = true,
    inference(equality_encoding,[status(esa)],[c9]) ).

cnf(h28,plain,
    ra_Px1(i2003_11_14_17_21_33997,sk2(i2003_11_14_17_21_33997)) = true,
    inference(hyper_resolution,[status(thm)],[hi5,h27]) ).

fof(f2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
     => ca(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f2_nnf,plain,
    ! [X] :
      ( ca(X)
      | ~ cUnsatisfiable(X) ),
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ! [X] :
      ( ca(X)
      | ~ cUnsatisfiable(X) ),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c4,plain,
    ( ca(X0)
    | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(hi1,axiom,
    ifeq(cUnsatisfiable(X0),true,ca(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c4]) ).

cnf(h2,plain,
    ca(i2003_11_14_17_21_33997) = true,
    inference(hyper_resolution,[status(thm)],[hi1,hi57]) ).

fof(f4,axiom,
    ! [X] :
      ( ca(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f4_nnf,plain,
    ! [X] :
      ( ( ? [Y] : ra_Px1(X,Y)
        | ca(X) )
      & ( ! [Y] : ~ ra_Px1(X,Y)
        | ~ ca(X) ) ),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [X,Y] :
      ( ( ra_Px1(X,sk1(X))
        | ca(X) )
      & ( ~ ra_Px1(X,Y)
        | ~ ca(X) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).

cnf(c7,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ ca(X0) ),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(hi61,axiom,
    ifeq(ca(X0),true,ifeq(ra_Px1(X0,X1),true,false,true),true) = true,
    inference(equality_encoding,[status(esa)],[c7]) ).

cnf(t0,plain,
    true = false,
    inference(hyper_resolution,[status(thm)],[hi61,h2,h28]) ).

cnf(t348,plain,
    false = true,
    inference(orient,[status(thm)],[t0]) ).

fof(f0,axiom,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

fof(f0_nnf,plain,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    inference(skolemisation,[status(esa)],[f0_nnf]) ).

cnf(c1,plain,
    ~ cowlNothing(X0),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

fof(f1,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f1_nnf,plain,
    ! [X] :
      ( ( xsd_integer(X)
        | xsd_string(X) )
      & ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [X] :
      ( ( xsd_integer(X)
        | xsd_string(X) )
      & ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(skolemisation,[status(esa)],[f1_nnf]) ).

cnf(c2,plain,
    ( ~ xsd_integer(X0)
    | ~ xsd_string(X0) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(goal_0,negated_conjecture,
    true != false,
    inference(equality_encoding,[status(esa)],[c1,c2,c7]) ).

cnf(g0_0,plain,
    true != true,
    inference(rw,[status(thm)],[goal_0,t348]) ).

cnf(contradiction_0,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS116+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37  % Computer : n006.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Wed Sep 23 19:25:41 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.90/1.61  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.90/1.61  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------