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ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : KRS142+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n017.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 : Thu Sep 24 08:47:22 AM UTC 2026

% Result   : Theorem 0.14s 0.40s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(cc_substitution_1,axiom,
    ! [A,B] :
      ( ( cc(A)
        & A = B )
     => cc(B) ),
    file('theBenchmark.p',cc_substitution_1) ).

fof(cowlNothing_substitution_1,axiom,
    ! [A,B] :
      ( ( cowlNothing(A)
        & A = B )
     => cowlNothing(B) ),
    file('theBenchmark.p',cowlNothing_substitution_1) ).

fof(cowlThing_substitution_1,axiom,
    ! [A,B] :
      ( ( cowlThing(A)
        & A = B )
     => cowlThing(B) ),
    file('theBenchmark.p',cowlThing_substitution_1) ).

fof(rp_substitution_1,axiom,
    ! [A,B,C] :
      ( ( rp(A,C)
        & A = B )
     => rp(B,C) ),
    file('theBenchmark.p',rp_substitution_1) ).

fof(rp_substitution_2,axiom,
    ! [A,B,C] :
      ( ( rp(C,A)
        & A = B )
     => rp(C,B) ),
    file('theBenchmark.p',rp_substitution_2) ).

fof(xsd_integer_substitution_1,axiom,
    ! [A,B] :
      ( ( xsd_integer(A)
        & A = B )
     => xsd_integer(B) ),
    file('theBenchmark.p',xsd_integer_substitution_1) ).

fof(xsd_string_substitution_1,axiom,
    ! [A,B] :
      ( ( xsd_string(A)
        & A = B )
     => xsd_string(B) ),
    file('theBenchmark.p',xsd_string_substitution_1) ).

fof(axiom_0,axiom,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    file('theBenchmark.p',axiom_0) ).

fof(axiom_1,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ),
    file('theBenchmark.p',axiom_1) ).

fof(axiom_2,axiom,
    ! [X] :
      ( cc(X)
     => ( ! [Y0,Y1] :
            ( ( rp(X,Y1)
              & rp(X,Y0) )
           => Y0 = Y1 )
        & ? [Y0] : rp(X,Y0) ) ),
    file('theBenchmark.p',axiom_2) ).

fof(the_axiom,conjecture,
    ( ! [X] :
        ( cc(X)
       => ! [Y0,Y1] :
            ( ( rp(X,Y1)
              & rp(X,Y0) )
           => Y0 = Y1 ) )
    & ! [X] :
        ( cc(X)
       => ? [Y0] : rp(X,Y0) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( ~ cowlNothing(X)
        & cowlThing(X) ) ),
    file('theBenchmark.p',the_axiom) ).

fof(f_1_1,plain,
    ! [A,B] :
      ( cc(B)
      | ~ cc(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cc_substitution_1]) ).

fof(f_1_2,plain,
    ! [U_1,U_0] :
      ( cc(U_0)
      | ~ cc(U_1)
      | U_1 != U_0 ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

cnf(f_1_3,plain,
    ( cc(U_0)
    | ~ cc(U_1)
    | U_1 != U_0 ),
    inference(clausify,[status(thm)],[f_1_2]) ).

fof(f_2_1,plain,
    ! [A,B] :
      ( cowlNothing(B)
      | ~ cowlNothing(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cowlNothing_substitution_1]) ).

fof(f_2_2,plain,
    ! [U_3,U_2] :
      ( cowlNothing(U_2)
      | ~ cowlNothing(U_3)
      | U_3 != U_2 ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    ( cowlNothing(U_2)
    | ~ cowlNothing(U_3)
    | U_3 != U_2 ),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [A,B] :
      ( cowlThing(B)
      | ~ cowlThing(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cowlThing_substitution_1]) ).

fof(f_3_2,plain,
    ! [U_5,U_4] :
      ( cowlThing(U_4)
      | ~ cowlThing(U_5)
      | U_5 != U_4 ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    ( cowlThing(U_4)
    | ~ cowlThing(U_5)
    | U_5 != U_4 ),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [A,B,C] :
      ( rp(B,C)
      | ~ rp(A,C)
      | A != B ),
    inference(fof_nnf,[status(thm)],[rp_substitution_1]) ).

fof(f_4_2,plain,
    ! [U_8,U_7,U_6] :
      ( rp(U_7,U_6)
      | ~ rp(U_8,U_6)
      | U_8 != U_7 ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( rp(U_7,U_6)
    | ~ rp(U_8,U_6)
    | U_8 != U_7 ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    ! [A,B,C] :
      ( rp(C,B)
      | ~ rp(C,A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[rp_substitution_2]) ).

fof(f_5_2,plain,
    ! [U_11,U_10,U_9] :
      ( rp(U_9,U_10)
      | ~ rp(U_9,U_11)
      | U_11 != U_10 ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( rp(U_9,U_10)
    | ~ rp(U_9,U_11)
    | U_11 != U_10 ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [A,B] :
      ( xsd_integer(B)
      | ~ xsd_integer(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[xsd_integer_substitution_1]) ).

fof(f_6_2,plain,
    ! [U_13,U_12] :
      ( xsd_integer(U_12)
      | ~ xsd_integer(U_13)
      | U_13 != U_12 ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( xsd_integer(U_12)
    | ~ xsd_integer(U_13)
    | U_13 != U_12 ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [A,B] :
      ( xsd_string(B)
      | ~ xsd_string(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[xsd_string_substitution_1]) ).

fof(f_7_2,plain,
    ! [U_15,U_14] :
      ( xsd_string(U_14)
      | ~ xsd_string(U_15)
      | U_15 != U_14 ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( xsd_string(U_14)
    | ~ xsd_string(U_15)
    | U_15 != U_14 ),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    inference(fof_nnf,[status(thm)],[axiom_0]) ).

fof(f_8_2,plain,
    ! [U_16] :
      ( ~ cowlNothing(U_16)
      & cowlThing(U_16) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ( ! [U_18] : ~ cowlNothing(U_18)
    & ! [U_17] : cowlThing(U_17) ),
    inference(miniscope,[status(thm)],[f_8_2]) ).

cnf(f_8_4,plain,
    cowlThing(U_17),
    inference(clausify,[status(thm)],[f_8_3]) ).

cnf(f_8_5,plain,
    ~ cowlNothing(U_18),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ! [X] :
      ( ( xsd_string(X)
        | xsd_integer(X) )
      & ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(fof_nnf,[status(thm)],[axiom_1]) ).

fof(f_9_2,plain,
    ! [U_19] :
      ( ( xsd_string(U_19)
        | xsd_integer(U_19) )
      & ( ~ xsd_integer(U_19)
        | ~ xsd_string(U_19) ) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ( ! [U_21] :
        ( xsd_string(U_21)
        | xsd_integer(U_21) )
    & ! [U_20] :
        ( ~ xsd_integer(U_20)
        | ~ xsd_string(U_20) ) ),
    inference(miniscope,[status(thm)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( ~ xsd_integer(U_20)
    | ~ xsd_string(U_20) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

cnf(f_9_5,plain,
    ( xsd_string(U_21)
    | xsd_integer(U_21) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ! [X] :
      ( ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & ? [Y0] : rp(X,Y0) )
      | ~ cc(X) ),
    inference(fof_nnf,[status(thm)],[axiom_2]) ).

fof(f_10_2,plain,
    ! [U_25] :
      ( ( ! [U_24,U_23] :
            ( U_24 = U_23
            | ~ rp(U_25,U_23)
            | ~ rp(U_25,U_24) )
        & ? [U_22] : rp(U_25,U_22) )
      | ~ cc(U_25) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_25] :
      ( ( ! [U_24,U_23] :
            ( U_24 = U_23
            | ~ rp(U_25,U_23)
            | ~ rp(U_25,U_24) )
        & rp(U_25,sK1(U_25)) )
      | ~ cc(U_25) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_22,sK1(U_25))],[f_10_2]) ).

cnf(f_10_4,plain,
    ( rp(U_25,sK1(U_25))
    | ~ cc(U_25) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

cnf(f_10_5,plain,
    ( U_24 = U_23
    | ~ rp(U_25,U_23)
    | ~ rp(U_25,U_24)
    | ~ cc(U_25) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,negated_conjecture,
    ~ ( ! [X] :
          ( cc(X)
         => ! [Y0,Y1] :
              ( ( rp(X,Y1)
                & rp(X,Y0) )
             => Y0 = Y1 ) )
      & ! [X] :
          ( cc(X)
         => ? [Y0] : rp(X,Y0) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & ! [X] :
          ( ~ cowlNothing(X)
          & cowlThing(X) ) ),
    inference(negate,[status(cth)],[the_axiom]) ).

fof(f_11_2,negated_conjecture,
    ( ? [X] :
        ( ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) )
        & cc(X) )
    | ? [X] :
        ( ! [Y0] : ~ rp(X,Y0)
        & cc(X) )
    | ? [X] :
        ( ( ~ xsd_string(X)
          & ~ xsd_integer(X) )
        | ( xsd_integer(X)
          & xsd_string(X) ) )
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(fof_nnf,[status(thm)],[f_11_1]) ).

fof(f_11_3,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ? [U_27] :
        ( ( ~ xsd_string(U_27)
          & ~ xsd_integer(U_27) )
        | ( xsd_integer(U_27)
          & xsd_string(U_27) ) )
    | ? [U_26] :
        ( cowlNothing(U_26)
        | ~ cowlThing(U_26) ) ),
    inference(variable_rename,[status(thm)],[f_11_2]) ).

fof(f_11_4,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ? [U_36] :
        ( ~ xsd_string(U_36)
        & ~ xsd_integer(U_36) )
    | ? [U_35] :
        ( xsd_integer(U_35)
        & xsd_string(U_35) )
    | ? [U_34] : cowlNothing(U_34)
    | ? [U_33] : ~ cowlThing(U_33) ),
    inference(miniscope,[status(thm)],[f_11_3]) ).

fof(f_11_5,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ? [U_36] :
        ( ~ xsd_string(U_36)
        & ~ xsd_integer(U_36) )
    | ? [U_35] :
        ( xsd_integer(U_35)
        & xsd_string(U_35) )
    | ? [U_34] : cowlNothing(U_34)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_33,sK2)],[f_11_4]) ).

fof(f_11_6,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ? [U_36] :
        ( ~ xsd_string(U_36)
        & ~ xsd_integer(U_36) )
    | ? [U_35] :
        ( xsd_integer(U_35)
        & xsd_string(U_35) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3)],[f_11_5]) ).

fof(f_11_7,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ? [U_36] :
        ( ~ xsd_string(U_36)
        & ~ xsd_integer(U_36) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4)],[f_11_6]) ).

fof(f_11_8,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ? [U_29] :
        ( ! [U_28] : ~ rp(U_29,U_28)
        & cc(U_29) )
    | ( ~ xsd_string(sK5)
      & ~ xsd_integer(sK5) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5)],[f_11_7]) ).

fof(f_11_9,negated_conjecture,
    ( ? [U_32] :
        ( ? [U_31,U_30] :
            ( U_31 != U_30
            & rp(U_32,U_30)
            & rp(U_32,U_31) )
        & cc(U_32) )
    | ( ! [U_28] : ~ rp(sK6,U_28)
      & cc(sK6) )
    | ( ~ xsd_string(sK5)
      & ~ xsd_integer(sK5) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6)],[f_11_8]) ).

fof(f_11_10,negated_conjecture,
    ( ( ? [U_31,U_30] :
          ( U_31 != U_30
          & rp(sK7,U_30)
          & rp(sK7,U_31) )
      & cc(sK7) )
    | ( ! [U_28] : ~ rp(sK6,U_28)
      & cc(sK6) )
    | ( ~ xsd_string(sK5)
      & ~ xsd_integer(sK5) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_32,sK7)],[f_11_9]) ).

fof(f_11_11,negated_conjecture,
    ( ( ? [U_30] :
          ( sK8 != U_30
          & rp(sK7,U_30)
          & rp(sK7,sK8) )
      & cc(sK7) )
    | ( ! [U_28] : ~ rp(sK6,U_28)
      & cc(sK6) )
    | ( ~ xsd_string(sK5)
      & ~ xsd_integer(sK5) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_31,sK8)],[f_11_10]) ).

fof(f_11_12,negated_conjecture,
    ( ( sK8 != sK9
      & rp(sK7,sK9)
      & rp(sK7,sK8)
      & cc(sK7) )
    | ( ! [U_28] : ~ rp(sK6,U_28)
      & cc(sK6) )
    | ( ~ xsd_string(sK5)
      & ~ xsd_integer(sK5) )
    | ( xsd_integer(sK4)
      & xsd_string(sK4) )
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_30,sK9)],[f_11_11]) ).

fof(f_11_13,negated_conjecture,
    ( ( sK8 != sK9
      | ~ sP3 )
    & ( rp(sK7,sK9)
      | ~ sP3 )
    & ( rp(sK7,sK8)
      | ~ sP3 )
    & ( cc(sK7)
      | ~ sP3 )
    & ! [U_28] :
        ( ~ rp(sK6,U_28)
        | ~ sP2(U_28) )
    & ! [U_28] :
        ( cc(sK6)
        | ~ sP2(U_28) )
    & ( ~ xsd_string(sK5)
      | ~ sP1 )
    & ( ~ xsd_integer(sK5)
      | ~ sP1 )
    & ( xsd_integer(sK4)
      | ~ sP0 )
    & ( xsd_string(sK4)
      | ~ sP0 )
    & ! [U_28] :
        ( sP3
        | sP2(U_28)
        | sP1
        | sP0
        | cowlNothing(sK3)
        | ~ cowlThing(sK2) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_11_12]) ).

cnf(f_11_14,negated_conjecture,
    ( sP3
    | sP2(U_28)
    | sP1
    | sP0
    | cowlNothing(sK3)
    | ~ cowlThing(sK2) ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_15,negated_conjecture,
    ( xsd_string(sK4)
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_16,negated_conjecture,
    ( xsd_integer(sK4)
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_17,negated_conjecture,
    ( ~ xsd_integer(sK5)
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_18,negated_conjecture,
    ( ~ xsd_string(sK5)
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_19,negated_conjecture,
    ( cc(sK6)
    | ~ sP2(U_28) ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_20,negated_conjecture,
    ( ~ rp(sK6,U_28)
    | ~ sP2(U_28) ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_21,negated_conjecture,
    ( cc(sK7)
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_22,negated_conjecture,
    ( rp(sK7,sK8)
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_23,negated_conjecture,
    ( rp(sK7,sK9)
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(f_11_24,negated_conjecture,
    ( sK8 != sK9
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_11_13]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( sK1(Eq_x_0) = sK1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( cc(Eq_y_0)
    | ~ cc(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_6,axiom,
    ( cowlNothing(Eq_y_0)
    | ~ cowlNothing(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_7,axiom,
    ( cowlThing(Eq_y_0)
    | ~ cowlThing(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_8,axiom,
    ( rp(Eq_y_0,Eq_y_1)
    | ~ rp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_9,axiom,
    ( xsd_integer(Eq_y_0)
    | ~ xsd_integer(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_10,axiom,
    ( xsd_string(Eq_y_0)
    | ~ xsd_string(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_11,axiom,
    ( sP2(Eq_y_0)
    | ~ sP2(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS142+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n017.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Sat Sep 19 12:11:26 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------