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ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : KRS174+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n005.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 08:47:27 AM UTC 2026

% Result   : Theorem 0.13s 0.42s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(cA_substitution_1,axiom,
    ! [A,B] :
      ( ( cA(A)
        & A = B )
     => cA(B) ),
    file('theBenchmark.p',cA_substitution_1) ).

fof(cA_and_B_substitution_1,axiom,
    ! [A,B] :
      ( ( cA_and_B(A)
        & A = B )
     => cA_and_B(B) ),
    file('theBenchmark.p',cA_and_B_substitution_1) ).

fof(cB_substitution_1,axiom,
    ! [A,B] :
      ( ( cB(A)
        & A = B )
     => cB(B) ),
    file('theBenchmark.p',cB_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(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] :
      ( cA(X)
    <=> X = ia ),
    file('theBenchmark.p',axiom_2) ).

fof(axiom_3,axiom,
    ! [X] :
      ( cA_and_B(X)
    <=> ( X = ia
        | X = ib ) ),
    file('theBenchmark.p',axiom_3) ).

fof(axiom_4,axiom,
    ! [X] :
      ( cB(X)
    <=> X = ib ),
    file('theBenchmark.p',axiom_4) ).

fof(axiom_5,axiom,
    cowlThing(ia),
    file('theBenchmark.p',axiom_5) ).

fof(axiom_6,axiom,
    cowlThing(ib),
    file('theBenchmark.p',axiom_6) ).

fof(the_axiom,conjecture,
    ( ! [X] :
        ( cA_and_B(X)
      <=> ( cA(X)
          | cB(X) ) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( ~ cowlNothing(X)
        & cowlThing(X) ) ),
    file('theBenchmark.p',the_axiom) ).

fof(f_1_1,plain,
    ! [A,B] :
      ( cA(B)
      | ~ cA(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cA_substitution_1]) ).

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

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

fof(f_2_1,plain,
    ! [A,B] :
      ( cA_and_B(B)
      | ~ cA_and_B(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cA_and_B_substitution_1]) ).

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

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

fof(f_3_1,plain,
    ! [A,B] :
      ( cB(B)
      | ~ cB(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cB_substitution_1]) ).

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

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

fof(f_4_1,plain,
    ! [A,B] :
      ( cowlNothing(B)
      | ~ cowlNothing(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cowlNothing_substitution_1]) ).

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

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

fof(f_5_1,plain,
    ! [A,B] :
      ( cowlThing(B)
      | ~ cowlThing(A)
      | A != B ),
    inference(fof_nnf,[status(thm)],[cowlThing_substitution_1]) ).

fof(f_5_2,plain,
    ! [U_9,U_8] :
      ( cowlThing(U_8)
      | ~ cowlThing(U_9)
      | U_9 != U_8 ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( cowlThing(U_8)
    | ~ cowlThing(U_9)
    | U_9 != U_8 ),
    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_11,U_10] :
      ( xsd_integer(U_10)
      | ~ xsd_integer(U_11)
      | U_11 != U_10 ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( xsd_integer(U_10)
    | ~ xsd_integer(U_11)
    | U_11 != U_10 ),
    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_13,U_12] :
      ( xsd_string(U_12)
      | ~ xsd_string(U_13)
      | U_13 != U_12 ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( xsd_string(U_12)
    | ~ xsd_string(U_13)
    | U_13 != U_12 ),
    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_14] :
      ( ~ cowlNothing(U_14)
      & cowlThing(U_14) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ( ! [U_16] : ~ cowlNothing(U_16)
    & ! [U_15] : cowlThing(U_15) ),
    inference(miniscope,[status(thm)],[f_8_2]) ).

cnf(f_8_4,plain,
    cowlThing(U_15),
    inference(clausify,[status(thm)],[f_8_3]) ).

cnf(f_8_5,plain,
    ~ cowlNothing(U_16),
    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_17] :
      ( ( xsd_string(U_17)
        | xsd_integer(U_17) )
      & ( ~ xsd_integer(U_17)
        | ~ xsd_string(U_17) ) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ( ! [U_19] :
        ( xsd_string(U_19)
        | xsd_integer(U_19) )
    & ! [U_18] :
        ( ~ xsd_integer(U_18)
        | ~ xsd_string(U_18) ) ),
    inference(miniscope,[status(thm)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( ~ xsd_integer(U_18)
    | ~ xsd_string(U_18) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

cnf(f_9_5,plain,
    ( xsd_string(U_19)
    | xsd_integer(U_19) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ! [X] :
      ( ( cA(X)
        | X != ia )
      & ( X = ia
        | ~ cA(X) ) ),
    inference(fof_nnf,[status(thm)],[axiom_2]) ).

fof(f_10_2,plain,
    ! [U_20] :
      ( ( cA(U_20)
        | U_20 != ia )
      & ( U_20 = ia
        | ~ cA(U_20) ) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ( ! [U_22] :
        ( cA(U_22)
        | U_22 != ia )
    & ! [U_21] :
        ( U_21 = ia
        | ~ cA(U_21) ) ),
    inference(miniscope,[status(thm)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( U_21 = ia
    | ~ cA(U_21) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

cnf(f_10_5,plain,
    ( cA(U_22)
    | U_22 != ia ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [X] :
      ( ( cA_and_B(X)
        | ( X != ia
          & X != ib ) )
      & ( X = ia
        | X = ib
        | ~ cA_and_B(X) ) ),
    inference(fof_nnf,[status(thm)],[axiom_3]) ).

fof(f_11_2,plain,
    ! [U_23] :
      ( ( cA_and_B(U_23)
        | ( U_23 != ia
          & U_23 != ib ) )
      & ( U_23 = ia
        | U_23 = ib
        | ~ cA_and_B(U_23) ) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ( ! [U_25] :
        ( cA_and_B(U_25)
        | ( U_25 != ia
          & U_25 != ib ) )
    & ! [U_24] :
        ( U_24 = ia
        | U_24 = ib
        | ~ cA_and_B(U_24) ) ),
    inference(miniscope,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( U_24 = ia
    | U_24 = ib
    | ~ cA_and_B(U_24) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_5,plain,
    ( U_25 != ib
    | cA_and_B(U_25) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_6,plain,
    ( U_25 != ia
    | cA_and_B(U_25) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [X] :
      ( ( cB(X)
        | X != ib )
      & ( X = ib
        | ~ cB(X) ) ),
    inference(fof_nnf,[status(thm)],[axiom_4]) ).

fof(f_12_2,plain,
    ! [U_26] :
      ( ( cB(U_26)
        | U_26 != ib )
      & ( U_26 = ib
        | ~ cB(U_26) ) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ( ! [U_28] :
        ( cB(U_28)
        | U_28 != ib )
    & ! [U_27] :
        ( U_27 = ib
        | ~ cB(U_27) ) ),
    inference(miniscope,[status(thm)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( U_27 = ib
    | ~ cB(U_27) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

cnf(f_12_5,plain,
    ( cB(U_28)
    | U_28 != ib ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    cowlThing(ia),
    inference(fof_nnf,[status(thm)],[axiom_5]) ).

cnf(f_13_2,plain,
    cowlThing(ia),
    inference(clausify,[status(thm)],[f_13_1]) ).

fof(f_14_1,plain,
    cowlThing(ib),
    inference(fof_nnf,[status(thm)],[axiom_6]) ).

cnf(f_14_2,plain,
    cowlThing(ib),
    inference(clausify,[status(thm)],[f_14_1]) ).

fof(f_15_1,negated_conjecture,
    ~ ( ! [X] :
          ( cA_and_B(X)
        <=> ( cA(X)
            | cB(X) ) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & ! [X] :
          ( ~ cowlNothing(X)
          & cowlThing(X) ) ),
    inference(negate,[status(cth)],[the_axiom]) ).

fof(f_15_2,negated_conjecture,
    ( ? [X] :
        ( ( ~ cA_and_B(X)
          & ( cA(X)
            | cB(X) ) )
        | ( ~ cA(X)
          & ~ cB(X)
          & cA_and_B(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_15_1]) ).

fof(f_15_3,negated_conjecture,
    ( ? [U_31] :
        ( ( ~ cA_and_B(U_31)
          & ( cA(U_31)
            | cB(U_31) ) )
        | ( ~ cA(U_31)
          & ~ cB(U_31)
          & cA_and_B(U_31) ) )
    | ? [U_30] :
        ( ( ~ xsd_string(U_30)
          & ~ xsd_integer(U_30) )
        | ( xsd_integer(U_30)
          & xsd_string(U_30) ) )
    | ? [U_29] :
        ( cowlNothing(U_29)
        | ~ cowlThing(U_29) ) ),
    inference(variable_rename,[status(thm)],[f_15_2]) ).

fof(f_15_4,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ? [U_36] :
        ( ~ cA(U_36)
        & ~ cB(U_36)
        & cA_and_B(U_36) )
    | ? [U_35] :
        ( ~ xsd_string(U_35)
        & ~ xsd_integer(U_35) )
    | ? [U_34] :
        ( xsd_integer(U_34)
        & xsd_string(U_34) )
    | ? [U_33] : cowlNothing(U_33)
    | ? [U_32] : ~ cowlThing(U_32) ),
    inference(miniscope,[status(thm)],[f_15_3]) ).

fof(f_15_5,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ? [U_36] :
        ( ~ cA(U_36)
        & ~ cB(U_36)
        & cA_and_B(U_36) )
    | ? [U_35] :
        ( ~ xsd_string(U_35)
        & ~ xsd_integer(U_35) )
    | ? [U_34] :
        ( xsd_integer(U_34)
        & xsd_string(U_34) )
    | ? [U_33] : cowlNothing(U_33)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_15_4]) ).

fof(f_15_6,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ? [U_36] :
        ( ~ cA(U_36)
        & ~ cB(U_36)
        & cA_and_B(U_36) )
    | ? [U_35] :
        ( ~ xsd_string(U_35)
        & ~ xsd_integer(U_35) )
    | ? [U_34] :
        ( xsd_integer(U_34)
        & xsd_string(U_34) )
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_33,sK2)],[f_15_5]) ).

fof(f_15_7,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ? [U_36] :
        ( ~ cA(U_36)
        & ~ cB(U_36)
        & cA_and_B(U_36) )
    | ? [U_35] :
        ( ~ xsd_string(U_35)
        & ~ xsd_integer(U_35) )
    | ( xsd_integer(sK3)
      & xsd_string(sK3) )
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3)],[f_15_6]) ).

fof(f_15_8,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ? [U_36] :
        ( ~ cA(U_36)
        & ~ cB(U_36)
        & cA_and_B(U_36) )
    | ( ~ xsd_string(sK4)
      & ~ xsd_integer(sK4) )
    | ( xsd_integer(sK3)
      & xsd_string(sK3) )
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4)],[f_15_7]) ).

fof(f_15_9,negated_conjecture,
    ( ? [U_37] :
        ( ~ cA_and_B(U_37)
        & ( cA(U_37)
          | cB(U_37) ) )
    | ( ~ cA(sK5)
      & ~ cB(sK5)
      & cA_and_B(sK5) )
    | ( ~ xsd_string(sK4)
      & ~ xsd_integer(sK4) )
    | ( xsd_integer(sK3)
      & xsd_string(sK3) )
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5)],[f_15_8]) ).

fof(f_15_10,negated_conjecture,
    ( ( ~ cA_and_B(sK6)
      & ( cA(sK6)
        | cB(sK6) ) )
    | ( ~ cA(sK5)
      & ~ cB(sK5)
      & cA_and_B(sK5) )
    | ( ~ xsd_string(sK4)
      & ~ xsd_integer(sK4) )
    | ( xsd_integer(sK3)
      & xsd_string(sK3) )
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_37,sK6)],[f_15_9]) ).

fof(f_15_11,negated_conjecture,
    ( ( ~ cA_and_B(sK6)
      | ~ sP3 )
    & ( cA(sK6)
      | cB(sK6)
      | ~ sP3 )
    & ( ~ cA(sK5)
      | ~ sP2 )
    & ( ~ cB(sK5)
      | ~ sP2 )
    & ( cA_and_B(sK5)
      | ~ sP2 )
    & ( ~ xsd_string(sK4)
      | ~ sP1 )
    & ( ~ xsd_integer(sK4)
      | ~ sP1 )
    & ( xsd_integer(sK3)
      | ~ sP0 )
    & ( xsd_string(sK3)
      | ~ sP0 )
    & ( sP3
      | sP2
      | sP1
      | sP0
      | cowlNothing(sK2)
      | ~ cowlThing(sK1) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_15_10]) ).

cnf(f_15_12,negated_conjecture,
    ( sP3
    | sP2
    | sP1
    | sP0
    | cowlNothing(sK2)
    | ~ cowlThing(sK1) ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_13,negated_conjecture,
    ( xsd_string(sK3)
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_14,negated_conjecture,
    ( xsd_integer(sK3)
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_15,negated_conjecture,
    ( ~ xsd_integer(sK4)
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_16,negated_conjecture,
    ( ~ xsd_string(sK4)
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_17,negated_conjecture,
    ( cA_and_B(sK5)
    | ~ sP2 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_18,negated_conjecture,
    ( ~ cB(sK5)
    | ~ sP2 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_19,negated_conjecture,
    ( ~ cA(sK5)
    | ~ sP2 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_20,negated_conjecture,
    ( cA(sK6)
    | cB(sK6)
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

cnf(f_15_21,negated_conjecture,
    ( ~ cA_and_B(sK6)
    | ~ sP3 ),
    inference(clausify,[status(thm)],[f_15_11]) ).

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,
    ( cA(Eq_y_0)
    | ~ cA(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

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

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

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

cnf(equality_8,axiom,
    ( cowlThing(Eq_y_0)
    | ~ cowlThing(Eq_x_0)
    | 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(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS174+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36  % Computer : n005.cluster.edu
% 0.11/0.36  % Model    : x86_64 x86_64
% 0.11/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36  % Memory   : 8046.5625MB
% 0.11/0.36  % OS       : Linux 6.8.0-71-generic
% 0.11/0.36  % CPULimit : 300
% 0.11/0.36  % WCLimit  : 300
% 0.11/0.36  % DateTime : Sat Sep 19 12:16:18 UTC 2026
% 0.11/0.36  % CPUTime  : 
% 0.13/0.42  % SZS status Theorem for theBenchmark
% 0.13/0.42  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------