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ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n001.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 08:58:07 AM UTC 2026

% Result   : Theorem 2.44s 7.78s
% Output   : Proof 2.54s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('theBenchmark.p',antisymmetry_r2_hidden) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('theBenchmark.p',commutativity_k3_xboole_0) ).

fof(d3_tarski,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('theBenchmark.p',d3_tarski) ).

fof(d3_xboole_0,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,B)
            & in(D,A) ) ) ),
    file('theBenchmark.p',d3_xboole_0) ).

fof(dt_k1_xboole_0,axiom,
    $true,
    file('theBenchmark.p',dt_k1_xboole_0) ).

fof(dt_k3_xboole_0,axiom,
    $true,
    file('theBenchmark.p',dt_k3_xboole_0) ).

fof(fc1_xboole_0,axiom,
    empty(empty_set),
    file('theBenchmark.p',fc1_xboole_0) ).

fof(idempotence_k3_xboole_0,axiom,
    ! [A,B] : set_intersection2(A,A) = A,
    file('theBenchmark.p',idempotence_k3_xboole_0) ).

fof(rc1_xboole_0,axiom,
    ? [A] : empty(A),
    file('theBenchmark.p',rc1_xboole_0) ).

fof(rc2_xboole_0,axiom,
    ? [A] : ~ empty(A),
    file('theBenchmark.p',rc2_xboole_0) ).

fof(reflexivity_r1_tarski,axiom,
    ! [A,B] : subset(A,A),
    file('theBenchmark.p',reflexivity_r1_tarski) ).

fof(t26_xboole_1,conjecture,
    ! [A,B,C] :
      ( subset(A,B)
     => subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    file('theBenchmark.p',t26_xboole_1) ).

fof(t2_boole,axiom,
    ! [A] : set_intersection2(A,empty_set) = empty_set,
    file('theBenchmark.p',t2_boole) ).

fof(t6_boole,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ),
    file('theBenchmark.p',t6_boole) ).

fof(t7_boole,axiom,
    ! [A,B] :
      ~ ( empty(B)
        & in(A,B) ),
    file('theBenchmark.p',t7_boole) ).

fof(t8_boole,axiom,
    ! [A,B] :
      ~ ( empty(B)
        & A != B
        & empty(A) ),
    file('theBenchmark.p',t8_boole) ).

fof(f_1_1,plain,
    ! [A,B] :
      ( ~ in(B,A)
      | ~ in(A,B) ),
    inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).

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

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

fof(f_2_1,plain,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(f_2_2,plain,
    ! [U_3,U_2] : set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [A,B] :
      ( ( subset(A,B)
        | ? [C] :
            ( ~ in(C,B)
            & in(C,A) ) )
      & ( ! [C] :
            ( in(C,B)
            | ~ in(C,A) )
        | ~ subset(A,B) ) ),
    inference(fof_nnf,[status(thm)],[d3_tarski]) ).

fof(f_3_2,plain,
    ! [U_7,U_6] :
      ( ( subset(U_7,U_6)
        | ? [U_5] :
            ( ~ in(U_5,U_6)
            & in(U_5,U_7) ) )
      & ( ! [U_4] :
            ( in(U_4,U_6)
            | ~ in(U_4,U_7) )
        | ~ subset(U_7,U_6) ) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ( ! [U_11,U_9] :
        ( subset(U_11,U_9)
        | ? [U_5] :
            ( ~ in(U_5,U_9)
            & in(U_5,U_11) ) )
    & ! [U_10,U_8] :
        ( ! [U_4] :
            ( in(U_4,U_8)
            | ~ in(U_4,U_10) )
        | ~ subset(U_10,U_8) ) ),
    inference(miniscope,[status(thm)],[f_3_2]) ).

fof(f_3_4,plain,
    ( ! [U_11,U_9] :
        ( subset(U_11,U_9)
        | ( ~ in(sK1(U_11,U_9),U_9)
          & in(sK1(U_11,U_9),U_11) ) )
    & ! [U_10,U_8] :
        ( ! [U_4] :
            ( in(U_4,U_8)
            | ~ in(U_4,U_10) )
        | ~ subset(U_10,U_8) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_11,U_9))],[f_3_3]) ).

cnf(f_3_5,plain,
    ( in(U_4,U_8)
    | ~ in(U_4,U_10)
    | ~ subset(U_10,U_8) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_6,plain,
    ( in(sK1(U_11,U_9),U_11)
    | subset(U_11,U_9) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_7,plain,
    ( ~ in(sK1(U_11,U_9),U_9)
    | subset(U_11,U_9) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

fof(f_4_1,plain,
    ! [A,B,C] :
      ( ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              & in(D,B)
              & in(D,A) )
            | ( ( ~ in(D,B)
                | ~ in(D,A) )
              & in(D,C) ) ) )
      & ( ! [D] :
            ( ( in(D,C)
              | ~ in(D,B)
              | ~ in(D,A) )
            & ( ( in(D,B)
                & in(D,A) )
              | ~ in(D,C) ) )
        | C != set_intersection2(A,B) ) ),
    inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).

fof(f_4_2,plain,
    ! [U_16,U_15,U_14] :
      ( ( U_14 = set_intersection2(U_16,U_15)
        | ? [U_13] :
            ( ( ~ in(U_13,U_14)
              & in(U_13,U_15)
              & in(U_13,U_16) )
            | ( ( ~ in(U_13,U_15)
                | ~ in(U_13,U_16) )
              & in(U_13,U_14) ) ) )
      & ( ! [U_12] :
            ( ( in(U_12,U_14)
              | ~ in(U_12,U_15)
              | ~ in(U_12,U_16) )
            & ( ( in(U_12,U_15)
                & in(U_12,U_16) )
              | ~ in(U_12,U_14) ) )
        | U_14 != set_intersection2(U_16,U_15) ) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ( ! [U_26,U_24,U_22] :
        ( U_22 = set_intersection2(U_26,U_24)
        | ? [U_20] :
            ( ~ in(U_20,U_22)
            & in(U_20,U_24)
            & in(U_20,U_26) )
        | ? [U_19] :
            ( ( ~ in(U_19,U_24)
              | ~ in(U_19,U_26) )
            & in(U_19,U_22) ) )
    & ! [U_25,U_23,U_21] :
        ( ( ! [U_18] :
              ( in(U_18,U_21)
              | ~ in(U_18,U_23)
              | ~ in(U_18,U_25) )
          & ! [U_17] :
              ( ( in(U_17,U_23)
                & in(U_17,U_25) )
              | ~ in(U_17,U_21) ) )
        | U_21 != set_intersection2(U_25,U_23) ) ),
    inference(miniscope,[status(thm)],[f_4_2]) ).

fof(f_4_4,plain,
    ( ! [U_26,U_24,U_22] :
        ( U_22 = set_intersection2(U_26,U_24)
        | ? [U_20] :
            ( ~ in(U_20,U_22)
            & in(U_20,U_24)
            & in(U_20,U_26) )
        | ( ( ~ in(sK2(U_26,U_24,U_22),U_24)
            | ~ in(sK2(U_26,U_24,U_22),U_26) )
          & in(sK2(U_26,U_24,U_22),U_22) ) )
    & ! [U_25,U_23,U_21] :
        ( ( ! [U_18] :
              ( in(U_18,U_21)
              | ~ in(U_18,U_23)
              | ~ in(U_18,U_25) )
          & ! [U_17] :
              ( ( in(U_17,U_23)
                & in(U_17,U_25) )
              | ~ in(U_17,U_21) ) )
        | U_21 != set_intersection2(U_25,U_23) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2(U_26,U_24,U_22))],[f_4_3]) ).

fof(f_4_5,plain,
    ( ! [U_26,U_24,U_22] :
        ( U_22 = set_intersection2(U_26,U_24)
        | ( ~ in(sK3(U_26,U_24,U_22),U_22)
          & in(sK3(U_26,U_24,U_22),U_24)
          & in(sK3(U_26,U_24,U_22),U_26) )
        | ( ( ~ in(sK2(U_26,U_24,U_22),U_24)
            | ~ in(sK2(U_26,U_24,U_22),U_26) )
          & in(sK2(U_26,U_24,U_22),U_22) ) )
    & ! [U_25,U_23,U_21] :
        ( ( ! [U_18] :
              ( in(U_18,U_21)
              | ~ in(U_18,U_23)
              | ~ in(U_18,U_25) )
          & ! [U_17] :
              ( ( in(U_17,U_23)
                & in(U_17,U_25) )
              | ~ in(U_17,U_21) ) )
        | U_21 != set_intersection2(U_25,U_23) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_26,U_24,U_22))],[f_4_4]) ).

cnf(f_4_6,plain,
    ( in(U_17,U_25)
    | ~ in(U_17,U_21)
    | U_21 != set_intersection2(U_25,U_23) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_7,plain,
    ( in(U_17,U_23)
    | ~ in(U_17,U_21)
    | U_21 != set_intersection2(U_25,U_23) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_8,plain,
    ( in(U_18,U_21)
    | ~ in(U_18,U_23)
    | ~ in(U_18,U_25)
    | U_21 != set_intersection2(U_25,U_23) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_9,plain,
    ( in(sK3(U_26,U_24,U_22),U_26)
    | in(sK2(U_26,U_24,U_22),U_22)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_10,plain,
    ( in(sK3(U_26,U_24,U_22),U_24)
    | in(sK2(U_26,U_24,U_22),U_22)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_11,plain,
    ( ~ in(sK3(U_26,U_24,U_22),U_22)
    | in(sK2(U_26,U_24,U_22),U_22)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_12,plain,
    ( in(sK3(U_26,U_24,U_22),U_26)
    | ~ in(sK2(U_26,U_24,U_22),U_24)
    | ~ in(sK2(U_26,U_24,U_22),U_26)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_13,plain,
    ( in(sK3(U_26,U_24,U_22),U_24)
    | ~ in(sK2(U_26,U_24,U_22),U_24)
    | ~ in(sK2(U_26,U_24,U_22),U_26)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

cnf(f_4_14,plain,
    ( ~ in(sK3(U_26,U_24,U_22),U_22)
    | ~ in(sK2(U_26,U_24,U_22),U_24)
    | ~ in(sK2(U_26,U_24,U_22),U_26)
    | U_22 = set_intersection2(U_26,U_24) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

fof(f_5_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).

cnf(f_5_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_5_1]) ).

fof(f_6_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).

cnf(f_6_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_6_1]) ).

fof(f_7_1,plain,
    empty(empty_set),
    inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).

cnf(f_7_2,plain,
    empty(empty_set),
    inference(clausify,[status(thm)],[f_7_1]) ).

fof(f_8_1,plain,
    ! [A,B] : set_intersection2(A,A) = A,
    inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).

fof(f_8_2,plain,
    ! [U_28,U_27] : set_intersection2(U_28,U_28) = U_28,
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_28] : set_intersection2(U_28,U_28) = U_28,
    inference(miniscope,[status(thm)],[f_8_2]) ).

cnf(f_8_4,plain,
    set_intersection2(U_28,U_28) = U_28,
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ? [A] : empty(A),
    inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).

fof(f_9_2,plain,
    ? [U_29] : empty(U_29),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    empty(sK4),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4)],[f_9_2]) ).

cnf(f_9_4,plain,
    empty(sK4),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ? [A] : ~ empty(A),
    inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).

fof(f_10_2,plain,
    ? [U_30] : ~ empty(U_30),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ~ empty(sK5),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_30,sK5)],[f_10_2]) ).

cnf(f_10_4,plain,
    ~ empty(sK5),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [A,B] : subset(A,A),
    inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).

fof(f_11_2,plain,
    ! [U_32,U_31] : subset(U_32,U_32),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_32] : subset(U_32,U_32),
    inference(miniscope,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    subset(U_32,U_32),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(A,B)
       => subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(negate,[status(cth)],[t26_xboole_1]) ).

fof(f_12_2,negated_conjecture,
    ? [A,B,C] :
      ( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
      & subset(A,B) ),
    inference(fof_nnf,[status(thm)],[f_12_1]) ).

fof(f_12_3,negated_conjecture,
    ? [U_35,U_34,U_33] :
      ( ~ subset(set_intersection2(U_35,U_33),set_intersection2(U_34,U_33))
      & subset(U_35,U_34) ),
    inference(variable_rename,[status(thm)],[f_12_2]) ).

fof(f_12_4,negated_conjecture,
    ? [U_35,U_34] :
      ( ? [U_33] : ~ subset(set_intersection2(U_35,U_33),set_intersection2(U_34,U_33))
      & subset(U_35,U_34) ),
    inference(miniscope,[status(thm)],[f_12_3]) ).

fof(f_12_5,negated_conjecture,
    ? [U_34] :
      ( ? [U_33] : ~ subset(set_intersection2(sK6,U_33),set_intersection2(U_34,U_33))
      & subset(sK6,U_34) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6)],[f_12_4]) ).

fof(f_12_6,negated_conjecture,
    ( ? [U_33] : ~ subset(set_intersection2(sK6,U_33),set_intersection2(sK7,U_33))
    & subset(sK6,sK7) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_34,sK7)],[f_12_5]) ).

fof(f_12_7,negated_conjecture,
    ( ~ subset(set_intersection2(sK6,sK8),set_intersection2(sK7,sK8))
    & subset(sK6,sK7) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_33,sK8)],[f_12_6]) ).

fof(f_12_8,negated_conjecture,
    ( ~ subset(set_intersection2(sK6,sK8),set_intersection2(sK7,sK8))
    & subset(sK6,sK7) ),
    inference(definitional_conversion,[status(esa)],[f_12_7]) ).

cnf(f_12_9,negated_conjecture,
    subset(sK6,sK7),
    inference(clausify,[status(thm)],[f_12_8]) ).

cnf(f_12_10,negated_conjecture,
    ~ subset(set_intersection2(sK6,sK8),set_intersection2(sK7,sK8)),
    inference(clausify,[status(thm)],[f_12_8]) ).

fof(f_13_1,plain,
    ! [A] : set_intersection2(A,empty_set) = empty_set,
    inference(fof_nnf,[status(thm)],[t2_boole]) ).

fof(f_13_2,plain,
    ! [U_36] : set_intersection2(U_36,empty_set) = empty_set,
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    set_intersection2(U_36,empty_set) = empty_set,
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [A] :
      ( A = empty_set
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[t6_boole]) ).

fof(f_14_2,plain,
    ! [U_37] :
      ( U_37 = empty_set
      | ~ empty(U_37) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

cnf(f_14_3,plain,
    ( U_37 = empty_set
    | ~ empty(U_37) ),
    inference(clausify,[status(thm)],[f_14_2]) ).

fof(f_15_1,plain,
    ! [A,B] :
      ( ~ empty(B)
      | ~ in(A,B) ),
    inference(fof_nnf,[status(thm)],[t7_boole]) ).

fof(f_15_2,plain,
    ! [U_39,U_38] :
      ( ~ empty(U_38)
      | ~ in(U_39,U_38) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

cnf(f_15_3,plain,
    ( ~ empty(U_38)
    | ~ in(U_39,U_38) ),
    inference(clausify,[status(thm)],[f_15_2]) ).

fof(f_16_1,plain,
    ! [A,B] :
      ( ~ empty(B)
      | A = B
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[t8_boole]) ).

fof(f_16_2,plain,
    ! [U_41,U_40] :
      ( ~ empty(U_40)
      | U_41 = U_40
      | ~ empty(U_41) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_41] :
      ( ! [U_40] :
          ( ~ empty(U_40)
          | U_41 = U_40 )
      | ~ empty(U_41) ),
    inference(miniscope,[status(thm)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( ~ empty(U_40)
    | U_41 = U_40
    | ~ empty(U_41) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

cnf(f_5_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_5_2]) ).

cnf(f_6_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_6_2]) ).

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,
    ( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

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

cnf(equality_10,axiom,
    ( empty(Eq_y_0)
    | ~ empty(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
% 0.00/0.02  % Problem  : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.10/5.37  % Computer : n001.cluster.edu
% 0.10/5.37  % Model    : x86_64 x86_64
% 0.10/5.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37  % Memory   : 8046.5625MB
% 0.10/5.37  % OS       : Linux 6.8.0-71-generic
% 0.10/5.37  % CPULimit : 300
% 0.10/5.37  % WCLimit  : 300
% 0.10/5.37  % DateTime : Sat Sep 19 23:26:31 UTC 2026
% 0.10/5.37  % CPUTime  : 
% 2.44/7.78  % SZS status Theorem for theBenchmark
% 2.44/7.78  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------