↑ Up

ConnectPP---0.7.2.THM-Prf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n004.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 08:58:24 AM UTC 2026

% Result   : Theorem 0.13s 5.49s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(existence_m1_subset_1,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('theBenchmark.p',existence_m1_subset_1) ).

fof(dt_m1_subset_1,axiom,
    $true,
    file('theBenchmark.p',dt_m1_subset_1) ).

fof(t2_subset,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( in(A,B)
        | empty(B) ) ),
    file('theBenchmark.p',t2_subset) ).

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

fof(t1_subset,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('theBenchmark.p',t1_subset) ).

fof(rc1_relat_1,axiom,
    ? [A] :
      ( relation(A)
      & empty(A) ),
    file('theBenchmark.p',rc1_relat_1) ).

fof(cc1_relat_1,axiom,
    ! [A] :
      ( empty(A)
     => relation(A) ),
    file('theBenchmark.p',cc1_relat_1) ).

fof(rc2_relat_1,axiom,
    ? [A] :
      ( relation(A)
      & ~ empty(A) ),
    file('theBenchmark.p',rc2_relat_1) ).

fof(fc5_relat_1,axiom,
    ! [A] :
      ( ( relation(A)
        & ~ empty(A) )
     => ~ empty(relation_dom(A)) ),
    file('theBenchmark.p',fc5_relat_1) ).

fof(fc6_relat_1,axiom,
    ! [A] :
      ( ( relation(A)
        & ~ empty(A) )
     => ~ empty(relation_rng(A)) ),
    file('theBenchmark.p',fc6_relat_1) ).

fof(fc7_relat_1,axiom,
    ! [A] :
      ( empty(A)
     => ( relation(relation_dom(A))
        & empty(relation_dom(A)) ) ),
    file('theBenchmark.p',fc7_relat_1) ).

fof(fc8_relat_1,axiom,
    ! [A] :
      ( empty(A)
     => ( relation(relation_rng(A))
        & empty(relation_rng(A)) ) ),
    file('theBenchmark.p',fc8_relat_1) ).

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(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(dt_k1_relat_1,axiom,
    $true,
    file('theBenchmark.p',dt_k1_relat_1) ).

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

fof(dt_k2_relat_1,axiom,
    $true,
    file('theBenchmark.p',dt_k2_relat_1) ).

fof(fc4_relat_1,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('theBenchmark.p',fc4_relat_1) ).

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

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

fof(t65_relat_1,conjecture,
    ! [A] :
      ( relation(A)
     => ( relation_dom(A) = empty_set
      <=> relation_rng(A) = empty_set ) ),
    file('theBenchmark.p',t65_relat_1) ).

fof(t60_relat_1,axiom,
    ( relation_rng(empty_set) = empty_set
    & relation_dom(empty_set) = empty_set ),
    file('theBenchmark.p',t60_relat_1) ).

fof(t64_relat_1,axiom,
    ! [A] :
      ( relation(A)
     => ( ( relation_rng(A) = empty_set
          | relation_dom(A) = empty_set )
       => A = empty_set ) ),
    file('theBenchmark.p',t64_relat_1) ).

fof(f_1_1,plain,
    ! [A] :
    ? [B] : element(B,A),
    inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).

fof(f_1_2,plain,
    ! [U_1] :
    ? [U_0] : element(U_0,U_1),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_1] : element(sK1(U_1),U_1),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_1))],[f_1_2]) ).

cnf(f_1_4,plain,
    element(sK1(U_1),U_1),
    inference(clausify,[status(thm)],[f_1_3]) ).

fof(f_2_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).

cnf(f_2_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_2_1]) ).

fof(f_3_1,plain,
    ! [A,B] :
      ( in(A,B)
      | empty(B)
      | ~ element(A,B) ),
    inference(fof_nnf,[status(thm)],[t2_subset]) ).

fof(f_3_2,plain,
    ! [U_3,U_2] :
      ( in(U_3,U_2)
      | empty(U_2)
      | ~ element(U_3,U_2) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    ( in(U_3,U_2)
    | empty(U_2)
    | ~ element(U_3,U_2) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [A,B] :
      ( ~ in(B,A)
      | ~ in(A,B) ),
    inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).

fof(f_4_2,plain,
    ! [U_5,U_4] :
      ( ~ in(U_4,U_5)
      | ~ in(U_5,U_4) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( ~ in(U_4,U_5)
    | ~ in(U_5,U_4) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    ! [A,B] :
      ( element(A,B)
      | ~ in(A,B) ),
    inference(fof_nnf,[status(thm)],[t1_subset]) ).

fof(f_5_2,plain,
    ! [U_7,U_6] :
      ( element(U_7,U_6)
      | ~ in(U_7,U_6) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( element(U_7,U_6)
    | ~ in(U_7,U_6) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ? [A] :
      ( relation(A)
      & empty(A) ),
    inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).

fof(f_6_2,plain,
    ? [U_8] :
      ( relation(U_8)
      & empty(U_8) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ( relation(sK2)
    & empty(sK2) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2)],[f_6_2]) ).

cnf(f_6_4,plain,
    empty(sK2),
    inference(clausify,[status(thm)],[f_6_3]) ).

cnf(f_6_5,plain,
    relation(sK2),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [A] :
      ( relation(A)
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).

fof(f_7_2,plain,
    ! [U_9] :
      ( relation(U_9)
      | ~ empty(U_9) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( relation(U_9)
    | ~ empty(U_9) ),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ? [A] :
      ( relation(A)
      & ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).

fof(f_8_2,plain,
    ? [U_10] :
      ( relation(U_10)
      & ~ empty(U_10) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ( relation(sK3)
    & ~ empty(sK3) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_10,sK3)],[f_8_2]) ).

cnf(f_8_4,plain,
    ~ empty(sK3),
    inference(clausify,[status(thm)],[f_8_3]) ).

cnf(f_8_5,plain,
    relation(sK3),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ! [A] :
      ( ~ empty(relation_dom(A))
      | ~ relation(A)
      | empty(A) ),
    inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).

fof(f_9_2,plain,
    ! [U_11] :
      ( ~ empty(relation_dom(U_11))
      | ~ relation(U_11)
      | empty(U_11) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

cnf(f_9_3,plain,
    ( ~ empty(relation_dom(U_11))
    | ~ relation(U_11)
    | empty(U_11) ),
    inference(clausify,[status(thm)],[f_9_2]) ).

fof(f_10_1,plain,
    ! [A] :
      ( ~ empty(relation_rng(A))
      | ~ relation(A)
      | empty(A) ),
    inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).

fof(f_10_2,plain,
    ! [U_12] :
      ( ~ empty(relation_rng(U_12))
      | ~ relation(U_12)
      | empty(U_12) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    ( ~ empty(relation_rng(U_12))
    | ~ relation(U_12)
    | empty(U_12) ),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [A] :
      ( ( relation(relation_dom(A))
        & empty(relation_dom(A)) )
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).

fof(f_11_2,plain,
    ! [U_13] :
      ( ( relation(relation_dom(U_13))
        & empty(relation_dom(U_13)) )
      | ~ empty(U_13) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

cnf(f_11_3,plain,
    ( empty(relation_dom(U_13))
    | ~ empty(U_13) ),
    inference(clausify,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( relation(relation_dom(U_13))
    | ~ empty(U_13) ),
    inference(clausify,[status(thm)],[f_11_2]) ).

fof(f_12_1,plain,
    ! [A] :
      ( ( relation(relation_rng(A))
        & empty(relation_rng(A)) )
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).

fof(f_12_2,plain,
    ! [U_14] :
      ( ( relation(relation_rng(U_14))
        & empty(relation_rng(U_14)) )
      | ~ empty(U_14) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

cnf(f_12_3,plain,
    ( empty(relation_rng(U_14))
    | ~ empty(U_14) ),
    inference(clausify,[status(thm)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( relation(relation_rng(U_14))
    | ~ empty(U_14) ),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_1,plain,
    ? [A] : empty(A),
    inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).

fof(f_13_2,plain,
    ? [U_15] : empty(U_15),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    empty(sK4),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4)],[f_13_2]) ).

cnf(f_13_4,plain,
    empty(sK4),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_1,plain,
    ? [A] : ~ empty(A),
    inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).

fof(f_14_2,plain,
    ? [U_16] : ~ empty(U_16),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ~ empty(sK5),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_16,sK5)],[f_14_2]) ).

cnf(f_14_4,plain,
    ~ empty(sK5),
    inference(clausify,[status(thm)],[f_14_3]) ).

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_18,U_17] :
      ( ~ empty(U_17)
      | ~ in(U_18,U_17) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

cnf(f_15_3,plain,
    ( ~ empty(U_17)
    | ~ in(U_18,U_17) ),
    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_20,U_19] :
      ( ~ empty(U_19)
      | U_20 = U_19
      | ~ empty(U_20) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_20] :
      ( ! [U_19] :
          ( ~ empty(U_19)
          | U_20 = U_19 )
      | ~ empty(U_20) ),
    inference(miniscope,[status(thm)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( ~ empty(U_19)
    | U_20 = U_19
    | ~ empty(U_20) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).

cnf(f_17_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_17_1]) ).

fof(f_18_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).

cnf(f_18_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_18_1]) ).

fof(f_19_1,plain,
    $true,
    inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).

cnf(f_19_2,plain,
    $true,
    inference(clausify,[status(thm)],[f_19_1]) ).

fof(f_20_1,plain,
    ( relation(empty_set)
    & empty(empty_set) ),
    inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).

cnf(f_20_2,plain,
    empty(empty_set),
    inference(clausify,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    relation(empty_set),
    inference(clausify,[status(thm)],[f_20_1]) ).

fof(f_21_1,plain,
    empty(empty_set),
    inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).

cnf(f_21_2,plain,
    empty(empty_set),
    inference(clausify,[status(thm)],[f_21_1]) ).

fof(f_22_1,plain,
    ! [A] :
      ( A = empty_set
      | ~ empty(A) ),
    inference(fof_nnf,[status(thm)],[t6_boole]) ).

fof(f_22_2,plain,
    ! [U_21] :
      ( U_21 = empty_set
      | ~ empty(U_21) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    ( U_21 = empty_set
    | ~ empty(U_21) ),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( relation_dom(A) = empty_set
        <=> relation_rng(A) = empty_set ) ),
    inference(negate,[status(cth)],[t65_relat_1]) ).

fof(f_23_2,negated_conjecture,
    ? [A] :
      ( ( ( relation_dom(A) != empty_set
          & relation_rng(A) = empty_set )
        | ( relation_rng(A) != empty_set
          & relation_dom(A) = empty_set ) )
      & relation(A) ),
    inference(fof_nnf,[status(thm)],[f_23_1]) ).

fof(f_23_3,negated_conjecture,
    ? [U_22] :
      ( ( ( relation_dom(U_22) != empty_set
          & relation_rng(U_22) = empty_set )
        | ( relation_rng(U_22) != empty_set
          & relation_dom(U_22) = empty_set ) )
      & relation(U_22) ),
    inference(variable_rename,[status(thm)],[f_23_2]) ).

fof(f_23_4,negated_conjecture,
    ( ( ( relation_dom(sK6) != empty_set
        & relation_rng(sK6) = empty_set )
      | ( relation_rng(sK6) != empty_set
        & relation_dom(sK6) = empty_set ) )
    & relation(sK6) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_23_3]) ).

fof(f_23_5,negated_conjecture,
    ( ( relation_dom(sK6) != empty_set
      | ~ sP1 )
    & ( relation_rng(sK6) = empty_set
      | ~ sP1 )
    & ( relation_rng(sK6) != empty_set
      | ~ sP0 )
    & ( relation_dom(sK6) = empty_set
      | ~ sP0 )
    & ( sP1
      | sP0 )
    & relation(sK6) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_23_4]) ).

cnf(f_23_6,negated_conjecture,
    relation(sK6),
    inference(clausify,[status(thm)],[f_23_5]) ).

cnf(f_23_7,negated_conjecture,
    ( sP1
    | sP0 ),
    inference(clausify,[status(thm)],[f_23_5]) ).

cnf(f_23_8,negated_conjecture,
    ( relation_dom(sK6) = empty_set
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_23_5]) ).

cnf(f_23_9,negated_conjecture,
    ( relation_rng(sK6) != empty_set
    | ~ sP0 ),
    inference(clausify,[status(thm)],[f_23_5]) ).

cnf(f_23_10,negated_conjecture,
    ( relation_rng(sK6) = empty_set
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_23_5]) ).

cnf(f_23_11,negated_conjecture,
    ( relation_dom(sK6) != empty_set
    | ~ sP1 ),
    inference(clausify,[status(thm)],[f_23_5]) ).

fof(f_24_1,plain,
    ( relation_rng(empty_set) = empty_set
    & relation_dom(empty_set) = empty_set ),
    inference(fof_nnf,[status(thm)],[t60_relat_1]) ).

cnf(f_24_2,plain,
    relation_dom(empty_set) = empty_set,
    inference(clausify,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    relation_rng(empty_set) = empty_set,
    inference(clausify,[status(thm)],[f_24_1]) ).

fof(f_25_1,plain,
    ! [A] :
      ( A = empty_set
      | ( relation_rng(A) != empty_set
        & relation_dom(A) != empty_set )
      | ~ relation(A) ),
    inference(fof_nnf,[status(thm)],[t64_relat_1]) ).

fof(f_25_2,plain,
    ! [U_23] :
      ( U_23 = empty_set
      | ( relation_rng(U_23) != empty_set
        & relation_dom(U_23) != empty_set )
      | ~ relation(U_23) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ( relation_dom(U_23) != empty_set
    | U_23 = empty_set
    | ~ relation(U_23) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( relation_rng(U_23) != empty_set
    | U_23 = empty_set
    | ~ relation(U_23) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

cnf(f_2_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2_2]) ).

cnf(f_17_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_17_2]) ).

cnf(f_18_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_18_2]) ).

cnf(f_19_2_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_19_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,
    ( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

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

cnf(equality_6,axiom,
    ( sK1(Eq_x_0) = sK1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( element(Eq_y_0,Eq_y_1)
    | ~ element(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

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

cnf(equality_9,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_10,axiom,
    ( relation(Eq_y_0)
    | ~ relation(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  : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36  % Computer : n004.cluster.edu
% 0.09/5.36  % Model    : x86_64 x86_64
% 0.09/5.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36  % Memory   : 8046.5625MB
% 0.09/5.36  % OS       : Linux 6.8.0-71-generic
% 0.09/5.36  % CPULimit : 300
% 0.09/5.36  % WCLimit  : 300
% 0.09/5.36  % DateTime : Sat Sep 19 23:28:13 UTC 2026
% 0.09/5.36  % CPUTime  : 
% 0.13/5.49  % SZS status Theorem for theBenchmark
% 0.13/5.49  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------