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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LCL686+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n012.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 : Sun Sep 27 07:52:34 AM UTC 2026

% Result   : Theorem 7.23s 3.94s
% Output   : Refutation 7.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    8 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  878 (   0 equ;   0 cnn)
%            Maximal formula atoms :  290 ( 109 avg)
%            Number of connectives : 2649 ( 710   ~; 530   |; 338   &;1069   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  102 (  41 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  31 usr;   1 con; 0-2 aty)
%            Number of variables   :  197 (   0   ^; 194   !;   3   ?; 197   :)

% Comments : 
%------------------------------------------------------------------------------
thf(r1_decl,type,
    r1: $i > $i > $o ).

thf(p30_decl,type,
    p30: $i > $o ).

thf(p1_decl,type,
    p1: $i > $o ).

thf(p29_decl,type,
    p29: $i > $o ).

thf(p28_decl,type,
    p28: $i > $o ).

thf(p27_decl,type,
    p27: $i > $o ).

thf(p26_decl,type,
    p26: $i > $o ).

thf(p25_decl,type,
    p25: $i > $o ).

thf(p24_decl,type,
    p24: $i > $o ).

thf(p23_decl,type,
    p23: $i > $o ).

thf(p22_decl,type,
    p22: $i > $o ).

thf(p21_decl,type,
    p21: $i > $o ).

thf(p20_decl,type,
    p20: $i > $o ).

thf(p19_decl,type,
    p19: $i > $o ).

thf(p18_decl,type,
    p18: $i > $o ).

thf(p17_decl,type,
    p17: $i > $o ).

thf(p16_decl,type,
    p16: $i > $o ).

thf(p15_decl,type,
    p15: $i > $o ).

thf(p14_decl,type,
    p14: $i > $o ).

thf(p13_decl,type,
    p13: $i > $o ).

thf(p12_decl,type,
    p12: $i > $o ).

thf(p11_decl,type,
    p11: $i > $o ).

thf(p10_decl,type,
    p10: $i > $o ).

thf(p9_decl,type,
    p9: $i > $o ).

thf(p8_decl,type,
    p8: $i > $o ).

thf(p7_decl,type,
    p7: $i > $o ).

thf(p6_decl,type,
    p6: $i > $o ).

thf(p5_decl,type,
    p5: $i > $o ).

thf(p4_decl,type,
    p4: $i > $o ).

thf(p3_decl,type,
    p3: $i > $o ).

thf(p2_decl,type,
    p2: $i > $o ).

thf(1,conjecture,
    ~ ? [A: $i] :
        ~ ( ! [B: $i] :
              ( ~ ! [C: $i] :
                    ( ~ ( ! [D: $i] :
                            ( ( ( D @ p1 )
                              & ( D @ p2 ) )
                            | ( ~ ( D @ p2 )
                              & ~ ( D @ p1 ) )
                            | ( ( D @ p2 )
                              & ( D @ p3 ) )
                            | ( ~ ( D @ p3 )
                              & ~ ( D @ p2 ) )
                            | ( ( D @ p3 )
                              & ( D @ p4 ) )
                            | ( ~ ( D @ p4 )
                              & ~ ( D @ p3 ) )
                            | ( ( D @ p4 )
                              & ( D @ p5 ) )
                            | ( ~ ( D @ p5 )
                              & ~ ( D @ p4 ) )
                            | ( ( D @ p5 )
                              & ( D @ p6 ) )
                            | ( ~ ( D @ p6 )
                              & ~ ( D @ p5 ) )
                            | ( ( D @ p6 )
                              & ( D @ p7 ) )
                            | ( ~ ( D @ p7 )
                              & ~ ( D @ p6 ) )
                            | ( ( D @ p7 )
                              & ( D @ p8 ) )
                            | ( ~ ( D @ p8 )
                              & ~ ( D @ p7 ) )
                            | ( ( D @ p8 )
                              & ( D @ p9 ) )
                            | ( ~ ( D @ p9 )
                              & ~ ( D @ p8 ) )
                            | ( ( D @ p9 )
                              & ( D @ p10 ) )
                            | ( ~ ( D @ p10 )
                              & ~ ( D @ p9 ) )
                            | ( ( D @ p10 )
                              & ( D @ p11 ) )
                            | ( ~ ( D @ p11 )
                              & ~ ( D @ p10 ) )
                            | ( ( D @ p11 )
                              & ( D @ p12 ) )
                            | ( ~ ( D @ p12 )
                              & ~ ( D @ p11 ) )
                            | ( ( D @ p12 )
                              & ( D @ p13 ) )
                            | ( ~ ( D @ p13 )
                              & ~ ( D @ p12 ) )
                            | ( ( D @ p13 )
                              & ( D @ p14 ) )
                            | ( ~ ( D @ p14 )
                              & ~ ( D @ p13 ) )
                            | ( ( D @ p14 )
                              & ( D @ p15 ) )
                            | ( ~ ( D @ p15 )
                              & ~ ( D @ p14 ) )
                            | ( ( D @ p15 )
                              & ( D @ p16 ) )
                            | ( ~ ( D @ p16 )
                              & ~ ( D @ p15 ) )
                            | ( ( D @ p16 )
                              & ( D @ p17 ) )
                            | ( ~ ( D @ p17 )
                              & ~ ( D @ p16 ) )
                            | ( ( D @ p17 )
                              & ( D @ p18 ) )
                            | ( ~ ( D @ p18 )
                              & ~ ( D @ p17 ) )
                            | ( ( D @ p18 )
                              & ( D @ p19 ) )
                            | ( ~ ( D @ p19 )
                              & ~ ( D @ p18 ) )
                            | ( ( D @ p19 )
                              & ( D @ p20 ) )
                            | ( ~ ( D @ p20 )
                              & ~ ( D @ p19 ) )
                            | ( ( D @ p20 )
                              & ( D @ p21 ) )
                            | ( ~ ( D @ p21 )
                              & ~ ( D @ p20 ) )
                            | ( ( D @ p21 )
                              & ( D @ p22 ) )
                            | ( ~ ( D @ p22 )
                              & ~ ( D @ p21 ) )
                            | ( ( D @ p22 )
                              & ( D @ p23 ) )
                            | ( ~ ( D @ p23 )
                              & ~ ( D @ p22 ) )
                            | ( ( D @ p23 )
                              & ( D @ p24 ) )
                            | ( ~ ( D @ p24 )
                              & ~ ( D @ p23 ) )
                            | ( ( D @ p24 )
                              & ( D @ p25 ) )
                            | ( ~ ( D @ p25 )
                              & ~ ( D @ p24 ) )
                            | ( ( D @ p25 )
                              & ( D @ p26 ) )
                            | ( ~ ( D @ p26 )
                              & ~ ( D @ p25 ) )
                            | ( ( D @ p26 )
                              & ( D @ p27 ) )
                            | ( ~ ( D @ p27 )
                              & ~ ( D @ p26 ) )
                            | ( ( D @ p27 )
                              & ( D @ p28 ) )
                            | ( ~ ( D @ p28 )
                              & ~ ( D @ p27 ) )
                            | ( ( D @ p28 )
                              & ( D @ p29 ) )
                            | ( ~ ( D @ p29 )
                              & ~ ( D @ p28 ) )
                            | ~ ( D @ ( C @ r1 ) ) )
                        | ! [D: $i] :
                            ( ( D @ p30 )
                            | ~ ( D @ ( C @ r1 ) ) )
                        | ~ ! [D: $i] :
                              ( ~ ( ( ( D @ p1 )
                                    & ~ ( D @ p2 ) )
                                  | ( ~ ( D @ p1 )
                                    & ( D @ p2 ) ) )
                              | ~ ( D @ ( C @ r1 ) ) )
                        | ! [D: $i] :
                            ( ~ ! [E: $i] :
                                  ( ~ ( ( ( E @ p2 )
                                        & ~ ( E @ p3 ) )
                                      | ( ~ ( E @ p2 )
                                        & ( E @ p3 ) ) )
                                  | ~ ( E @ ( D @ r1 ) ) )
                            | ! [E: $i] :
                                ( ~ ! [F: $i] :
                                      ( ~ ( ( ( F @ p3 )
                                            & ~ ( F @ p4 ) )
                                          | ( ~ ( F @ p3 )
                                            & ( F @ p4 ) ) )
                                      | ~ ( F @ ( E @ r1 ) ) )
                                | ! [F: $i] :
                                    ( ~ ! [G: $i] :
                                          ( ~ ( ( ( G @ p4 )
                                                & ~ ( G @ p5 ) )
                                              | ( ~ ( G @ p4 )
                                                & ( G @ p5 ) ) )
                                          | ~ ( G @ ( F @ r1 ) ) )
                                    | ! [G: $i] :
                                        ( ~ ! [H: $i] :
                                              ( ~ ( ( ( H @ p5 )
                                                    & ~ ( H @ p6 ) )
                                                  | ( ~ ( H @ p5 )
                                                    & ( H @ p6 ) ) )
                                              | ~ ( H @ ( G @ r1 ) ) )
                                        | ! [H: $i] :
                                            ( ~ ! [I: $i] :
                                                  ( ~ ( ( ( I @ p6 )
                                                        & ~ ( I @ p7 ) )
                                                      | ( ~ ( I @ p6 )
                                                        & ( I @ p7 ) ) )
                                                  | ~ ( I @ ( H @ r1 ) ) )
                                            | ! [I: $i] :
                                                ( ~ ! [J: $i] :
                                                      ( ~ ( ( ( J @ p7 )
                                                            & ~ ( J @ p8 ) )
                                                          | ( ~ ( J @ p7 )
                                                            & ( J @ p8 ) ) )
                                                      | ~ ( J @ ( I @ r1 ) ) )
                                                | ! [J: $i] :
                                                    ( ~ ! [K: $i] :
                                                          ( ~ ( ( ( K @ p8 )
                                                                & ~ ( K @ p9 ) )
                                                              | ( ~ ( K @ p8 )
                                                                & ( K @ p9 ) ) )
                                                          | ~ ( K @ ( J @ r1 ) ) )
                                                    | ! [K: $i] :
                                                        ( ~ ! [L: $i] :
                                                              ( ~ ( ( ( L @ p9 )
                                                                    & ~ ( L @ p10 ) )
                                                                  | ( ~ ( L @ p9 )
                                                                    & ( L @ p10 ) ) )
                                                              | ~ ( L @ ( K @ r1 ) ) )
                                                        | ! [L: $i] :
                                                            ( ~ ! [M: $i] :
                                                                  ( ~ ( ( ( M @ p10 )
                                                                        & ~ ( M @ p11 ) )
                                                                      | ( ~ ( M @ p10 )
                                                                        & ( M @ p11 ) ) )
                                                                  | ~ ( M @ ( L @ r1 ) ) )
                                                            | ! [M: $i] :
                                                                ( ~ ! [N: $i] :
                                                                      ( ~ ( ( ( N @ p11 )
                                                                            & ~ ( N @ p12 ) )
                                                                          | ( ~ ( N @ p11 )
                                                                            & ( N @ p12 ) ) )
                                                                      | ~ ( N @ ( M @ r1 ) ) )
                                                                | ! [N: $i] :
                                                                    ( ~ ! [O: $i] :
                                                                          ( ~ ( ( ( O @ p12 )
                                                                                & ~ ( O @ p13 ) )
                                                                              | ( ~ ( O @ p12 )
                                                                                & ( O @ p13 ) ) )
                                                                          | ~ ( O @ ( N @ r1 ) ) )
                                                                    | ! [O: $i] :
                                                                        ( ~ ! [P: $i] :
                                                                              ( ~ ( ( ( P @ p13 )
                                                                                    & ~ ( P @ p14 ) )
                                                                                  | ( ~ ( P @ p13 )
                                                                                    & ( P @ p14 ) ) )
                                                                              | ~ ( P @ ( O @ r1 ) ) )
                                                                        | ! [P: $i] :
                                                                            ( ~ ! [Q: $i] :
                                                                                  ( ~ ( ( ( Q @ p14 )
                                                                                        & ~ ( Q @ p15 ) )
                                                                                      | ( ~ ( Q @ p14 )
                                                                                        & ( Q @ p15 ) ) )
                                                                                  | ~ ( Q @ ( P @ r1 ) ) )
                                                                            | ! [Q: $i] :
                                                                                ( ~ ! [R: $i] :
                                                                                      ( ~ ( ( ( R @ p15 )
                                                                                            & ~ ( R @ p16 ) )
                                                                                          | ( ~ ( R @ p15 )
                                                                                            & ( R @ p16 ) ) )
                                                                                      | ~ ( R @ ( Q @ r1 ) ) )
                                                                                | ! [R: $i] :
                                                                                    ( ~ ! [S: $i] :
                                                                                          ( ~ ( ( ( S @ p16 )
                                                                                                & ~ ( S @ p17 ) )
                                                                                              | ( ~ ( S @ p16 )
                                                                                                & ( S @ p17 ) ) )
                                                                                          | ~ ( S @ ( R @ r1 ) ) )
                                                                                    | ! [S: $i] :
                                                                                        ( ~ ! [T: $i] :
                                                                                              ( ~ ( ( ( T @ p17 )
                                                                                                    & ~ ( T @ p18 ) )
                                                                                                  | ( ~ ( T @ p17 )
                                                                                                    & ( T @ p18 ) ) )
                                                                                              | ~ ( T @ ( S @ r1 ) ) )
                                                                                        | ! [T: $i] :
                                                                                            ( ~ ! [U: $i] :
                                                                                                  ( ~ ( ( ( U @ p18 )
                                                                                                        & ~ ( U @ p19 ) )
                                                                                                      | ( ~ ( U @ p18 )
                                                                                                        & ( U @ p19 ) ) )
                                                                                                  | ~ ( U @ ( T @ r1 ) ) )
                                                                                            | ! [U: $i] :
                                                                                                ( ~ ! [V: $i] :
                                                                                                      ( ~ ( ( ( V @ p19 )
                                                                                                            & ~ ( V @ p20 ) )
                                                                                                          | ( ~ ( V @ p19 )
                                                                                                            & ( V @ p20 ) ) )
                                                                                                      | ~ ( V @ ( U @ r1 ) ) )
                                                                                                | ! [V: $i] :
                                                                                                    ( ~ ! [W: $i] :
                                                                                                          ( ~ ( ( ( W @ p20 )
                                                                                                                & ~ ( W @ p21 ) )
                                                                                                              | ( ~ ( W @ p20 )
                                                                                                                & ( W @ p21 ) ) )
                                                                                                          | ~ ( W @ ( V @ r1 ) ) )
                                                                                                    | ! [W: $i] :
                                                                                                        ( ~ ! [X: $i] :
                                                                                                              ( ~ ( ( ( X @ p21 )
                                                                                                                    & ~ ( X @ p22 ) )
                                                                                                                  | ( ~ ( X @ p21 )
                                                                                                                    & ( X @ p22 ) ) )
                                                                                                              | ~ ( X @ ( W @ r1 ) ) )
                                                                                                        | ! [X: $i] :
                                                                                                            ( ~ ! [Y: $i] :
                                                                                                                  ( ~ ( ( ( Y @ p22 )
                                                                                                                        & ~ ( Y @ p23 ) )
                                                                                                                      | ( ~ ( Y @ p22 )
                                                                                                                        & ( Y @ p23 ) ) )
                                                                                                                  | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                            | ! [Y: $i] :
                                                                                                                ( ~ ! [Z: $i] :
                                                                                                                      ( ~ ( ( ( Z @ p23 )
                                                                                                                            & ~ ( Z @ p24 ) )
                                                                                                                          | ( ~ ( Z @ p23 )
                                                                                                                            & ( Z @ p24 ) ) )
                                                                                                                      | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                | ! [Z: $i] :
                                                                                                                    ( ~ ! [ZA: $i] :
                                                                                                                          ( ~ ( ( ( ZA @ p24 )
                                                                                                                                & ~ ( ZA @ p25 ) )
                                                                                                                              | ( ~ ( ZA @ p24 )
                                                                                                                                & ( ZA @ p25 ) ) )
                                                                                                                          | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                    | ! [ZA: $i] :
                                                                                                                        ( ~ ! [ZB: $i] :
                                                                                                                              ( ~ ( ( ( ZB @ p25 )
                                                                                                                                    & ~ ( ZB @ p26 ) )
                                                                                                                                  | ( ~ ( ZB @ p25 )
                                                                                                                                    & ( ZB @ p26 ) ) )
                                                                                                                              | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                        | ! [ZB: $i] :
                                                                                                                            ( ~ ! [ZC: $i] :
                                                                                                                                  ( ~ ( ( ( ZC @ p26 )
                                                                                                                                        & ~ ( ZC @ p27 ) )
                                                                                                                                      | ( ~ ( ZC @ p26 )
                                                                                                                                        & ( ZC @ p27 ) ) )
                                                                                                                                  | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                            | ! [ZC: $i] :
                                                                                                                                ( ~ ! [ZD: $i] :
                                                                                                                                      ( ~ ( ( ( ZD @ p27 )
                                                                                                                                            & ~ ( ZD @ p28 ) )
                                                                                                                                          | ( ~ ( ZD @ p27 )
                                                                                                                                            & ( ZD @ p28 ) ) )
                                                                                                                                      | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                | ! [ZD: $i] :
                                                                                                                                    ( ~ ! [ZE: $i] :
                                                                                                                                          ( ~ ( ( ( ZE @ p28 )
                                                                                                                                                & ~ ( ZE @ p29 ) )
                                                                                                                                              | ( ~ ( ZE @ p28 )
                                                                                                                                                & ( ZE @ p29 ) ) )
                                                                                                                                          | ~ ( ZE @ ( ZD @ r1 ) ) )
                                                                                                                                    | ! [ZE: $i] :
                                                                                                                                        ( $false
                                                                                                                                        | ~ ( ZE @ ( ZD @ r1 ) ) )
                                                                                                                                    | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                            | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                        | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                    | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                            | ~ ( X @ ( W @ r1 ) ) )
                                                                                                        | ~ ( W @ ( V @ r1 ) ) )
                                                                                                    | ~ ( V @ ( U @ r1 ) ) )
                                                                                                | ~ ( U @ ( T @ r1 ) ) )
                                                                                            | ~ ( T @ ( S @ r1 ) ) )
                                                                                        | ~ ( S @ ( R @ r1 ) ) )
                                                                                    | ~ ( R @ ( Q @ r1 ) ) )
                                                                                | ~ ( Q @ ( P @ r1 ) ) )
                                                                            | ~ ( P @ ( O @ r1 ) ) )
                                                                        | ~ ( O @ ( N @ r1 ) ) )
                                                                    | ~ ( N @ ( M @ r1 ) ) )
                                                                | ~ ( M @ ( L @ r1 ) ) )
                                                            | ~ ( L @ ( K @ r1 ) ) )
                                                        | ~ ( K @ ( J @ r1 ) ) )
                                                    | ~ ( J @ ( I @ r1 ) ) )
                                                | ~ ( I @ ( H @ r1 ) ) )
                                            | ~ ( H @ ( G @ r1 ) ) )
                                        | ~ ( G @ ( F @ r1 ) ) )
                                    | ~ ( F @ ( E @ r1 ) ) )
                                | ~ ( E @ ( D @ r1 ) ) )
                            | ~ ( D @ ( C @ r1 ) ) ) )
                    | ~ ( C @ ( B @ r1 ) ) )
              | ~ ( B @ ( A @ r1 ) ) )
          | ! [B: $i] :
              ( ! [C: $i] :
                  ( ~ ( C @ p1 )
                  | ~ ( C @ ( B @ r1 ) ) )
              | ~ ( B @ p30 )
              | ~ ( B @ ( A @ r1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

thf(2,negated_conjecture,
    ~ ~ ? [A: $i] :
          ~ ( ! [B: $i] :
                ( ~ ! [C: $i] :
                      ( ~ ( ! [D: $i] :
                              ( ( ( D @ p1 )
                                & ( D @ p2 ) )
                              | ( ~ ( D @ p2 )
                                & ~ ( D @ p1 ) )
                              | ( ( D @ p2 )
                                & ( D @ p3 ) )
                              | ( ~ ( D @ p3 )
                                & ~ ( D @ p2 ) )
                              | ( ( D @ p3 )
                                & ( D @ p4 ) )
                              | ( ~ ( D @ p4 )
                                & ~ ( D @ p3 ) )
                              | ( ( D @ p4 )
                                & ( D @ p5 ) )
                              | ( ~ ( D @ p5 )
                                & ~ ( D @ p4 ) )
                              | ( ( D @ p5 )
                                & ( D @ p6 ) )
                              | ( ~ ( D @ p6 )
                                & ~ ( D @ p5 ) )
                              | ( ( D @ p6 )
                                & ( D @ p7 ) )
                              | ( ~ ( D @ p7 )
                                & ~ ( D @ p6 ) )
                              | ( ( D @ p7 )
                                & ( D @ p8 ) )
                              | ( ~ ( D @ p8 )
                                & ~ ( D @ p7 ) )
                              | ( ( D @ p8 )
                                & ( D @ p9 ) )
                              | ( ~ ( D @ p9 )
                                & ~ ( D @ p8 ) )
                              | ( ( D @ p9 )
                                & ( D @ p10 ) )
                              | ( ~ ( D @ p10 )
                                & ~ ( D @ p9 ) )
                              | ( ( D @ p10 )
                                & ( D @ p11 ) )
                              | ( ~ ( D @ p11 )
                                & ~ ( D @ p10 ) )
                              | ( ( D @ p11 )
                                & ( D @ p12 ) )
                              | ( ~ ( D @ p12 )
                                & ~ ( D @ p11 ) )
                              | ( ( D @ p12 )
                                & ( D @ p13 ) )
                              | ( ~ ( D @ p13 )
                                & ~ ( D @ p12 ) )
                              | ( ( D @ p13 )
                                & ( D @ p14 ) )
                              | ( ~ ( D @ p14 )
                                & ~ ( D @ p13 ) )
                              | ( ( D @ p14 )
                                & ( D @ p15 ) )
                              | ( ~ ( D @ p15 )
                                & ~ ( D @ p14 ) )
                              | ( ( D @ p15 )
                                & ( D @ p16 ) )
                              | ( ~ ( D @ p16 )
                                & ~ ( D @ p15 ) )
                              | ( ( D @ p16 )
                                & ( D @ p17 ) )
                              | ( ~ ( D @ p17 )
                                & ~ ( D @ p16 ) )
                              | ( ( D @ p17 )
                                & ( D @ p18 ) )
                              | ( ~ ( D @ p18 )
                                & ~ ( D @ p17 ) )
                              | ( ( D @ p18 )
                                & ( D @ p19 ) )
                              | ( ~ ( D @ p19 )
                                & ~ ( D @ p18 ) )
                              | ( ( D @ p19 )
                                & ( D @ p20 ) )
                              | ( ~ ( D @ p20 )
                                & ~ ( D @ p19 ) )
                              | ( ( D @ p20 )
                                & ( D @ p21 ) )
                              | ( ~ ( D @ p21 )
                                & ~ ( D @ p20 ) )
                              | ( ( D @ p21 )
                                & ( D @ p22 ) )
                              | ( ~ ( D @ p22 )
                                & ~ ( D @ p21 ) )
                              | ( ( D @ p22 )
                                & ( D @ p23 ) )
                              | ( ~ ( D @ p23 )
                                & ~ ( D @ p22 ) )
                              | ( ( D @ p23 )
                                & ( D @ p24 ) )
                              | ( ~ ( D @ p24 )
                                & ~ ( D @ p23 ) )
                              | ( ( D @ p24 )
                                & ( D @ p25 ) )
                              | ( ~ ( D @ p25 )
                                & ~ ( D @ p24 ) )
                              | ( ( D @ p25 )
                                & ( D @ p26 ) )
                              | ( ~ ( D @ p26 )
                                & ~ ( D @ p25 ) )
                              | ( ( D @ p26 )
                                & ( D @ p27 ) )
                              | ( ~ ( D @ p27 )
                                & ~ ( D @ p26 ) )
                              | ( ( D @ p27 )
                                & ( D @ p28 ) )
                              | ( ~ ( D @ p28 )
                                & ~ ( D @ p27 ) )
                              | ( ( D @ p28 )
                                & ( D @ p29 ) )
                              | ( ~ ( D @ p29 )
                                & ~ ( D @ p28 ) )
                              | ~ ( D @ ( C @ r1 ) ) )
                          | ! [D: $i] :
                              ( ( D @ p30 )
                              | ~ ( D @ ( C @ r1 ) ) )
                          | ~ ! [D: $i] :
                                ( ~ ( ( ( D @ p1 )
                                      & ~ ( D @ p2 ) )
                                    | ( ~ ( D @ p1 )
                                      & ( D @ p2 ) ) )
                                | ~ ( D @ ( C @ r1 ) ) )
                          | ! [D: $i] :
                              ( ~ ! [E: $i] :
                                    ( ~ ( ( ( E @ p2 )
                                          & ~ ( E @ p3 ) )
                                        | ( ~ ( E @ p2 )
                                          & ( E @ p3 ) ) )
                                    | ~ ( E @ ( D @ r1 ) ) )
                              | ! [E: $i] :
                                  ( ~ ! [F: $i] :
                                        ( ~ ( ( ( F @ p3 )
                                              & ~ ( F @ p4 ) )
                                            | ( ~ ( F @ p3 )
                                              & ( F @ p4 ) ) )
                                        | ~ ( F @ ( E @ r1 ) ) )
                                  | ! [F: $i] :
                                      ( ~ ! [G: $i] :
                                            ( ~ ( ( ( G @ p4 )
                                                  & ~ ( G @ p5 ) )
                                                | ( ~ ( G @ p4 )
                                                  & ( G @ p5 ) ) )
                                            | ~ ( G @ ( F @ r1 ) ) )
                                      | ! [G: $i] :
                                          ( ~ ! [H: $i] :
                                                ( ~ ( ( ( H @ p5 )
                                                      & ~ ( H @ p6 ) )
                                                    | ( ~ ( H @ p5 )
                                                      & ( H @ p6 ) ) )
                                                | ~ ( H @ ( G @ r1 ) ) )
                                          | ! [H: $i] :
                                              ( ~ ! [I: $i] :
                                                    ( ~ ( ( ( I @ p6 )
                                                          & ~ ( I @ p7 ) )
                                                        | ( ~ ( I @ p6 )
                                                          & ( I @ p7 ) ) )
                                                    | ~ ( I @ ( H @ r1 ) ) )
                                              | ! [I: $i] :
                                                  ( ~ ! [J: $i] :
                                                        ( ~ ( ( ( J @ p7 )
                                                              & ~ ( J @ p8 ) )
                                                            | ( ~ ( J @ p7 )
                                                              & ( J @ p8 ) ) )
                                                        | ~ ( J @ ( I @ r1 ) ) )
                                                  | ! [J: $i] :
                                                      ( ~ ! [K: $i] :
                                                            ( ~ ( ( ( K @ p8 )
                                                                  & ~ ( K @ p9 ) )
                                                                | ( ~ ( K @ p8 )
                                                                  & ( K @ p9 ) ) )
                                                            | ~ ( K @ ( J @ r1 ) ) )
                                                      | ! [K: $i] :
                                                          ( ~ ! [L: $i] :
                                                                ( ~ ( ( ( L @ p9 )
                                                                      & ~ ( L @ p10 ) )
                                                                    | ( ~ ( L @ p9 )
                                                                      & ( L @ p10 ) ) )
                                                                | ~ ( L @ ( K @ r1 ) ) )
                                                          | ! [L: $i] :
                                                              ( ~ ! [M: $i] :
                                                                    ( ~ ( ( ( M @ p10 )
                                                                          & ~ ( M @ p11 ) )
                                                                        | ( ~ ( M @ p10 )
                                                                          & ( M @ p11 ) ) )
                                                                    | ~ ( M @ ( L @ r1 ) ) )
                                                              | ! [M: $i] :
                                                                  ( ~ ! [N: $i] :
                                                                        ( ~ ( ( ( N @ p11 )
                                                                              & ~ ( N @ p12 ) )
                                                                            | ( ~ ( N @ p11 )
                                                                              & ( N @ p12 ) ) )
                                                                        | ~ ( N @ ( M @ r1 ) ) )
                                                                  | ! [N: $i] :
                                                                      ( ~ ! [O: $i] :
                                                                            ( ~ ( ( ( O @ p12 )
                                                                                  & ~ ( O @ p13 ) )
                                                                                | ( ~ ( O @ p12 )
                                                                                  & ( O @ p13 ) ) )
                                                                            | ~ ( O @ ( N @ r1 ) ) )
                                                                      | ! [O: $i] :
                                                                          ( ~ ! [P: $i] :
                                                                                ( ~ ( ( ( P @ p13 )
                                                                                      & ~ ( P @ p14 ) )
                                                                                    | ( ~ ( P @ p13 )
                                                                                      & ( P @ p14 ) ) )
                                                                                | ~ ( P @ ( O @ r1 ) ) )
                                                                          | ! [P: $i] :
                                                                              ( ~ ! [Q: $i] :
                                                                                    ( ~ ( ( ( Q @ p14 )
                                                                                          & ~ ( Q @ p15 ) )
                                                                                        | ( ~ ( Q @ p14 )
                                                                                          & ( Q @ p15 ) ) )
                                                                                    | ~ ( Q @ ( P @ r1 ) ) )
                                                                              | ! [Q: $i] :
                                                                                  ( ~ ! [R: $i] :
                                                                                        ( ~ ( ( ( R @ p15 )
                                                                                              & ~ ( R @ p16 ) )
                                                                                            | ( ~ ( R @ p15 )
                                                                                              & ( R @ p16 ) ) )
                                                                                        | ~ ( R @ ( Q @ r1 ) ) )
                                                                                  | ! [R: $i] :
                                                                                      ( ~ ! [S: $i] :
                                                                                            ( ~ ( ( ( S @ p16 )
                                                                                                  & ~ ( S @ p17 ) )
                                                                                                | ( ~ ( S @ p16 )
                                                                                                  & ( S @ p17 ) ) )
                                                                                            | ~ ( S @ ( R @ r1 ) ) )
                                                                                      | ! [S: $i] :
                                                                                          ( ~ ! [T: $i] :
                                                                                                ( ~ ( ( ( T @ p17 )
                                                                                                      & ~ ( T @ p18 ) )
                                                                                                    | ( ~ ( T @ p17 )
                                                                                                      & ( T @ p18 ) ) )
                                                                                                | ~ ( T @ ( S @ r1 ) ) )
                                                                                          | ! [T: $i] :
                                                                                              ( ~ ! [U: $i] :
                                                                                                    ( ~ ( ( ( U @ p18 )
                                                                                                          & ~ ( U @ p19 ) )
                                                                                                        | ( ~ ( U @ p18 )
                                                                                                          & ( U @ p19 ) ) )
                                                                                                    | ~ ( U @ ( T @ r1 ) ) )
                                                                                              | ! [U: $i] :
                                                                                                  ( ~ ! [V: $i] :
                                                                                                        ( ~ ( ( ( V @ p19 )
                                                                                                              & ~ ( V @ p20 ) )
                                                                                                            | ( ~ ( V @ p19 )
                                                                                                              & ( V @ p20 ) ) )
                                                                                                        | ~ ( V @ ( U @ r1 ) ) )
                                                                                                  | ! [V: $i] :
                                                                                                      ( ~ ! [W: $i] :
                                                                                                            ( ~ ( ( ( W @ p20 )
                                                                                                                  & ~ ( W @ p21 ) )
                                                                                                                | ( ~ ( W @ p20 )
                                                                                                                  & ( W @ p21 ) ) )
                                                                                                            | ~ ( W @ ( V @ r1 ) ) )
                                                                                                      | ! [W: $i] :
                                                                                                          ( ~ ! [X: $i] :
                                                                                                                ( ~ ( ( ( X @ p21 )
                                                                                                                      & ~ ( X @ p22 ) )
                                                                                                                    | ( ~ ( X @ p21 )
                                                                                                                      & ( X @ p22 ) ) )
                                                                                                                | ~ ( X @ ( W @ r1 ) ) )
                                                                                                          | ! [X: $i] :
                                                                                                              ( ~ ! [Y: $i] :
                                                                                                                    ( ~ ( ( ( Y @ p22 )
                                                                                                                          & ~ ( Y @ p23 ) )
                                                                                                                        | ( ~ ( Y @ p22 )
                                                                                                                          & ( Y @ p23 ) ) )
                                                                                                                    | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                              | ! [Y: $i] :
                                                                                                                  ( ~ ! [Z: $i] :
                                                                                                                        ( ~ ( ( ( Z @ p23 )
                                                                                                                              & ~ ( Z @ p24 ) )
                                                                                                                            | ( ~ ( Z @ p23 )
                                                                                                                              & ( Z @ p24 ) ) )
                                                                                                                        | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                  | ! [Z: $i] :
                                                                                                                      ( ~ ! [ZA: $i] :
                                                                                                                            ( ~ ( ( ( ZA @ p24 )
                                                                                                                                  & ~ ( ZA @ p25 ) )
                                                                                                                                | ( ~ ( ZA @ p24 )
                                                                                                                                  & ( ZA @ p25 ) ) )
                                                                                                                            | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                      | ! [ZA: $i] :
                                                                                                                          ( ~ ! [ZB: $i] :
                                                                                                                                ( ~ ( ( ( ZB @ p25 )
                                                                                                                                      & ~ ( ZB @ p26 ) )
                                                                                                                                    | ( ~ ( ZB @ p25 )
                                                                                                                                      & ( ZB @ p26 ) ) )
                                                                                                                                | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                          | ! [ZB: $i] :
                                                                                                                              ( ~ ! [ZC: $i] :
                                                                                                                                    ( ~ ( ( ( ZC @ p26 )
                                                                                                                                          & ~ ( ZC @ p27 ) )
                                                                                                                                        | ( ~ ( ZC @ p26 )
                                                                                                                                          & ( ZC @ p27 ) ) )
                                                                                                                                    | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                              | ! [ZC: $i] :
                                                                                                                                  ( ~ ! [ZD: $i] :
                                                                                                                                        ( ~ ( ( ( ZD @ p27 )
                                                                                                                                              & ~ ( ZD @ p28 ) )
                                                                                                                                            | ( ~ ( ZD @ p27 )
                                                                                                                                              & ( ZD @ p28 ) ) )
                                                                                                                                        | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                  | ! [ZD: $i] :
                                                                                                                                      ( ~ ! [ZE: $i] :
                                                                                                                                            ( ~ ( ( ( ZE @ p28 )
                                                                                                                                                  & ~ ( ZE @ p29 ) )
                                                                                                                                                | ( ~ ( ZE @ p28 )
                                                                                                                                                  & ( ZE @ p29 ) ) )
                                                                                                                                            | ~ ( ZE @ ( ZD @ r1 ) ) )
                                                                                                                                      | ! [ZE: $i] :
                                                                                                                                          ( $false
                                                                                                                                          | ~ ( ZE @ ( ZD @ r1 ) ) )
                                                                                                                                      | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                  | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                              | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                          | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                      | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                  | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                              | ~ ( X @ ( W @ r1 ) ) )
                                                                                                          | ~ ( W @ ( V @ r1 ) ) )
                                                                                                      | ~ ( V @ ( U @ r1 ) ) )
                                                                                                  | ~ ( U @ ( T @ r1 ) ) )
                                                                                              | ~ ( T @ ( S @ r1 ) ) )
                                                                                          | ~ ( S @ ( R @ r1 ) ) )
                                                                                      | ~ ( R @ ( Q @ r1 ) ) )
                                                                                  | ~ ( Q @ ( P @ r1 ) ) )
                                                                              | ~ ( P @ ( O @ r1 ) ) )
                                                                          | ~ ( O @ ( N @ r1 ) ) )
                                                                      | ~ ( N @ ( M @ r1 ) ) )
                                                                  | ~ ( M @ ( L @ r1 ) ) )
                                                              | ~ ( L @ ( K @ r1 ) ) )
                                                          | ~ ( K @ ( J @ r1 ) ) )
                                                      | ~ ( J @ ( I @ r1 ) ) )
                                                  | ~ ( I @ ( H @ r1 ) ) )
                                              | ~ ( H @ ( G @ r1 ) ) )
                                          | ~ ( G @ ( F @ r1 ) ) )
                                      | ~ ( F @ ( E @ r1 ) ) )
                                  | ~ ( E @ ( D @ r1 ) ) )
                              | ~ ( D @ ( C @ r1 ) ) ) )
                      | ~ ( C @ ( B @ r1 ) ) )
                | ~ ( B @ ( A @ r1 ) ) )
            | ! [B: $i] :
                ( ! [C: $i] :
                    ( ~ ( C @ p1 )
                    | ~ ( C @ ( B @ r1 ) ) )
                | ~ ( B @ p30 )
                | ~ ( B @ ( A @ r1 ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ~ ? [A: $i] :
          ~ ( ! [B: $i] :
                ( ~ ! [C: $i] :
                      ( ~ ( ! [D: $i] :
                              ( ( ( D @ p1 )
                                & ( D @ p2 ) )
                              | ( ~ ( D @ p2 )
                                & ~ ( D @ p1 ) )
                              | ( ( D @ p2 )
                                & ( D @ p3 ) )
                              | ( ~ ( D @ p3 )
                                & ~ ( D @ p2 ) )
                              | ( ( D @ p3 )
                                & ( D @ p4 ) )
                              | ( ~ ( D @ p4 )
                                & ~ ( D @ p3 ) )
                              | ( ( D @ p4 )
                                & ( D @ p5 ) )
                              | ( ~ ( D @ p5 )
                                & ~ ( D @ p4 ) )
                              | ( ( D @ p5 )
                                & ( D @ p6 ) )
                              | ( ~ ( D @ p6 )
                                & ~ ( D @ p5 ) )
                              | ( ( D @ p6 )
                                & ( D @ p7 ) )
                              | ( ~ ( D @ p7 )
                                & ~ ( D @ p6 ) )
                              | ( ( D @ p7 )
                                & ( D @ p8 ) )
                              | ( ~ ( D @ p8 )
                                & ~ ( D @ p7 ) )
                              | ( ( D @ p8 )
                                & ( D @ p9 ) )
                              | ( ~ ( D @ p9 )
                                & ~ ( D @ p8 ) )
                              | ( ( D @ p9 )
                                & ( D @ p10 ) )
                              | ( ~ ( D @ p10 )
                                & ~ ( D @ p9 ) )
                              | ( ( D @ p10 )
                                & ( D @ p11 ) )
                              | ( ~ ( D @ p11 )
                                & ~ ( D @ p10 ) )
                              | ( ( D @ p11 )
                                & ( D @ p12 ) )
                              | ( ~ ( D @ p12 )
                                & ~ ( D @ p11 ) )
                              | ( ( D @ p12 )
                                & ( D @ p13 ) )
                              | ( ~ ( D @ p13 )
                                & ~ ( D @ p12 ) )
                              | ( ( D @ p13 )
                                & ( D @ p14 ) )
                              | ( ~ ( D @ p14 )
                                & ~ ( D @ p13 ) )
                              | ( ( D @ p14 )
                                & ( D @ p15 ) )
                              | ( ~ ( D @ p15 )
                                & ~ ( D @ p14 ) )
                              | ( ( D @ p15 )
                                & ( D @ p16 ) )
                              | ( ~ ( D @ p16 )
                                & ~ ( D @ p15 ) )
                              | ( ( D @ p16 )
                                & ( D @ p17 ) )
                              | ( ~ ( D @ p17 )
                                & ~ ( D @ p16 ) )
                              | ( ( D @ p17 )
                                & ( D @ p18 ) )
                              | ( ~ ( D @ p18 )
                                & ~ ( D @ p17 ) )
                              | ( ( D @ p18 )
                                & ( D @ p19 ) )
                              | ( ~ ( D @ p19 )
                                & ~ ( D @ p18 ) )
                              | ( ( D @ p19 )
                                & ( D @ p20 ) )
                              | ( ~ ( D @ p20 )
                                & ~ ( D @ p19 ) )
                              | ( ( D @ p20 )
                                & ( D @ p21 ) )
                              | ( ~ ( D @ p21 )
                                & ~ ( D @ p20 ) )
                              | ( ( D @ p21 )
                                & ( D @ p22 ) )
                              | ( ~ ( D @ p22 )
                                & ~ ( D @ p21 ) )
                              | ( ( D @ p22 )
                                & ( D @ p23 ) )
                              | ( ~ ( D @ p23 )
                                & ~ ( D @ p22 ) )
                              | ( ( D @ p23 )
                                & ( D @ p24 ) )
                              | ( ~ ( D @ p24 )
                                & ~ ( D @ p23 ) )
                              | ( ( D @ p24 )
                                & ( D @ p25 ) )
                              | ( ~ ( D @ p25 )
                                & ~ ( D @ p24 ) )
                              | ( ( D @ p25 )
                                & ( D @ p26 ) )
                              | ( ~ ( D @ p26 )
                                & ~ ( D @ p25 ) )
                              | ( ( D @ p26 )
                                & ( D @ p27 ) )
                              | ( ~ ( D @ p27 )
                                & ~ ( D @ p26 ) )
                              | ( ( D @ p27 )
                                & ( D @ p28 ) )
                              | ( ~ ( D @ p28 )
                                & ~ ( D @ p27 ) )
                              | ( ( D @ p28 )
                                & ( D @ p29 ) )
                              | ( ~ ( D @ p29 )
                                & ~ ( D @ p28 ) )
                              | ~ ( D @ ( C @ r1 ) ) )
                          | ! [D: $i] :
                              ( ( D @ p30 )
                              | ~ ( D @ ( C @ r1 ) ) )
                          | ~ ! [D: $i] :
                                ( ~ ( ( ( D @ p1 )
                                      & ~ ( D @ p2 ) )
                                    | ( ~ ( D @ p1 )
                                      & ( D @ p2 ) ) )
                                | ~ ( D @ ( C @ r1 ) ) )
                          | ! [D: $i] :
                              ( ~ ! [E: $i] :
                                    ( ~ ( ( ( E @ p2 )
                                          & ~ ( E @ p3 ) )
                                        | ( ~ ( E @ p2 )
                                          & ( E @ p3 ) ) )
                                    | ~ ( E @ ( D @ r1 ) ) )
                              | ! [E: $i] :
                                  ( ~ ! [F: $i] :
                                        ( ~ ( ( ( F @ p3 )
                                              & ~ ( F @ p4 ) )
                                            | ( ~ ( F @ p3 )
                                              & ( F @ p4 ) ) )
                                        | ~ ( F @ ( E @ r1 ) ) )
                                  | ! [F: $i] :
                                      ( ~ ! [G: $i] :
                                            ( ~ ( ( ( G @ p4 )
                                                  & ~ ( G @ p5 ) )
                                                | ( ~ ( G @ p4 )
                                                  & ( G @ p5 ) ) )
                                            | ~ ( G @ ( F @ r1 ) ) )
                                      | ! [G: $i] :
                                          ( ~ ! [H: $i] :
                                                ( ~ ( ( ( H @ p5 )
                                                      & ~ ( H @ p6 ) )
                                                    | ( ~ ( H @ p5 )
                                                      & ( H @ p6 ) ) )
                                                | ~ ( H @ ( G @ r1 ) ) )
                                          | ! [H: $i] :
                                              ( ~ ! [I: $i] :
                                                    ( ~ ( ( ( I @ p6 )
                                                          & ~ ( I @ p7 ) )
                                                        | ( ~ ( I @ p6 )
                                                          & ( I @ p7 ) ) )
                                                    | ~ ( I @ ( H @ r1 ) ) )
                                              | ! [I: $i] :
                                                  ( ~ ! [J: $i] :
                                                        ( ~ ( ( ( J @ p7 )
                                                              & ~ ( J @ p8 ) )
                                                            | ( ~ ( J @ p7 )
                                                              & ( J @ p8 ) ) )
                                                        | ~ ( J @ ( I @ r1 ) ) )
                                                  | ! [J: $i] :
                                                      ( ~ ! [K: $i] :
                                                            ( ~ ( ( ( K @ p8 )
                                                                  & ~ ( K @ p9 ) )
                                                                | ( ~ ( K @ p8 )
                                                                  & ( K @ p9 ) ) )
                                                            | ~ ( K @ ( J @ r1 ) ) )
                                                      | ! [K: $i] :
                                                          ( ~ ! [L: $i] :
                                                                ( ~ ( ( ( L @ p9 )
                                                                      & ~ ( L @ p10 ) )
                                                                    | ( ~ ( L @ p9 )
                                                                      & ( L @ p10 ) ) )
                                                                | ~ ( L @ ( K @ r1 ) ) )
                                                          | ! [L: $i] :
                                                              ( ~ ! [M: $i] :
                                                                    ( ~ ( ( ( M @ p10 )
                                                                          & ~ ( M @ p11 ) )
                                                                        | ( ~ ( M @ p10 )
                                                                          & ( M @ p11 ) ) )
                                                                    | ~ ( M @ ( L @ r1 ) ) )
                                                              | ! [M: $i] :
                                                                  ( ~ ! [N: $i] :
                                                                        ( ~ ( ( ( N @ p11 )
                                                                              & ~ ( N @ p12 ) )
                                                                            | ( ~ ( N @ p11 )
                                                                              & ( N @ p12 ) ) )
                                                                        | ~ ( N @ ( M @ r1 ) ) )
                                                                  | ! [N: $i] :
                                                                      ( ~ ! [O: $i] :
                                                                            ( ~ ( ( ( O @ p12 )
                                                                                  & ~ ( O @ p13 ) )
                                                                                | ( ~ ( O @ p12 )
                                                                                  & ( O @ p13 ) ) )
                                                                            | ~ ( O @ ( N @ r1 ) ) )
                                                                      | ! [O: $i] :
                                                                          ( ~ ! [P: $i] :
                                                                                ( ~ ( ( ( P @ p13 )
                                                                                      & ~ ( P @ p14 ) )
                                                                                    | ( ~ ( P @ p13 )
                                                                                      & ( P @ p14 ) ) )
                                                                                | ~ ( P @ ( O @ r1 ) ) )
                                                                          | ! [P: $i] :
                                                                              ( ~ ! [Q: $i] :
                                                                                    ( ~ ( ( ( Q @ p14 )
                                                                                          & ~ ( Q @ p15 ) )
                                                                                        | ( ~ ( Q @ p14 )
                                                                                          & ( Q @ p15 ) ) )
                                                                                    | ~ ( Q @ ( P @ r1 ) ) )
                                                                              | ! [Q: $i] :
                                                                                  ( ~ ! [R: $i] :
                                                                                        ( ~ ( ( ( R @ p15 )
                                                                                              & ~ ( R @ p16 ) )
                                                                                            | ( ~ ( R @ p15 )
                                                                                              & ( R @ p16 ) ) )
                                                                                        | ~ ( R @ ( Q @ r1 ) ) )
                                                                                  | ! [R: $i] :
                                                                                      ( ~ ! [S: $i] :
                                                                                            ( ~ ( ( ( S @ p16 )
                                                                                                  & ~ ( S @ p17 ) )
                                                                                                | ( ~ ( S @ p16 )
                                                                                                  & ( S @ p17 ) ) )
                                                                                            | ~ ( S @ ( R @ r1 ) ) )
                                                                                      | ! [S: $i] :
                                                                                          ( ~ ! [T: $i] :
                                                                                                ( ~ ( ( ( T @ p17 )
                                                                                                      & ~ ( T @ p18 ) )
                                                                                                    | ( ~ ( T @ p17 )
                                                                                                      & ( T @ p18 ) ) )
                                                                                                | ~ ( T @ ( S @ r1 ) ) )
                                                                                          | ! [T: $i] :
                                                                                              ( ~ ! [U: $i] :
                                                                                                    ( ~ ( ( ( U @ p18 )
                                                                                                          & ~ ( U @ p19 ) )
                                                                                                        | ( ~ ( U @ p18 )
                                                                                                          & ( U @ p19 ) ) )
                                                                                                    | ~ ( U @ ( T @ r1 ) ) )
                                                                                              | ! [U: $i] :
                                                                                                  ( ~ ! [V: $i] :
                                                                                                        ( ~ ( ( ( V @ p19 )
                                                                                                              & ~ ( V @ p20 ) )
                                                                                                            | ( ~ ( V @ p19 )
                                                                                                              & ( V @ p20 ) ) )
                                                                                                        | ~ ( V @ ( U @ r1 ) ) )
                                                                                                  | ! [V: $i] :
                                                                                                      ( ~ ! [W: $i] :
                                                                                                            ( ~ ( ( ( W @ p20 )
                                                                                                                  & ~ ( W @ p21 ) )
                                                                                                                | ( ~ ( W @ p20 )
                                                                                                                  & ( W @ p21 ) ) )
                                                                                                            | ~ ( W @ ( V @ r1 ) ) )
                                                                                                      | ! [W: $i] :
                                                                                                          ( ~ ! [X: $i] :
                                                                                                                ( ~ ( ( ( X @ p21 )
                                                                                                                      & ~ ( X @ p22 ) )
                                                                                                                    | ( ~ ( X @ p21 )
                                                                                                                      & ( X @ p22 ) ) )
                                                                                                                | ~ ( X @ ( W @ r1 ) ) )
                                                                                                          | ! [X: $i] :
                                                                                                              ( ~ ! [Y: $i] :
                                                                                                                    ( ~ ( ( ( Y @ p22 )
                                                                                                                          & ~ ( Y @ p23 ) )
                                                                                                                        | ( ~ ( Y @ p22 )
                                                                                                                          & ( Y @ p23 ) ) )
                                                                                                                    | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                              | ! [Y: $i] :
                                                                                                                  ( ~ ! [Z: $i] :
                                                                                                                        ( ~ ( ( ( Z @ p23 )
                                                                                                                              & ~ ( Z @ p24 ) )
                                                                                                                            | ( ~ ( Z @ p23 )
                                                                                                                              & ( Z @ p24 ) ) )
                                                                                                                        | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                  | ! [Z: $i] :
                                                                                                                      ( ~ ! [ZA: $i] :
                                                                                                                            ( ~ ( ( ( ZA @ p24 )
                                                                                                                                  & ~ ( ZA @ p25 ) )
                                                                                                                                | ( ~ ( ZA @ p24 )
                                                                                                                                  & ( ZA @ p25 ) ) )
                                                                                                                            | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                      | ! [ZA: $i] :
                                                                                                                          ( ~ ! [ZB: $i] :
                                                                                                                                ( ~ ( ( ( ZB @ p25 )
                                                                                                                                      & ~ ( ZB @ p26 ) )
                                                                                                                                    | ( ~ ( ZB @ p25 )
                                                                                                                                      & ( ZB @ p26 ) ) )
                                                                                                                                | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                          | ! [ZB: $i] :
                                                                                                                              ( ~ ! [ZC: $i] :
                                                                                                                                    ( ~ ( ( ( ZC @ p26 )
                                                                                                                                          & ~ ( ZC @ p27 ) )
                                                                                                                                        | ( ~ ( ZC @ p26 )
                                                                                                                                          & ( ZC @ p27 ) ) )
                                                                                                                                    | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                              | ! [ZC: $i] :
                                                                                                                                  ( ~ ! [ZD: $i] :
                                                                                                                                        ( ~ ( ( ( ZD @ p27 )
                                                                                                                                              & ~ ( ZD @ p28 ) )
                                                                                                                                            | ( ~ ( ZD @ p27 )
                                                                                                                                              & ( ZD @ p28 ) ) )
                                                                                                                                        | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                  | ! [ZD: $i] :
                                                                                                                                      ( ~ ! [ZE: $i] :
                                                                                                                                            ( ~ ( ( ( ZE @ p28 )
                                                                                                                                                  & ~ ( ZE @ p29 ) )
                                                                                                                                                | ( ~ ( ZE @ p28 )
                                                                                                                                                  & ( ZE @ p29 ) ) )
                                                                                                                                            | ~ ( ZE @ ( ZD @ r1 ) ) )
                                                                                                                                      | ! [ZE: $i] :
                                                                                                                                          ~ ( ZE @ ( ZD @ r1 ) )
                                                                                                                                      | ~ ( ZD @ ( ZC @ r1 ) ) )
                                                                                                                                  | ~ ( ZC @ ( ZB @ r1 ) ) )
                                                                                                                              | ~ ( ZB @ ( ZA @ r1 ) ) )
                                                                                                                          | ~ ( ZA @ ( Z @ r1 ) ) )
                                                                                                                      | ~ ( Z @ ( Y @ r1 ) ) )
                                                                                                                  | ~ ( Y @ ( X @ r1 ) ) )
                                                                                                              | ~ ( X @ ( W @ r1 ) ) )
                                                                                                          | ~ ( W @ ( V @ r1 ) ) )
                                                                                                      | ~ ( V @ ( U @ r1 ) ) )
                                                                                                  | ~ ( U @ ( T @ r1 ) ) )
                                                                                              | ~ ( T @ ( S @ r1 ) ) )
                                                                                          | ~ ( S @ ( R @ r1 ) ) )
                                                                                      | ~ ( R @ ( Q @ r1 ) ) )
                                                                                  | ~ ( Q @ ( P @ r1 ) ) )
                                                                              | ~ ( P @ ( O @ r1 ) ) )
                                                                          | ~ ( O @ ( N @ r1 ) ) )
                                                                      | ~ ( N @ ( M @ r1 ) ) )
                                                                  | ~ ( M @ ( L @ r1 ) ) )
                                                              | ~ ( L @ ( K @ r1 ) ) )
                                                          | ~ ( K @ ( J @ r1 ) ) )
                                                      | ~ ( J @ ( I @ r1 ) ) )
                                                  | ~ ( I @ ( H @ r1 ) ) )
                                              | ~ ( H @ ( G @ r1 ) ) )
                                          | ~ ( G @ ( F @ r1 ) ) )
                                      | ~ ( F @ ( E @ r1 ) ) )
                                  | ~ ( E @ ( D @ r1 ) ) )
                              | ~ ( D @ ( C @ r1 ) ) ) )
                      | ~ ( C @ ( B @ r1 ) ) )
                | ~ ( B @ ( A @ r1 ) ) )
            | ! [B: $i] :
                ( ! [C: $i] :
                    ( ~ ( C @ p1 )
                    | ~ ( C @ ( B @ r1 ) ) )
                | ~ ( B @ p30 )
                | ~ ( B @ ( A @ r1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] : ( A @ ( A @ r1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

thf(211,plain,
    ! [A: $i] : ( A @ ( A @ r1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1 ) )
        & ( B @ ( A @ r1 ) ) )
     => ( C @ ( A @ r1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

thf(213,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1 ) )
        & ( B @ ( A @ r1 ) ) )
     => ( C @ ( A @ r1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(226,plain,
    $false,
    inference(e,[status(thm)],[5,211,213]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL686+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.36  % Computer : n012.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Fri Sep 25 23:23:05 UTC 2026
% 0.10/0.36  % CPUTime  : 
% 0.10/0.36  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.72/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.90/1.04  % [INFO] 	 Parsing done (214ms). 
% 1.32/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.38  % [INFO] 	 eprover registered as external prover. 
% 1.94/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.60/1.65  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.76/1.73  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.76/1.74  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.76/1.76  % [INFO] 	 Type checking passed. 
% 2.76/1.76  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 7.23/3.93  % External prover 'e' found a proof!
% 7.23/3.93  % [INFO] 	 Killing All external provers ... 
% 7.23/3.93  % Time passed: 3444ms (effective reasoning time: 2878ms)
% 7.23/3.94  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.23/3.94  % Axioms used in derivation (2): reflexivity, transitivity
% 7.23/3.94  % No. of inferences in proof: 8
% 7.23/3.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3444 ms resp. 2878 ms w/o parsing
% 7.83/4.03  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.83/4.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------