TSTP Solution File: SYN067-2 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYN067-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:27:11 EDT 2023

% Result   : Unsatisfiable 13.00s 3.22s
% Output   : Refutation 13.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  187 (   3 unt;  14 typ;   0 def)
%            Number of atoms       :  891 (  69 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives : 2553 ( 473   ~; 666   |;   0   &;1414   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   8 con; 0-2 aty)
%            Number of variables   :  357 (   0   ^; 357   !;   0   ?; 357   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_r_type,type,
    big_r: $i > $i > $o ).

thf(sk2_type,type,
    sk2: $i > $i ).

thf(sk1_type,type,
    sk1: $i > $i ).

thf(sk6_type,type,
    sk6: $i > $i ).

thf(sk5_type,type,
    sk5: $i > $i ).

thf(big_p_type,type,
    big_p: $i > $o ).

thf(sk4_type,type,
    sk4: $i > $i ).

thf(sk3_type,type,
    sk3: $i > $i ).

thf(a_type,type,
    a: $i ).

thf(sk11_type,type,
    sk11: $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(sk7_type,type,
    sk7: $i ).

thf(sk9_type,type,
    sk9: $i ).

thf(sk10_type,type,
    sk10: $i ).

thf(52,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk7 @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_52) ).

thf(67,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk7 @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk7 @ D ) ),
    inference(cnf,[status(esa)],[67]) ).

thf(182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk7 @ D )
      | ( ( big_r @ sk10 @ C )
       != ( big_r @ C @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[117]) ).

thf(194,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ sk10 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ sk10 @ sk10 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( sk10 )),bind(B,$thf( B )),bind(C,$thf( sk10 ))]]) ).

thf(198,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ sk10 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ sk10 @ sk10 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    inference(simp,[status(thm)],[194]) ).

thf(207,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ sk10 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ sk10 @ sk10 )
      | ~ ( big_r @ sk7 @ B )
      | ( ( big_r @ B @ A )
       != ( big_r @ sk10 @ sk10 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[198]) ).

thf(215,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk10 @ sk10 )
    | ~ ( big_r @ sk7 @ sk10 ) ),
    inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( sk10 )),bind(B,$thf( sk10 ))]]) ).

thf(217,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk10 @ sk10 )
    | ~ ( big_r @ sk7 @ sk10 ) ),
    inference(simp,[status(thm)],[215]) ).

thf(37,negated_conjecture,
    big_p @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_37) ).

thf(65,plain,
    big_p @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(38,negated_conjecture,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_38) ).

thf(75,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(154,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    inference(cnf,[status(esa)],[75]) ).

thf(166,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ( ( big_p @ sk9 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,154]) ).

thf(169,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ( sk9 != a ) ),
    inference(simp,[status(thm)],[166]) ).

thf(165,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk9 )
    | ( ( big_p @ sk7 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,154]) ).

thf(168,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk9 )
    | ( sk7 != a ) ),
    inference(simp,[status(thm)],[165]) ).

thf(172,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ( sk7 != a )
    | ( ( big_p @ sk9 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,168]) ).

thf(173,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ( sk7 != a )
    | ( sk9 != a ) ),
    inference(simp,[status(thm)],[172]) ).

thf(20,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_20) ).

thf(69,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(40,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk10 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_40) ).

thf(101,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk10 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(54,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk7 @ D )
      | ~ ( big_r @ sk9 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_54) ).

thf(88,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk7 @ D )
      | ~ ( big_r @ sk9 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(36,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_p @ ( sk3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_36) ).

thf(105,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_p @ ( sk3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(139,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_p @ ( sk3 @ A ) ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(248,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( ( big_p @ ( sk3 @ A ) )
       != ( big_p @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[139]) ).

thf(261,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_p @ ( sk1 @ ( sk3 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( C )),bind(B,$thf( sk3 @ C ))]]) ).

thf(272,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_p @ ( sk1 @ ( sk3 @ A ) ) ) ),
    inference(simp,[status(thm)],[261]) ).

thf(384,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
       != ( big_p @ ( sk3 @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[272]) ).

thf(385,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
       != ( big_p @ ( sk3 @ A ) ) ) ),
    inference(simp,[status(thm)],[384]) ).

thf(5,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_5) ).

thf(56,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk5 @ B ) )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_15) ).

thf(110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk5 @ B ) )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(30,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_30) ).

thf(106,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(125,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) ) ),
    inference(cnf,[status(esa)],[106]) ).

thf(35,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ A @ ( sk4 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_35) ).

thf(93,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ A @ ( sk4 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(10,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_10) ).

thf(57,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(13,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_13) ).

thf(78,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(22,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_22) ).

thf(84,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(386,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( sk1 @ ( sk3 @ A ) )
       != ( sk3 @ A ) ) ),
    inference(simp,[status(thm)],[384]) ).

thf(754,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( ( sk1 @ ( sk3 @ A ) )
       != ( sk3 @ A ) )
      | ( ( big_p @ ( sk3 @ A ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[386]) ).

thf(766,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( ( sk1 @ ( sk3 @ A ) )
       != ( sk3 @ A ) )
      | ( ( sk3 @ A )
       != A ) ),
    inference(simp,[status(thm)],[754]) ).

thf(8,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk5 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_8) ).

thf(61,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk5 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(49,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk9 @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_49) ).

thf(89,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk9 @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(28,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_28) ).

thf(74,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(300,plain,
    ( ( big_p @ sk11 )
    | ( sk7 != a )
    | ( sk9 != a )
    | ( ( big_p @ sk8 )
     != ( big_p @ sk11 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[173]) ).

thf(307,plain,
    ( ( big_p @ sk11 )
    | ( sk7 != a )
    | ( sk9 != a )
    | ( sk8 != sk11 ) ),
    inference(simp,[status(thm)],[300]) ).

thf(44,negated_conjecture,
    ( ( big_p @ sk11 )
    | ( big_r @ sk7 @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_44) ).

thf(85,plain,
    ( ( big_p @ sk11 )
    | ( big_r @ sk7 @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(26,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_26) ).

thf(102,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(2,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk2 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_2) ).

thf(60,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk2 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(46,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk10 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_46) ).

thf(70,plain,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk10 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(245,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( big_p @ ( sk1 @ B ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[139]) ).

thf(264,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( big_p @ ( sk3 @ ( sk1 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( sk1 @ C )),bind(B,$thf( C ))]]) ).

thf(273,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( big_p @ ( sk3 @ ( sk1 @ A ) ) ) ),
    inference(simp,[status(thm)],[264]) ).

thf(421,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[273]) ).

thf(424,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( sk3 @ ( sk1 @ A ) )
       != A ) ),
    inference(simp,[status(thm)],[421]) ).

thf(3,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk6 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_3) ).

thf(92,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk6 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(16,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_16) ).

thf(97,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(47,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_47) ).

thf(109,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(53,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk7 @ D )
      | ~ ( big_r @ sk9 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_53) ).

thf(77,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk7 @ D )
      | ~ ( big_r @ sk9 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(50,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_50) ).

thf(96,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(33,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_p @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_33) ).

thf(73,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_p @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(489,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( ( big_r @ sk10 @ sk10 )
     != ( big_r @ sk7 @ sk10 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[217]) ).

thf(503,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( sk10 != sk10 ) ),
    inference(simp,[status(thm)],[489]) ).

thf(508,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 ) ),
    inference(simp,[status(thm)],[503]) ).

thf(420,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
       != ( big_p @ ( sk1 @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[273]) ).

thf(430,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
       != ( big_p @ ( sk1 @ A ) ) ) ),
    inference(simp,[status(thm)],[420]) ).

thf(24,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_p @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_24) ).

thf(64,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_p @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(423,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( big_p @ ( sk3 @ ( sk1 @ A ) ) )
       != ( big_p @ A ) ) ),
    inference(simp,[status(thm)],[421]) ).

thf(509,plain,
    ( ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( ( big_p @ sk10 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,508]) ).

thf(531,plain,
    ( ~ ( big_p @ sk9 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( sk10 != a ) ),
    inference(simp,[status(thm)],[509]) ).

thf(810,plain,
    ( ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( sk10 != a )
    | ( ( big_p @ sk9 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,531]) ).

thf(826,plain,
    ( ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( sk10 != a )
    | ( sk9 != a ) ),
    inference(simp,[status(thm)],[810]) ).

thf(6,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_6) ).

thf(59,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(29,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_29) ).

thf(71,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(27,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_27) ).

thf(86,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(113,plain,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk10 @ B ) ),
    inference(cnf,[status(esa)],[70]) ).

thf(17,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_17) ).

thf(81,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(9,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_9) ).

thf(76,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(31,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_31) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(55,negated_conjecture,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ C )
      | ~ ( big_r @ D @ A )
      | ~ ( big_r @ E @ B )
      | ~ ( big_r @ F @ C )
      | ~ ( big_r @ sk10 @ D )
      | ~ ( big_r @ sk7 @ F )
      | ~ ( big_r @ sk9 @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_55) ).

thf(103,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ C )
      | ~ ( big_r @ D @ A )
      | ~ ( big_r @ E @ B )
      | ~ ( big_r @ F @ C )
      | ~ ( big_r @ sk10 @ D )
      | ~ ( big_r @ sk7 @ F )
      | ~ ( big_r @ sk9 @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(122,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ A @ ( sk4 @ A ) ) ),
    inference(cnf,[status(esa)],[93]) ).

thf(581,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( ( big_p @ ( sk1 @ B ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[122]) ).

thf(601,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( big_r @ ( sk1 @ A ) @ ( sk4 @ ( sk1 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( sk1 @ C )),bind(B,$thf( C ))]]) ).

thf(609,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( big_r @ ( sk1 @ A ) @ ( sk4 @ ( sk1 @ A ) ) ) ),
    inference(simp,[status(thm)],[601]) ).

thf(39,negated_conjecture,
    ( ( big_p @ sk8 )
    | ( big_r @ sk10 @ sk11 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_39) ).

thf(91,plain,
    ( ( big_p @ sk8 )
    | ( big_r @ sk10 @ sk11 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(25,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_25) ).

thf(66,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(19,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_19) ).

thf(108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(383,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[272]) ).

thf(395,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( sk1 @ ( sk3 @ A ) )
       != A ) ),
    inference(simp,[status(thm)],[383]) ).

thf(457,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( ( sk1 @ ( sk3 @ A ) )
       != A )
      | ( ( big_p @ ( sk3 @ A ) )
       != ( big_p @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[395]) ).

thf(462,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( ( sk1 @ ( sk3 @ A ) )
       != A )
      | ( ( sk3 @ A )
       != A ) ),
    inference(simp,[status(thm)],[457]) ).

thf(394,plain,
    ! [A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( ( big_p @ ( sk1 @ ( sk3 @ A ) ) )
       != ( big_p @ A ) ) ),
    inference(simp,[status(thm)],[383]) ).

thf(431,plain,
    ! [A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_p @ A )
      | ( ( sk3 @ ( sk1 @ A ) )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[420]) ).

thf(45,negated_conjecture,
    ( ( big_r @ sk10 @ sk11 )
    | ( big_r @ sk7 @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_45) ).

thf(80,plain,
    ( ( big_r @ sk10 @ sk11 )
    | ( big_r @ sk7 @ sk8 )
    | ~ ( big_p @ sk7 )
    | ~ ( big_p @ sk9 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(167,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ( ( big_p @ sk9 )
     != ( big_p @ sk7 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[154]) ).

thf(171,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ~ ( big_p @ sk7 )
    | ( sk9 != sk7 ) ),
    inference(simp,[status(thm)],[167]) ).

thf(280,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ( sk9 != sk7 )
    | ( ( big_p @ sk7 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,171]) ).

thf(283,plain,
    ( ( big_p @ sk11 )
    | ( big_p @ sk8 )
    | ( sk9 != sk7 )
    | ( sk7 != a ) ),
    inference(simp,[status(thm)],[280]) ).

thf(642,plain,
    ( ( big_p @ sk11 )
    | ( sk9 != sk7 )
    | ( sk7 != a )
    | ( ( big_p @ sk8 )
     != ( big_p @ sk11 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[283]) ).

thf(653,plain,
    ( ( big_p @ sk11 )
    | ( sk9 != sk7 )
    | ( sk7 != a )
    | ( sk8 != sk11 ) ),
    inference(simp,[status(thm)],[642]) ).

thf(112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk5 @ B ) )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(cnf,[status(esa)],[110]) ).

thf(42,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_42) ).

thf(63,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(18,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_18) ).

thf(95,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(21,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_21) ).

thf(72,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ A @ ( sk4 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(11,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_11) ).

thf(99,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_12) ).

thf(87,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_r @ A @ ( sk2 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(23,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_23) ).

thf(104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk3 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(1,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_1) ).

thf(58,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(510,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( ( big_p @ sk9 )
     != ( big_p @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[65,508]) ).

thf(536,plain,
    ( ~ ( big_p @ sk10 )
    | ~ ( big_r @ sk7 @ sk10 )
    | ( sk10 != sk7 )
    | ( sk9 != a ) ),
    inference(simp,[status(thm)],[510]) ).

thf(32,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_32) ).

thf(82,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk1 @ A ) )
      | ( big_r @ B @ ( sk6 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(51,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_51) ).

thf(107,plain,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk9 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk7 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(41,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_41) ).

thf(79,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ sk11 )
      | ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(48,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_48) ).

thf(94,plain,
    ! [B: $i,A: $i] :
      ( ( big_r @ sk10 @ sk11 )
      | ( big_r @ sk7 @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ B @ A )
      | ~ ( big_r @ sk9 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(14,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk5 @ B ) )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_14) ).

thf(68,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ ( sk5 @ B ) )
      | ( big_r @ ( sk2 @ A ) @ ( sk1 @ A ) )
      | ~ ( big_p @ C )
      | ~ ( big_r @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(4,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk6 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_4) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ A @ ( sk6 @ A ) )
      | ( big_r @ B @ ( sk2 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(34,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_34) ).

thf(83,plain,
    ! [B: $i,A: $i] :
      ( ( big_p @ A )
      | ( big_p @ B )
      | ( big_p @ ( sk1 @ B ) )
      | ( big_r @ ( sk4 @ A ) @ ( sk3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(43,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk9 @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_43) ).

thf(100,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ sk8 )
      | ~ ( big_p @ A )
      | ~ ( big_p @ B )
      | ~ ( big_p @ sk7 )
      | ~ ( big_r @ C @ A )
      | ~ ( big_r @ D @ B )
      | ~ ( big_r @ sk10 @ C )
      | ~ ( big_r @ sk9 @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(7,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk5 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38_7) ).

thf(90,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk5 @ A ) )
      | ( big_r @ ( sk2 @ B ) @ ( sk1 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ A @ C )
      | ~ ( big_r @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk1 @ A ) )
      | ( big_r @ ( sk6 @ B ) @ ( sk5 @ B ) )
      | ~ ( big_p @ C )
      | ~ ( big_p @ D )
      | ~ ( big_r @ B @ C )
      | ~ ( big_r @ A @ D ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(2804,plain,
    $false,
    inference(cvc4,[status(thm)],[217,169,173,67,69,101,88,385,56,110,125,93,57,78,106,84,766,61,89,74,307,85,102,60,117,70,424,92,65,97,109,77,96,73,105,508,430,64,423,826,59,71,86,113,81,76,98,103,609,91,66,198,108,462,394,431,80,653,531,112,63,95,154,72,386,99,87,104,171,139,75,58,272,536,82,168,273,107,79,94,283,395,68,62,122,83,100,90,111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN067-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n004.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 19:26:10 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.87/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/1.00  % [INFO] 	 Parsing done (147ms). 
% 1.20/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.88/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.88/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.88/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.24/1.35  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.43/1.44  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.43/1.44  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.43/1.44  % [INFO] 	 Type checking passed. 
% 2.43/1.45  % [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 ... 
% 13.00/3.21  % External prover 'cvc4' found a proof!
% 13.00/3.22  % [INFO] 	 Killing All external provers ... 
% 13.00/3.22  % Time passed: 2687ms (effective reasoning time: 2206ms)
% 13.00/3.22  % 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)>
% 13.00/3.22  % Axioms used in derivation (0): 
% 13.00/3.22  % No. of inferences in proof: 173
% 13.00/3.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2687 ms resp. 2206 ms w/o parsing
% 13.00/3.27  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.00/3.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------