TSTP Solution File: GRP669-1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : GRP669-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 : Tue May  7 07:45:13 EDT 2024

% Result   : Unsatisfiable 15.63s 4.09s
% Output   : Refutation 15.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  101 (  53 unt;   7 typ;   0 def)
%            Number of atoms       :  190 ( 189 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  892 ( 136   ~;  96   |;   0   &; 660   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  139 (   0   ^ 139   !;   0   ?; 139   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mult_type,type,
    mult: $i > $i > $i ).

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

thf(b_type,type,
    b: $i ).

thf(c_type,type,
    c: $i ).

thf(ld_type,type,
    ld: $i > $i > $i ).

thf(rd_type,type,
    rd: $i > $i > $i ).

thf(unit_type,type,
    unit: $i ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    inference(lifteq,[status(thm)],[19]) ).

thf(1,negated_conjecture,
    ( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
   != ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(12,plain,
    ( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
   != ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,plain,
    ( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
   != ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(14,plain,
    ( ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b )
   != ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(291,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
      | ( ( mult @ ( rd @ A @ B ) @ B )
       != ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[20,14]) ).

thf(316,plain,
    ! [A: $i] :
      ( ( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ A )
       != ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) )
      | ( A != b ) ),
    inference(simp,[status(thm)],[291]) ).

thf(384,plain,
    ( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ b )
   != ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) ),
    inference(simp,[status(thm)],[316]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
      = ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
      = ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A )
      = ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) ) ),
    inference(lifteq,[status(thm)],[31]) ).

thf(1237,plain,
    ( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ b )
   != ( mult @ ( mult @ a @ b ) @ ( mult @ c @ a ) ) ),
    inference(rewrite,[status(thm)],[384,32]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    inference(lifteq,[status(thm)],[17]) ).

thf(305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ld @ C @ A )
        = D )
      | ( ( mult @ ( rd @ A @ B ) @ B )
       != ( mult @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[20,18]) ).

thf(306,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ ( rd @ A @ B ) @ A )
      = B ),
    inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).

thf(379,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ ( rd @ A @ B ) @ A )
      = B ),
    inference(simp,[status(thm)],[306]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).

thf(23,plain,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(24,plain,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    inference(lifteq,[status(thm)],[23]) ).

thf(53,plain,
    ( ( ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a )
     != ( mult @ a @ b ) )
    | ( ( mult @ c @ ( mult @ a @ b ) )
     != b ) ),
    inference(simp,[status(thm)],[14]) ).

thf(122,plain,
    ! [A: $i] :
      ( ( ( mult @ A @ a )
       != ( mult @ a @ b ) )
      | ( ( mult @ c @ ( mult @ a @ b ) )
       != b )
      | ( ( mult @ A @ unit )
       != ( mult @ a @ ( mult @ b @ c ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,53]) ).

thf(156,plain,
    ! [A: $i] :
      ( ( A != a )
      | ( b != a )
      | ( ( mult @ c @ ( mult @ a @ b ) )
       != b )
      | ( A != a )
      | ( ( mult @ b @ c )
       != unit ) ),
    inference(simp,[status(thm)],[122]) ).

thf(194,plain,
    ( ( b != a )
    | ( ( mult @ c @ ( mult @ a @ b ) )
     != b )
    | ( ( mult @ b @ c )
     != unit ) ),
    inference(simp,[status(thm)],[156]) ).

thf(209,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( A != b )
      | ( ( mult @ b @ c )
       != unit )
      | ( ( mult @ A @ unit )
       != ( mult @ c @ ( mult @ a @ b ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,194]) ).

thf(223,plain,
    ( ( b != a )
    | ( ( mult @ b @ c )
     != unit )
    | ( c != b )
    | ( ( mult @ a @ b )
     != unit ) ),
    inference(simp,[status(thm)],[209]) ).

thf(243,plain,
    ( ( b != a )
    | ( c != b )
    | ( ( mult @ a @ b )
     != unit )
    | ( ( mult @ b @ c )
     != ( mult @ a @ b ) )
    | ( unit != unit ) ),
    inference(eqfactor_ordered,[status(thm)],[223]) ).

thf(247,plain,
    ( ( b != a )
    | ( c != b )
    | ( ( mult @ a @ b )
     != unit )
    | ( b != a )
    | ( c != b ) ),
    inference(simp,[status(thm)],[243]) ).

thf(258,plain,
    ( ( b != a )
    | ( c != b )
    | ( ( mult @ a @ b )
     != unit ) ),
    inference(simp,[status(thm)],[247]) ).

thf(392,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( c != b )
      | ( A != unit )
      | ( ( mult @ A @ unit )
       != ( mult @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[24,258]) ).

thf(397,plain,
    ( ( b != a )
    | ( c != b )
    | ( unit != a )
    | ( unit != b ) ),
    inference(simp,[status(thm)],[392]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = B ),
    inference(lifteq,[status(thm)],[15]) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
      | ( ( mult @ A @ ( ld @ A @ B ) )
       != ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[16,14]) ).

thf(96,plain,
    ! [A: $i] :
      ( ( A
       != ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) )
      | ( ( ld @ A @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
       != b ) ),
    inference(simp,[status(thm)],[58]) ).

thf(120,plain,
    ( ( ld @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
   != b ),
    inference(simp,[status(thm)],[96]) ).

thf(1106,plain,
    ( ( ld @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ a ) ) @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
   != b ),
    inference(rewrite,[status(thm)],[120,32]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).

thf(25,plain,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(26,plain,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    inference(lifteq,[status(thm)],[25]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    inference(lifteq,[status(thm)],[21]) ).

thf(419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( rd @ A @ C )
        = B )
      | ( ( mult @ unit @ A )
       != ( mult @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[26,22]) ).

thf(420,plain,
    ! [A: $i] :
      ( ( rd @ A @ A )
      = unit ),
    inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).

thf(210,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( ( mult @ c @ ( mult @ a @ b ) )
       != b )
      | ( A != unit )
      | ( ( mult @ A @ unit )
       != ( mult @ b @ c ) ) ),
    inference(paramod_ordered,[status(thm)],[24,194]) ).

thf(226,plain,
    ( ( b != a )
    | ( ( mult @ c @ ( mult @ a @ b ) )
     != b )
    | ( unit != b )
    | ( unit != c ) ),
    inference(simp,[status(thm)],[210]) ).

thf(1041,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( ( mult @ c @ A )
       != b )
      | ( unit != b )
      | ( unit != c )
      | ( ( mult @ A @ unit )
       != ( mult @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[24,226]) ).

thf(1051,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( ( mult @ c @ A )
       != b )
      | ( unit != b )
      | ( unit != c )
      | ( A != a )
      | ( unit != b ) ),
    inference(simp,[status(thm)],[1041]) ).

thf(1078,plain,
    ( ( b != a )
    | ( ( mult @ c @ a )
     != b )
    | ( unit != b )
    | ( unit != c ) ),
    inference(simp,[status(thm)],[1051]) ).

thf(1086,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( A != b )
      | ( unit != b )
      | ( unit != c )
      | ( ( mult @ unit @ A )
       != ( mult @ c @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[26,1078]) ).

thf(1093,plain,
    ( ( b != a )
    | ( unit != b )
    | ( unit != c )
    | ( unit != c )
    | ( b != a ) ),
    inference(simp,[status(thm)],[1086]) ).

thf(1102,plain,
    ( ( b != a )
    | ( unit != b )
    | ( unit != c ) ),
    inference(simp,[status(thm)],[1093]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
      = ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
      = ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C )
      = ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ),
    inference(lifteq,[status(thm)],[27]) ).

thf(474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( mult @ ( mult @ A @ B ) @ D )
        = ( mult @ B @ ( mult @ C @ ( mult @ B @ D ) ) ) )
      | ( ( mult @ unit @ A )
       != ( mult @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[26,28]) ).

thf(475,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ unit ) @ B )
      = ( mult @ unit @ ( mult @ A @ ( mult @ unit @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).

thf(512,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ unit ) @ B )
      = ( mult @ unit @ ( mult @ A @ ( mult @ unit @ B ) ) ) ),
    inference(simp,[status(thm)],[475]) ).

thf(1737,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( mult @ unit @ B ) )
      = ( mult @ A @ B ) ),
    inference(rewrite,[status(thm)],[512,24,26]) ).

thf(394,plain,
    ! [B: $i,A: $i] :
      ( ( b != a )
      | ( c != b )
      | ( B != unit )
      | ( ( mult @ A @ ( ld @ A @ B ) )
       != ( mult @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[16,258]) ).

thf(401,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( c != b )
      | ( A != a )
      | ( ( ld @ A @ unit )
       != b ) ),
    inference(simp,[status(thm)],[394]) ).

thf(404,plain,
    ( ( b != a )
    | ( c != b )
    | ( ( ld @ a @ unit )
     != b ) ),
    inference(simp,[status(thm)],[401]) ).

thf(215,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( A != b )
      | ( ( mult @ b @ c )
       != unit )
      | ( ( mult @ unit @ A )
       != ( mult @ c @ ( mult @ a @ b ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,194]) ).

thf(228,plain,
    ( ( b != a )
    | ( ( mult @ b @ c )
     != unit )
    | ( unit != c )
    | ( ( mult @ a @ b )
     != b ) ),
    inference(simp,[status(thm)],[215]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
      = ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
      = ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
      = ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
      = ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
      = ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
    inference(lifteq,[status(thm)],[33]) ).

thf(39,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( mult @ A @ ( ld @ A @ B ) )
       != ( mult @ C @ unit ) ) ),
    inference(paramod_ordered,[status(thm)],[16,24]) ).

thf(45,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A != C )
      | ( ( ld @ A @ B )
       != unit ) ),
    inference(simp,[status(thm)],[39]) ).

thf(49,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( ld @ B @ A )
       != unit ) ),
    inference(simp,[status(thm)],[45]) ).

thf(393,plain,
    ! [B: $i,A: $i] :
      ( ( b != a )
      | ( c != b )
      | ( A != unit )
      | ( ( mult @ ( rd @ A @ B ) @ B )
       != ( mult @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[20,258]) ).

thf(399,plain,
    ! [A: $i] :
      ( ( b != a )
      | ( c != b )
      | ( ( rd @ unit @ A )
       != a )
      | ( A != b ) ),
    inference(simp,[status(thm)],[393]) ).

thf(406,plain,
    ( ( b != a )
    | ( c != b )
    | ( ( rd @ unit @ b )
     != a ) ),
    inference(simp,[status(thm)],[399]) ).

thf(287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( mult @ ( rd @ A @ B ) @ B )
       != ( mult @ C @ unit ) ) ),
    inference(paramod_ordered,[status(thm)],[20,24]) ).

thf(288,plain,
    ! [A: $i] :
      ( ( rd @ A @ unit )
      = A ),
    inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( rd @ D @ unit ))]]) ).

thf(377,plain,
    ! [A: $i] :
      ( ( rd @ A @ unit )
      = A ),
    inference(simp,[status(thm)],[288]) ).

thf(434,plain,
    ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ ( mult @ a @ b ) ) )
   != ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) ),
    inference(rewrite,[status(thm)],[14,28]) ).

thf(261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ld @ B @ A )
        = C )
      | ( ( mult @ A @ unit )
       != ( mult @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,18]) ).

thf(262,plain,
    ! [A: $i] :
      ( ( ld @ A @ A )
      = unit ),
    inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
      = ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) ),
    inference(lifteq,[status(thm)],[29]) ).

thf(417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( rd @ B @ D )
        = C )
      | ( ( mult @ A @ ( ld @ A @ B ) )
       != ( mult @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[16,22]) ).

thf(418,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ B @ ( ld @ A @ B ) )
      = A ),
    inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).

thf(422,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ B @ ( ld @ A @ B ) )
      = A ),
    inference(simp,[status(thm)],[418]) ).

thf(41,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( mult @ A @ ( ld @ A @ B ) )
       != ( mult @ unit @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[16,26]) ).

thf(42,plain,
    ! [A: $i] :
      ( ( ld @ unit @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( ld @ unit @ E ))]]) ).

thf(47,plain,
    ! [A: $i] :
      ( ( ld @ unit @ A )
      = A ),
    inference(simp,[status(thm)],[42]) ).

thf(3246,plain,
    $false,
    inference(cvc4,[status(thm)],[1237,379,397,1106,420,1102,194,18,1737,404,24,25,20,228,29,28,21,33,17,32,34,22,27,12,49,406,377,434,16,31,26,258,23,262,30,19,422,47,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : GRP669-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10  % Command  : run_Leo-III %s %d
% 0.10/0.28  % Computer : n032.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28  % CPULimit : 300
% 0.10/0.28  % WCLimit  : 300
% 0.10/0.28  % DateTime : Mon May  6 16:12:24 EDT 2024
% 0.10/0.28  % CPUTime  : 
% 0.69/0.69  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.97/0.80  % [INFO] 	 Parsing done (108ms). 
% 0.97/0.80  % [INFO] 	 Running in sequential loop mode. 
% 1.43/1.01  % [INFO] 	 eprover registered as external prover. 
% 1.43/1.01  % [INFO] 	 cvc4 registered as external prover. 
% 1.43/1.02  % [INFO] 	 Scanning for conjecture ... 
% 1.59/1.07  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.59/1.09  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.59/1.11  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.59/1.11  % [INFO] 	 Type checking passed. 
% 1.59/1.11  % [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 ... 
% 15.63/4.08  % External prover 'cvc4' found a proof!
% 15.63/4.08  % [INFO] 	 Killing All external provers ... 
% 15.63/4.08  % Time passed: 3684ms (effective reasoning time: 3275ms)
% 15.63/4.08  % 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)>
% 15.63/4.08  % Axioms used in derivation (10): c05, c08, c01, c03, c06, c02, c07, c10, c09, c04
% 15.63/4.08  % No. of inferences in proof: 94
% 15.63/4.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3684 ms resp. 3275 ms w/o parsing
% 15.63/4.15  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.63/4.15  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------