TSTP Solution File: GRP118-1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP118-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 : Mon May 20 21:03:10 EDT 2024

% Result   : Unsatisfiable 119.28s 22.55s
% Output   : Refutation 119.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   75 (  48 unt;   5 typ;   0 def)
%            Number of atoms       :   94 (  93 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 1019 (  49   ~;  24   |;   0   &; 946   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :  127 (   0   ^ 127   !;   0   ?; 127   :)

% Comments : 
%------------------------------------------------------------------------------
thf(multiply_type,type,
    multiply: $i > $i > $i ).

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

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

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

thf(identity_type,type,
    identity: $i ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
      = B ),
    inference(lifteq,[status(thm)],[6]) ).

thf(17,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ F ) ) @ B ) )
        = E )
      | ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
       != ( multiply @ identity @ ( multiply @ F @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,7]) ).

thf(18,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ C ) @ ( multiply @ identity @ C ) ) ) ) ) @ C ) )
      = B ),
    inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( identity )),bind(B,$thf( N )),bind(C,$thf( multiply @ identity @ N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( multiply @ identity @ ( multiply @ ( multiply @ identity @ N ) @ ( multiply @ identity @ N ) ) ))]]) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ C ) @ ( multiply @ identity @ C ) ) ) ) ) @ C ) )
      = B ),
    inference(simp,[status(thm)],[18]) ).

thf(194,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ B @ F ) )
        = E )
      | ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
       != ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ F ) @ ( multiply @ identity @ F ) ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,29]) ).

thf(195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
      = ( multiply @ A @ ( multiply @ B @ C ) ) ),
    inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( multiply @ identity @ L )),bind(D,$thf( I )),bind(E,$thf( multiply @ ( multiply @ I @ J ) @ ( multiply @ identity @ L ) )),bind(F,$thf( L ))]]) ).

thf(290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
      = ( multiply @ A @ ( multiply @ B @ C ) ) ),
    inference(simp,[status(thm)],[195]) ).

thf(15,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ F @ F ) ) ) )
        = E )
      | ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
       != ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,7]) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
      = ( multiply @ ( multiply @ A @ B ) @ C ) ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( N )),bind(D,$thf( I )),bind(E,$thf( multiply @ ( multiply @ I @ J ) @ N )),bind(F,$thf( multiply @ identity @ ( multiply @ N @ N ) ))]]) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
      = ( multiply @ ( multiply @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[16]) ).

thf(392,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ F ) )
        = E )
      | ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
       != ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ F ) @ ( multiply @ identity @ F ) ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[28,29]) ).

thf(393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ C ) @ ( multiply @ C @ C ) ) )
      = B ),
    inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( G )),bind(B,$thf( multiply @ G @ H )),bind(C,$thf( J )),bind(D,$thf( G )),bind(E,$thf( H )),bind(F,$thf( multiply @ J @ J ))]]) ).

thf(737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ C ) @ ( multiply @ C @ C ) ) )
      = B ),
    inference(simp,[status(thm)],[393]) ).

thf(2204,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) )
        = E )
      | ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
       != ( multiply @ ( multiply @ ( multiply @ D @ ( multiply @ D @ E ) ) @ F ) @ ( multiply @ F @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[290,737]) ).

thf(2205,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ ( multiply @ identity @ identity ) ) )
      = B ),
    inference(pattern_uni,[status(thm)],[2204:[bind(A,$thf( multiply @ I @ ( multiply @ I @ J ) )),bind(B,$thf( identity )),bind(C,$thf( identity )),bind(D,$thf( I )),bind(E,$thf( J )),bind(F,$thf( identity ))]]) ).

thf(2411,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ ( multiply @ identity @ identity ) ) )
      = B ),
    inference(simp,[status(thm)],[2205]) ).

thf(2804,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
      = B ),
    inference(rewrite,[status(thm)],[2411,290]) ).

thf(2888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ C @ ( multiply @ C @ ( multiply @ B @ identity ) ) )
        = D )
      | ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
       != ( multiply @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[2804,2804]) ).

thf(2889,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
      = ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) ),
    inference(pattern_uni,[status(thm)],[2888:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( multiply @ I @ ( multiply @ ( multiply @ I @ J ) @ identity ) ))]]) ).

thf(3161,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
      = ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) ),
    inference(simp,[status(thm)],[2889]) ).

thf(3529,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
      = B ),
    inference(rewrite,[status(thm)],[2804,3161]) ).

thf(4845,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( multiply @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) ) )
        = E )
      | ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
       != ( multiply @ D @ ( multiply @ E @ identity ) ) ) ),
    inference(paramod_ordered,[status(thm)],[290,3529]) ).

thf(4846,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
      = identity ),
    inference(pattern_uni,[status(thm)],[4845:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( identity )),bind(D,$thf( multiply @ F @ G )),bind(E,$thf( identity ))]]) ).

thf(5102,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
      = identity ),
    inference(simp,[status(thm)],[4846]) ).

thf(6632,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ ( multiply @ D @ E ) @ ( multiply @ A @ ( multiply @ B @ C ) ) )
        = identity )
      | ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
       != ( multiply @ ( multiply @ D @ E ) @ ( multiply @ D @ ( multiply @ E @ identity ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[290,5102]) ).

thf(6633,plain,
    ! [A: $i] :
      ( ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
      = identity ),
    inference(pattern_uni,[status(thm)],[6632:[bind(A,$thf( identity )),bind(B,$thf( F )),bind(C,$thf( multiply @ F @ identity )),bind(D,$thf( identity )),bind(E,$thf( F ))]]) ).

thf(7091,plain,
    ! [A: $i] :
      ( ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
      = identity ),
    inference(simp,[status(thm)],[6633]) ).

thf(7601,plain,
    ! [A: $i] :
      ( ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
      = identity ),
    inference(rewrite,[status(thm)],[7091,290]) ).

thf(7740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ B @ ( multiply @ ( multiply @ identity @ D ) @ ( multiply @ D @ D ) ) )
        = C )
      | ( ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
       != ( multiply @ B @ ( multiply @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7601,737]) ).

thf(7741,plain,
    ! [A: $i] :
      ( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ A @ A ) ) )
      = ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
    inference(pattern_uni,[status(thm)],[7740:[bind(A,$thf( identity )),bind(B,$thf( identity )),bind(C,$thf( multiply @ identity @ ( multiply @ identity @ identity ) )),bind(D,$thf( D ))]]) ).

thf(8183,plain,
    ! [A: $i] :
      ( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ A @ A ) ) )
      = ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
    inference(simp,[status(thm)],[7741]) ).

thf(9542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ identity @ ( multiply @ A @ ( multiply @ B @ C ) ) )
        = ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
      | ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
       != ( multiply @ ( multiply @ identity @ D ) @ ( multiply @ D @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[290,8183]) ).

thf(9543,plain,
    ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
    = ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
    inference(pattern_uni,[status(thm)],[9542:[bind(A,$thf( identity )),bind(B,$thf( identity )),bind(C,$thf( identity )),bind(D,$thf( identity ))]]) ).

thf(11767,plain,
    ! [A: $i] :
      ( ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
        = identity )
      | ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
       != ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9543,7601]) ).

thf(11768,plain,
    ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
    = identity ),
    inference(pattern_uni,[status(thm)],[11767:[bind(A,$thf( identity ))]]) ).

thf(12692,plain,
    ( ( multiply @ identity @ ( multiply @ identity @ identity ) )
    = identity ),
    inference(rewrite,[status(thm)],[11768,9543]) ).

thf(12693,plain,
    ( ( multiply @ identity @ identity )
    = identity ),
    inference(rewrite,[status(thm)],[9543,12692]) ).

thf(13832,plain,
    ! [B: $i,A: $i] :
      ( ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
        = B )
      | ( ( multiply @ identity @ identity )
       != ( multiply @ B @ identity ) ) ),
    inference(paramod_ordered,[status(thm)],[12693,3529]) ).

thf(13833,plain,
    ! [A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
      = identity ),
    inference(pattern_uni,[status(thm)],[13832:[bind(A,$thf( A )),bind(B,$thf( identity ))]]) ).

thf(20270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( multiply @ B @ identity )
        = C )
      | ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
       != ( multiply @ B @ ( multiply @ B @ ( multiply @ C @ identity ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13833,3529]) ).

thf(20271,plain,
    ! [A: $i] :
      ( ( multiply @ A @ identity )
      = A ),
    inference(pattern_uni,[status(thm)],[20270:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(21052,plain,
    ! [A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ A ) )
      = identity ),
    inference(rewrite,[status(thm)],[13833,20271]) ).

thf(1,negated_conjecture,
    ( ( multiply @ ( multiply @ a @ b ) @ c )
   != ( multiply @ a @ ( multiply @ b @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).

thf(3,plain,
    ( ( multiply @ ( multiply @ a @ b ) @ c )
   != ( multiply @ a @ ( multiply @ b @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,plain,
    ( ( multiply @ ( multiply @ a @ b ) @ c )
   != ( multiply @ a @ ( multiply @ b @ c ) ) ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( multiply @ ( multiply @ a @ b ) @ c )
   != ( multiply @ a @ ( multiply @ b @ c ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
       != ( multiply @ a @ ( multiply @ b @ c ) ) )
      | ( ( multiply @ ( multiply @ A @ B ) @ C )
       != ( multiply @ ( multiply @ a @ b ) @ c ) ) ),
    inference(paramod_ordered,[status(thm)],[28,5]) ).

thf(386,plain,
    ( ( multiply @ a @ ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) ) )
   != ( multiply @ a @ ( multiply @ b @ c ) ) ),
    inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( c ))]]) ).

thf(775,plain,
    ( ( a != a )
    | ( ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) )
     != ( multiply @ b @ c ) ) ),
    inference(simp,[status(thm)],[386]) ).

thf(898,plain,
    ( ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) )
   != ( multiply @ b @ c ) ),
    inference(simp,[status(thm)],[775]) ).

thf(1249,plain,
    ( ( multiply @ b @ ( multiply @ identity @ ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) )
   != ( multiply @ b @ c ) ),
    inference(rewrite,[status(thm)],[898,290]) ).

thf(2838,plain,
    ! [B: $i,A: $i] :
      ( ( ( multiply @ b @ B )
       != ( multiply @ b @ c ) )
      | ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
       != ( multiply @ identity @ ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2804,1249]) ).

thf(3080,plain,
    ! [B: $i,A: $i] :
      ( ( b != b )
      | ( B != c )
      | ( A != identity )
      | ( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
       != ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) ),
    inference(simp,[status(thm)],[2838]) ).

thf(3122,plain,
    ( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ c ) @ identity ) )
   != ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ),
    inference(simp,[status(thm)],[3080]) ).

thf(3528,plain,
    ( ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) )
   != ( multiply @ identity @ ( multiply @ identity @ ( multiply @ c @ identity ) ) ) ),
    inference(rewrite,[status(thm)],[3122,3161]) ).

thf(4259,plain,
    ( ( identity != identity )
    | ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) )
     != ( multiply @ identity @ ( multiply @ c @ identity ) ) ) ),
    inference(simp,[status(thm)],[3528]) ).

thf(4339,plain,
    ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) )
   != ( multiply @ identity @ ( multiply @ c @ identity ) ) ),
    inference(simp,[status(thm)],[4259]) ).

thf(4770,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( multiply @ identity @ ( multiply @ c @ identity ) ) )
      | ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
       != ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3529,4339]) ).

thf(5028,plain,
    ! [A: $i] :
      ( ( A
       != ( multiply @ c @ c ) )
      | ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ identity ) ) @ identity ) ) )
       != ( multiply @ c @ c ) ) ),
    inference(simp,[status(thm)],[4770]) ).

thf(5261,plain,
    ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ identity ) ) @ identity ) ) )
   != ( multiply @ c @ c ) ),
    inference(simp,[status(thm)],[5028]) ).

thf(21061,plain,
    ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ identity @ ( multiply @ c @ identity ) ) ) )
   != ( multiply @ c @ c ) ),
    inference(rewrite,[status(thm)],[5261,20271]) ).

thf(36953,plain,
    ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) ) )
   != ( multiply @ c @ c ) ),
    inference(rewrite,[status(thm)],[21061,290]) ).

thf(36996,plain,
    ! [A: $i] :
      ( ( A
       != ( multiply @ c @ c ) )
      | ( ( multiply @ A @ identity )
       != ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[20271,36953]) ).

thf(37052,plain,
    ( ( ( multiply @ c @ c )
     != ( multiply @ c @ c ) )
    | ( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) )
     != identity ) ),
    inference(simp,[status(thm)],[36996]) ).

thf(37235,plain,
    ( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) )
   != identity ),
    inference(simp,[status(thm)],[37052]) ).

thf(39491,plain,
    ( ( multiply @ c @ ( multiply @ c @ c ) )
   != identity ),
    inference(rewrite,[status(thm)],[37235,20271]) ).

thf(39500,plain,
    ! [A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ A ) )
     != ( multiply @ c @ ( multiply @ c @ c ) ) ),
    inference(paramod_ordered,[status(thm)],[21052,39491]) ).

thf(39501,plain,
    $false,
    inference(pattern_uni,[status(thm)],[39500:[bind(A,$thf( c ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP118-1 : TPTP v8.2.0. Released v1.2.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n007.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 : Sun May 19 04:19:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.14/0.97  % [INFO] 	 Parsing done (93ms). 
% 1.14/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.65/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.80/1.25  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.80/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.80/1.26  % [INFO] 	 Type checking passed. 
% 1.80/1.26  % [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 ... 
% 119.28/22.55  % [INFO] 	 Killing All external provers ... 
% 119.28/22.55  % Time passed: 22012ms (effective reasoning time: 21567ms)
% 119.28/22.55  % Axioms used in derivation (1): single_axiom
% 119.28/22.55  % No. of inferences in proof: 70
% 119.28/22.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 22012 ms resp. 21567 ms w/o parsing
% 119.28/22.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.28/22.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------