TSTP Solution File: GRP558-1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP558-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 21:04:18 EDT 2024

% Result   : Unsatisfiable 32.59s 5.92s
% Output   : Refutation 32.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   57 (  34 unt;   5 typ;   0 def)
%            Number of atoms       :   72 (  71 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  494 (  46   ~;  20   |;   0   &; 428   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  117 (   0   ^ 117   !;   0   ?; 117   :)

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

thf(inverse_type,type,
    inverse: $i > $i ).

thf(b2_type,type,
    b2: $i ).

thf(a2_type,type,
    a2: $i ).

thf(divide_type,type,
    divide: $i > $i > $i ).

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

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( divide @ A @ ( inverse @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) ) )
      = B ),
    inference(lifteq,[status(thm)],[7]) ).

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

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( divide @ A @ ( inverse @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ A @ ( inverse @ B ) )
      = ( multiply @ A @ B ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
      = B ),
    inference(rewrite,[status(thm)],[8,10]) ).

thf(16,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ C @ ( divide @ ( multiply @ A @ B ) @ ( divide @ C @ E ) ) )
        = D )
      | ( ( divide @ A @ ( inverse @ B ) )
       != ( divide @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[10,11]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( divide @ B @ ( inverse @ C ) ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( inverse @ F ))]]) ).

thf(23,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( divide @ B @ ( inverse @ C ) ) ) )
      = A ),
    inference(simp,[status(thm)],[17]) ).

thf(55,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ B @ ( divide @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) )
      = A ),
    inference(rewrite,[status(thm)],[23,10]) ).

thf(65,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ E @ ( divide @ B @ ( multiply @ E @ F ) ) )
        = D )
      | ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
       != ( multiply @ D @ F ) ) ),
    inference(paramod_ordered,[status(thm)],[11,55]) ).

thf(66,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ B @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) ) )
      = C ),
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( L )),bind(D,$thf( K )),bind(E,$thf( E )),bind(F,$thf( divide @ ( divide @ I @ L ) @ ( divide @ K @ L ) ))]]) ).

thf(83,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ B @ ( multiply @ A @ ( divide @ ( divide @ B @ D ) @ ( divide @ C @ D ) ) ) ) )
      = C ),
    inference(simp,[status(thm)],[66]) ).

thf(601,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ D @ ( divide @ E @ B ) )
        = F )
      | ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
       != ( multiply @ D @ ( divide @ ( divide @ E @ G ) @ ( divide @ F @ G ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,83]) ).

thf(602,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ B @ B ) )
      = A ),
    inference(pattern_uni,[status(thm)],[601:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).

thf(778,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ C @ ( divide @ D @ A ) )
        = E )
      | ( ( multiply @ A @ ( divide @ B @ B ) )
       != ( multiply @ C @ ( divide @ ( divide @ D @ F ) @ ( divide @ E @ F ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[602,83]) ).

thf(779,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ B @ A ) )
      = B ),
    inference(pattern_uni,[status(thm)],[778:[bind(A,$thf( A )),bind(B,$thf( divide @ G @ H )),bind(C,$thf( A )),bind(D,$thf( G )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).

thf(826,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ ( divide @ B @ A ) )
      = B ),
    inference(simp,[status(thm)],[779]) ).

thf(908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ C @ ( multiply @ A @ B ) )
        = D )
      | ( ( divide @ A @ ( inverse @ B ) )
       != ( divide @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[10,826]) ).

thf(909,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
      = A ),
    inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( inverse @ E )),bind(D,$thf( A ))]]) ).

thf(1009,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ B ) @ ( multiply @ A @ B ) )
      = A ),
    inference(simp,[status(thm)],[909]) ).

thf(2579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ ( inverse @ D ) @ B )
        = C )
      | ( ( multiply @ A @ ( divide @ B @ A ) )
       != ( multiply @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[826,1009]) ).

thf(2580,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
      = B ),
    inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( divide @ E @ F ))]]) ).

thf(2728,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
      = B ),
    inference(simp,[status(thm)],[2580]) ).

thf(1,negated_conjecture,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

thf(4,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(lifteq,[status(thm)],[5]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B != a2 )
      | ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
       != ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,6]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( multiply @ ( inverse @ b2 ) @ b2 ) )
      | ( ( divide @ ( divide @ a2 @ B ) @ ( divide @ A @ B ) )
       != a2 ) ),
    inference(simp,[status(thm)],[12]) ).

thf(26,plain,
    ! [A: $i] :
      ( ( divide @ ( divide @ a2 @ A ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
     != a2 ),
    inference(simp,[status(thm)],[21]) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( divide @ ( divide @ a2 @ C ) @ ( multiply @ A @ B ) )
       != a2 )
      | ( ( divide @ A @ ( inverse @ B ) )
       != ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[10,26]) ).

thf(32,plain,
    ! [A: $i] :
      ( ( divide @ ( divide @ a2 @ ( inverse @ A ) ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
     != a2 ),
    inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(B,$thf( G )),bind(C,$thf( inverse @ G ))]]) ).

thf(37,plain,
    ! [A: $i] :
      ( ( divide @ ( divide @ a2 @ ( inverse @ A ) ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
     != a2 ),
    inference(simp,[status(thm)],[32]) ).

thf(41,plain,
    ! [A: $i] :
      ( ( divide @ ( multiply @ a2 @ A ) @ ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ A ) )
     != a2 ),
    inference(rewrite,[status(thm)],[37,10]) ).

thf(43,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( divide @ ( multiply @ a2 @ D ) @ B )
       != a2 )
      | ( ( multiply @ A @ ( divide @ ( divide @ B @ C ) @ ( divide @ A @ C ) ) )
       != ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[11,41]) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ ( multiply @ a2 @ ( divide @ ( divide @ A @ B ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ B ) ) ) @ A )
     != a2 ),
    inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(B,$thf( J )),bind(C,$thf( M )),bind(D,$thf( divide @ ( divide @ J @ M ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ M ) ))]]) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ ( multiply @ a2 @ ( divide @ ( divide @ A @ B ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ B ) ) ) @ A )
     != a2 ),
    inference(simp,[status(thm)],[44]) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( divide @ A @ C )
       != a2 )
      | ( ( multiply @ A @ ( divide @ B @ B ) )
       != ( multiply @ a2 @ ( divide @ ( divide @ C @ D ) @ ( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ D ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[602,52]) ).

thf(737,plain,
    ( ( divide @ a2 @ ( multiply @ ( inverse @ b2 ) @ b2 ) )
   != a2 ),
    inference(pattern_uni,[status(thm)],[736:[bind(A,$thf( a2 )),bind(B,$thf( divide @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ F )),bind(C,$thf( multiply @ ( inverse @ b2 ) @ b2 )),bind(D,$thf( F ))]]) ).

thf(958,plain,
    ! [B: $i,A: $i] :
      ( ( ( divide @ a2 @ B )
       != a2 )
      | ( ( multiply @ A @ ( divide @ B @ A ) )
       != ( multiply @ ( inverse @ b2 ) @ b2 ) ) ),
    inference(paramod_ordered,[status(thm)],[826,737]) ).

thf(978,plain,
    ! [B: $i,A: $i] :
      ( ( ( divide @ a2 @ B )
       != a2 )
      | ( A
       != ( inverse @ b2 ) )
      | ( ( divide @ B @ A )
       != b2 ) ),
    inference(simp,[status(thm)],[958]) ).

thf(1029,plain,
    ! [A: $i] :
      ( ( ( divide @ a2 @ A )
       != a2 )
      | ( ( divide @ A @ ( inverse @ b2 ) )
       != b2 ) ),
    inference(simp,[status(thm)],[978]) ).

thf(3918,plain,
    ! [A: $i] :
      ( ( ( divide @ a2 @ A )
       != a2 )
      | ( ( multiply @ A @ b2 )
       != b2 ) ),
    inference(rewrite,[status(thm)],[1029,10]) ).

thf(4846,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( divide @ a2 @ C )
       != a2 )
      | ( B != b2 )
      | ( ( multiply @ ( inverse @ ( divide @ A @ B ) ) @ A )
       != ( multiply @ C @ b2 ) ) ),
    inference(paramod_ordered,[status(thm)],[2728,3918]) ).

thf(4847,plain,
    ! [A: $i] :
      ( ( ( divide @ a2 @ ( inverse @ ( divide @ b2 @ A ) ) )
       != a2 )
      | ( A != b2 ) ),
    inference(pattern_uni,[status(thm)],[4846:[bind(A,$thf( b2 )),bind(B,$thf( F )),bind(C,$thf( inverse @ ( divide @ b2 @ F ) ))]]) ).

thf(5197,plain,
    ( ( divide @ a2 @ ( inverse @ ( divide @ b2 @ b2 ) ) )
   != a2 ),
    inference(simp,[status(thm)],[4847]) ).

thf(5441,plain,
    ( ( multiply @ a2 @ ( divide @ b2 @ b2 ) )
   != a2 ),
    inference(rewrite,[status(thm)],[5197,10]) ).

thf(5443,plain,
    ! [B: $i,A: $i] :
      ( ( A != a2 )
      | ( ( multiply @ A @ ( divide @ B @ B ) )
       != ( multiply @ a2 @ ( divide @ b2 @ b2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[602,5441]) ).

thf(5444,plain,
    a2 != a2,
    inference(pattern_uni,[status(thm)],[5443:[bind(A,$thf( a2 )),bind(B,$thf( b2 ))]]) ).

thf(5485,plain,
    $false,
    inference(simp,[status(thm)],[5444]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP558-1 : TPTP v8.2.0. Released v2.6.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n005.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 04:50:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.87/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.94  % [INFO] 	 Parsing done (96ms). 
% 1.20/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.45/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.45/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.77/1.27  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.77/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.77/1.28  % [INFO] 	 Type checking passed. 
% 1.77/1.28  % [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 ... 
% 32.59/5.91  % [INFO] 	 Killing All external provers ... 
% 32.59/5.91  % Time passed: 5397ms (effective reasoning time: 4957ms)
% 32.59/5.91  % Axioms used in derivation (2): single_axiom, multiply
% 32.59/5.91  % No. of inferences in proof: 52
% 32.59/5.92  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5397 ms resp. 4957 ms w/o parsing
% 32.68/5.96  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.68/5.96  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------