TSTP Solution File: GRP525-1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : GRP525-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 10:33:46 EDT 2024

% Result   : Unsatisfiable 10.59s 2.96s
% Output   : Refutation 10.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   49 (  30 unt;   5 typ;   0 def)
%            Number of atoms       :   59 (  58 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  344 (  34   ~;  15   |;   0   &; 295   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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   :   80 (   0   ^  80   !;   0   ?;  80   :)

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

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

thf(a1_type,type,
    a1: $i ).

thf(b1_type,type,
    b1: $i ).

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

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

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
      = C ),
    inference(lifteq,[status(thm)],[8]) ).

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

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ( inverse @ A )
      = ( divide @ ( divide @ B @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ ( divide @ B @ B ) @ A )
      = ( inverse @ A ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(132,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( divide @ C @ ( inverse @ A ) )
        = E )
      | ( ( divide @ ( divide @ B @ B ) @ A )
       != ( divide @ ( divide @ C @ D ) @ ( divide @ E @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,9]) ).

thf(133,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( divide @ F @ G )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).

thf(157,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
      = A ),
    inference(simp,[status(thm)],[133]) ).

thf(207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( inverse @ C ) )
      | ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
       != ( divide @ ( divide @ D @ D ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[157,13]) ).

thf(208,plain,
    ! [B: $i,A: $i] :
      ( ( inverse @ ( inverse @ ( divide @ A @ ( divide @ B @ B ) ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( H )),bind(B,$thf( divide @ K @ K )),bind(C,$thf( inverse @ ( divide @ H @ ( divide @ K @ K ) ) )),bind(D,$thf( K ))]]) ).

thf(238,plain,
    ! [B: $i,A: $i] :
      ( ( inverse @ ( inverse @ ( divide @ A @ ( divide @ B @ B ) ) ) )
      = A ),
    inference(simp,[status(thm)],[208]) ).

thf(270,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( inverse @ ( inverse @ C ) )
        = D )
      | ( ( divide @ A @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) )
       != ( divide @ D @ ( divide @ E @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,238]) ).

thf(271,plain,
    ! [A: $i] :
      ( ( inverse @ ( inverse @ A ) )
      = A ),
    inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( C )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( divide @ C @ G ))]]) ).

thf(303,plain,
    ! [A: $i] :
      ( ( inverse @ ( inverse @ A ) )
      = A ),
    inference(simp,[status(thm)],[271]) ).

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

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

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

thf(467,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ A @ B )
        = F )
      | ( ( divide @ A @ ( divide @ ( divide @ C @ C ) @ B ) )
       != ( divide @ D @ ( divide @ ( divide @ D @ E ) @ ( divide @ F @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,9]) ).

thf(468,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ B @ ( divide @ A @ B ) )
      = A ),
    inference(pattern_uni,[status(thm)],[467:[bind(A,$thf( H )),bind(B,$thf( divide @ G @ H )),bind(C,$thf( H )),bind(D,$thf( H )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).

thf(541,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ B @ ( divide @ A @ B ) )
      = A ),
    inference(simp,[status(thm)],[468]) ).

thf(1,negated_conjecture,
    ( ( multiply @ ( inverse @ a1 ) @ a1 )
   != ( multiply @ ( inverse @ b1 ) @ b1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).

thf(5,plain,
    ( ( multiply @ ( inverse @ a1 ) @ a1 )
   != ( multiply @ ( inverse @ b1 ) @ b1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,plain,
    ( ( multiply @ ( inverse @ a1 ) @ a1 )
   != ( multiply @ ( inverse @ b1 ) @ b1 ) ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( multiply @ ( inverse @ b1 ) @ b1 )
   != ( multiply @ ( inverse @ a1 ) @ a1 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(760,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( multiply @ ( inverse @ a1 ) @ a1 ) )
      | ( ( multiply @ B @ ( divide @ A @ B ) )
       != ( multiply @ ( inverse @ b1 ) @ b1 ) ) ),
    inference(paramod_ordered,[status(thm)],[541,7]) ).

thf(768,plain,
    ! [A: $i] :
      ( ( A
       != ( inverse @ b1 ) )
      | ( ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ A )
       != b1 ) ),
    inference(simp,[status(thm)],[760]) ).

thf(773,plain,
    ( ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ ( inverse @ b1 ) )
   != b1 ),
    inference(simp,[status(thm)],[768]) ).

thf(788,plain,
    ! [B: $i,A: $i] :
      ( ( A != b1 )
      | ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
       != ( divide @ ( multiply @ ( inverse @ a1 ) @ a1 ) @ ( inverse @ b1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,773]) ).

thf(805,plain,
    ! [A: $i] :
      ( ( A
       != ( multiply @ ( inverse @ a1 ) @ a1 ) )
      | ( ( inverse @ ( divide @ b1 @ A ) )
       != ( inverse @ b1 ) ) ),
    inference(simp,[status(thm)],[788]) ).

thf(820,plain,
    ( ( inverse @ ( divide @ b1 @ ( multiply @ ( inverse @ a1 ) @ a1 ) ) )
   != ( inverse @ b1 ) ),
    inference(simp,[status(thm)],[805]) ).

thf(885,plain,
    ! [B: $i,A: $i] :
      ( ( ( inverse @ A )
       != ( inverse @ b1 ) )
      | ( ( divide @ B @ ( inverse @ ( divide @ A @ B ) ) )
       != ( divide @ b1 @ ( multiply @ ( inverse @ a1 ) @ a1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[157,820]) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ( A != b1 )
      | ( B != b1 )
      | ( ( inverse @ ( divide @ A @ B ) )
       != ( multiply @ ( inverse @ a1 ) @ a1 ) ) ),
    inference(simp,[status(thm)],[885]) ).

thf(938,plain,
    ( ( inverse @ ( divide @ b1 @ b1 ) )
   != ( multiply @ ( inverse @ a1 ) @ a1 ) ),
    inference(simp,[status(thm)],[900]) ).

thf(1197,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( inverse @ ( divide @ b1 @ b1 ) ) )
      | ( ( multiply @ B @ ( divide @ A @ B ) )
       != ( multiply @ ( inverse @ a1 ) @ a1 ) ) ),
    inference(paramod_ordered,[status(thm)],[541,938]) ).

thf(1218,plain,
    ! [A: $i] :
      ( ( A
       != ( inverse @ a1 ) )
      | ( ( divide @ ( inverse @ ( divide @ b1 @ b1 ) ) @ A )
       != a1 ) ),
    inference(simp,[status(thm)],[1197]) ).

thf(1222,plain,
    ( ( divide @ ( inverse @ ( divide @ b1 @ b1 ) ) @ ( inverse @ a1 ) )
   != a1 ),
    inference(simp,[status(thm)],[1218]) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( divide @ ( inverse @ A ) @ C )
        = ( inverse @ C ) )
      | ( ( divide @ ( divide @ B @ B ) @ A )
       != ( divide @ D @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[13,13]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
      = ( inverse @ A ) ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( divide @ H @ H )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( divide @ H @ H ))]]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( divide @ ( inverse @ ( divide @ B @ B ) ) @ A )
      = ( inverse @ A ) ),
    inference(simp,[status(thm)],[16]) ).

thf(1400,plain,
    ( ( inverse @ ( inverse @ a1 ) )
   != a1 ),
    inference(rewrite,[status(thm)],[1222,17]) ).

thf(1401,plain,
    ! [A: $i] :
      ( ( A != a1 )
      | ( ( inverse @ ( inverse @ A ) )
       != ( inverse @ ( inverse @ a1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[303,1400]) ).

thf(1402,plain,
    a1 != a1,
    inference(pattern_uni,[status(thm)],[1401:[bind(A,$thf( a1 ))]]) ).

thf(1405,plain,
    $false,
    inference(simp,[status(thm)],[1402]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : GRP525-1 : TPTP v8.1.2. Released v2.6.0.
% 0.09/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May  6 23:52:54 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.83/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.11/0.88  % [INFO] 	 Parsing done (110ms). 
% 1.11/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.13  % [INFO] 	 nitpick registered as external prover. 
% 1.51/1.13  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.18  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.76/1.20  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.76/1.21  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.76/1.21  % [INFO] 	 Type checking passed. 
% 1.76/1.21  % [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 ... 
% 10.59/2.95  % [INFO] 	 Killing All external provers ... 
% 10.59/2.96  % Time passed: 2488ms (effective reasoning time: 2058ms)
% 10.59/2.96  % 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)>
% 10.59/2.96  % Axioms used in derivation (3): single_axiom, inverse, multiply
% 10.59/2.96  % No. of inferences in proof: 44
% 10.59/2.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2488 ms resp. 2058 ms w/o parsing
% 10.94/3.09  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.94/3.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------