TSTP Solution File: GRP683+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 11:15:08 EDT 2023

% Result   : Theorem 2.90s 1.77s
% Output   : Refutation 3.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   21 (  15 unt;   3 typ;   0 def)
%            Number of atoms       :   21 (  20 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  189 (   2   ~;   0   |;   3   &; 184   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   41 (   0   ^;  41   !;   0   ?;  41   :)

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

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

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

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
        = ( mult @ A @ C ) )
      & ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
        = ( mult @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
          = ( mult @ A @ C ) )
        & ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
          = ( mult @ A @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( mult @ A @ ( ld @ B @ ( mult @ B @ C ) ) )
          = ( mult @ A @ C ) )
        & ( ( mult @ ( rd @ ( mult @ A @ B ) @ B ) @ C )
          = ( mult @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ld @ A @ ( mult @ A @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

thf(14,plain,
    ! [A: $i] :
      ( ( ld @ A @ ( mult @ A @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( mult @ B @ ( ld @ B @ A ) )
      = ( ld @ B @ ( mult @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

thf(20,plain,
    ! [A: $i,B: $i] :
      ( ( mult @ B @ ( ld @ B @ A ) )
      = ( ld @ B @ ( mult @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( rd @ ( mult @ ( mult @ D @ C ) @ ( rd @ B @ A ) ) @ ( rd @ B @ A ) )
      = ( mult @ D @ ( rd @ ( mult @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).

thf(29,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( rd @ ( mult @ ( mult @ D @ C ) @ ( rd @ B @ A ) ) @ ( rd @ B @ A ) )
      = ( mult @ D @ ( rd @ ( mult @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ld @ B @ ( mult @ B @ ( ld @ A @ A ) ) )
      = ( rd @ ( mult @ ( rd @ B @ B ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).

thf(32,plain,
    ! [A: $i,B: $i] :
      ( ( ld @ B @ ( mult @ B @ ( ld @ A @ A ) ) )
      = ( rd @ ( mult @ ( rd @ B @ B ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( rd @ ( mult @ A @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

thf(17,plain,
    ! [A: $i] :
      ( ( rd @ ( mult @ A @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ld @ ( ld @ D @ C ) @ ( mult @ ( ld @ D @ C ) @ ( mult @ B @ A ) ) )
      = ( mult @ ( ld @ D @ ( mult @ D @ B ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

thf(26,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ld @ ( ld @ D @ C ) @ ( mult @ ( ld @ D @ C ) @ ( mult @ B @ A ) ) )
      = ( mult @ ( ld @ D @ ( mult @ D @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( mult @ ( rd @ B @ A ) @ A )
      = ( rd @ ( mult @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

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

thf(45,plain,
    $false,
    inference(e,[status(thm)],[10,14,20,29,32,17,26,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n009.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
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Fri May 19 01:35:33 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.12/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.12/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.26  % [INFO] 	 Found a conjecture and 7 axioms. Running axiom selection ... 
% 1.80/1.28  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.80/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.80/1.30  % [INFO] 	 Type checking passed. 
% 1.80/1.31  % [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 ... 
% 2.90/1.77  % External prover 'e' found a proof!
% 2.90/1.77  % [INFO] 	 Killing All external provers ... 
% 2.90/1.77  % Time passed: 1231ms (effective reasoning time: 774ms)
% 2.90/1.77  % 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)>
% 2.90/1.77  % Axioms used in derivation (7): f03, f02, f07, f06, f05, f04, f01
% 2.90/1.77  % No. of inferences in proof: 18
% 2.90/1.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1231 ms resp. 774 ms w/o parsing
% 3.36/1.80  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.36/1.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------