%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP098-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : Fri May 19 11:13:09 EDT 2023

% Result   : Unsatisfiable 3.33s 1.72s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   19 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :   13 (  12 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   88 (   8   ~;   6   |;   0   &;  74   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   10 (   0   ^;  10   !;   0   ?;  10   :)

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

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

thf(a3_type,type,
    a3: $i ).

thf(b3_type,type,
    b3: $i ).

thf(c3_type,type,
    c3: $i ).

thf(a4_type,type,
    a4: $i ).

thf(b4_type,type,
    b4: $i ).

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

thf(1,negated_conjecture,
    ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
     != ( multiply @ ( inverse @ b1 ) @ b1 ) )
    | ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
     != a2 )
    | ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
     != ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
    | ( ( multiply @ a4 @ b4 )
     != ( multiply @ b4 @ a4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).

thf(4,plain,
    ( ( ( multiply @ ( inverse @ a1 ) @ a1 )
     != ( multiply @ ( inverse @ b1 ) @ b1 ) )
    | ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
     != a2 )
    | ( ( multiply @ ( multiply @ a3 @ b3 ) @ c3 )
     != ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ) )
    | ( ( multiply @ a4 @ b4 )
     != ( multiply @ b4 @ a4 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

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(30,plain,
    $false,
    inference(e,[status(thm)],[4,7,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP098-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.13/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n020.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 : Fri May 19 01:58:48 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.95/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/0.97  % [INFO] 	 Parsing done (112ms). 
% 1.25/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.61/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.61/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.26  % [INFO] 	 Found a conjecture and 2 axioms. Running axiom selection ... 
% 1.85/1.28  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.85/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.29  % [INFO] 	 Type checking passed. 
% 1.85/1.29  % [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 ... 
% 3.33/1.72  % External prover 'e' found a proof!
% 3.33/1.72  % [INFO] 	 Killing All external provers ... 
% 3.33/1.72  % Time passed: 1188ms (effective reasoning time: 736ms)
% 3.33/1.72  % 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)>
% 3.33/1.72  % Axioms used in derivation (2): single_axiom, multiply
% 3.33/1.72  % No. of inferences in proof: 7
% 3.33/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1188 ms resp. 736 ms w/o parsing
% 3.33/1.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.33/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------