TSTP Solution File: GRP135-1.002 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.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 11:13:18 EDT 2023

% Result   : Unsatisfiable 2.44s 1.49s
% Output   : Refutation 2.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   24 (   9 unt;   5 typ;   0 def)
%            Number of atoms       :   41 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  140 (  24   ~;  22   |;   0   &;  94   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   36 (   0   ^;  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(product_type,type,
    product: $i > $i > $i > $o ).

thf(group_element_type,type,
    group_element: $i > $o ).

thf(e_1_type,type,
    e_1: $i ).

thf(e_2_type,type,
    e_2: $i ).

thf(equalish_type,type,
    equalish: $i > $i > $o ).

thf(1,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ C @ A @ D )
      | ( product @ D @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).

thf(10,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ C @ A @ D )
      | ( product @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ C )
      | ( equalish @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

thf(24,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ C )
      | ( equalish @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(4,axiom,
    ~ ( equalish @ e_1 @ e_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

thf(14,plain,
    ~ ( equalish @ e_1 @ e_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).

thf(20,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(3,axiom,
    group_element @ e_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

thf(13,plain,
    group_element @ e_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

thf(22,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    group_element @ e_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

thf(12,plain,
    group_element @ e_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product @ A @ B @ e_1 )
      | ( product @ A @ B @ e_2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product @ A @ B @ e_1 )
      | ( product @ A @ B @ e_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ~ ( equalish @ e_2 @ e_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

thf(16,plain,
    ~ ( equalish @ e_2 @ e_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(26,plain,
    $false,
    inference(e,[status(thm)],[10,24,14,20,13,22,12,18,16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n031.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 : Fri May 19 02:15:12 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.84/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/0.94  % [INFO] 	 Parsing done (107ms). 
% 1.24/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.47/1.14  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.19  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.82/1.21  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.82/1.22  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.82/1.22  % [INFO] 	 Type checking passed. 
% 1.82/1.23  % [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 ... 
% 2.44/1.49  % External prover 'e' found a proof!
% 2.44/1.49  % [INFO] 	 Killing All external provers ... 
% 2.44/1.49  % Time passed: 979ms (effective reasoning time: 541ms)
% 2.44/1.49  % 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)>
% 2.44/1.49  % Axioms used in derivation (8): element_2, product_right_cancellation, product_total_function2, product_total_function1, e_1_is_not_e_2, e_2_is_not_e_1, element_1, product_left_cancellation
% 2.44/1.49  % No. of inferences in proof: 19
% 2.44/1.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 979 ms resp. 541 ms w/o parsing
% 2.66/1.51  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.66/1.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------