TSTP Solution File: GRP133-2.003 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP133-2.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 2.29s 1.45s
% Output   : Refutation 2.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   49 (  29 unt;   8 typ;   0 def)
%            Number of atoms       :   69 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  218 (  38   ~;  28   |;   0   &; 152   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   42 (   0   ^;  42   !;   0   ?;  42   :)

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

thf(e_3_type,type,
    e_3: $i ).

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

thf(next_type,type,
    next: $i > $i > $o ).

thf(greater_type,type,
    greater: $i > $i > $o ).

thf(3,axiom,
    ~ ( equalish @ e_3 @ e_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

thf(24,plain,
    ~ ( equalish @ e_3 @ e_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    next @ e_1 @ e_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).

thf(29,plain,
    next @ e_1 @ e_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(15,axiom,
    ~ ( equalish @ e_3 @ e_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

thf(41,plain,
    ~ ( equalish @ e_3 @ e_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,axiom,
    ~ ( equalish @ e_1 @ e_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

thf(27,plain,
    ~ ( equalish @ e_1 @ e_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

thf(49,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)],[19]) ).

thf(14,axiom,
    ~ ( equalish @ e_2 @ e_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

thf(39,plain,
    ~ ( equalish @ e_2 @ e_3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(11,axiom,
    greater @ e_3 @ e_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).

thf(35,plain,
    greater @ e_3 @ e_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    next @ e_2 @ e_3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).

thf(31,plain,
    next @ e_2 @ e_3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product @ A @ B @ e_1 )
      | ( product @ A @ B @ e_2 )
      | ( product @ A @ B @ e_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product @ A @ B @ e_1 )
      | ( product @ A @ B @ e_2 )
      | ( product @ A @ B @ e_3 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ e_1 @ B )
      | ~ ( next @ A @ C )
      | ~ ( greater @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).

thf(47,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ e_1 @ B )
      | ~ ( next @ A @ C )
      | ~ ( greater @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(13,axiom,
    greater @ e_3 @ e_1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).

thf(38,plain,
    greater @ e_3 @ e_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ A @ D )
      | ( product @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(10,axiom,
    ~ ( equalish @ e_1 @ e_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

thf(33,plain,
    ~ ( equalish @ e_1 @ e_3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    greater @ e_2 @ e_1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_1) ).

thf(32,plain,
    greater @ e_2 @ e_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ C )
      | ( equalish @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

thf(45,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)],[17]) ).

thf(4,axiom,
    group_element @ e_3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

thf(26,plain,
    group_element @ e_3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(23,plain,
    group_element @ e_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,axiom,
    ~ ( equalish @ e_2 @ e_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

thf(36,plain,
    ~ ( equalish @ e_2 @ e_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(7,axiom,
    group_element @ e_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

thf(30,plain,
    group_element @ e_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

thf(51,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)],[20]) ).

thf(53,plain,
    $false,
    inference(e,[status(thm)],[24,29,41,27,49,39,35,31,43,47,38,21,33,32,45,26,23,36,30,51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : GRP133-2.003 : TPTP v8.1.2. Released v1.2.0.
% 0.02/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Fri May 19 01:37:43 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.61/0.71  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.83/0.82  % [INFO] 	 Parsing done (108ms). 
% 0.83/0.83  % [INFO] 	 Running in sequential loop mode. 
% 1.37/1.02  % [INFO] 	 eprover registered as external prover. 
% 1.37/1.02  % [INFO] 	 cvc4 registered as external prover. 
% 1.37/1.02  % [INFO] 	 Scanning for conjecture ... 
% 1.37/1.07  % [INFO] 	 Found a conjecture and 19 axioms. Running axiom selection ... 
% 1.55/1.12  % [INFO] 	 Axiom selection finished. Selected 19 axioms (removed 0 axioms). 
% 1.55/1.13  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.55/1.13  % [INFO] 	 Type checking passed. 
% 1.55/1.13  % [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 ... 
% 2.29/1.44  % External prover 'e' found a proof!
% 2.29/1.45  % [INFO] 	 Killing All external provers ... 
% 2.29/1.45  % Time passed: 1004ms (effective reasoning time: 617ms)
% 2.29/1.45  % 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)>
% 2.29/1.45  % Axioms used in derivation (19): e_3_is_not_e_2, e_2_then_e_3, element_2, product_right_cancellation, e_3_greater_e_2, product_total_function2, product_total_function1, e_1_is_not_e_2, element_1, e_1_is_not_e_3, e_3_is_not_e_1, product_left_cancellation, e_1_then_e_2, e_2_is_not_e_3, element_3, e_2_greater_e_1, e_2_is_not_e_1, no_redundancy, e_3_greater_e_1
% 2.29/1.45  % No. of inferences in proof: 41
% 2.29/1.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1004 ms resp. 617 ms w/o parsing
% 2.61/1.49  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.61/1.49  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------