TSTP Solution File: RNG038-2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG038-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 21 02:37:31 EDT 2024

% Result   : Unsatisfiable 4.05s 2.37s
% Output   : Refutation 4.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   71 (  19 unt;  10 typ;   0 def)
%            Number of atoms       :  159 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  674 ( 102   ~;  98   |;   0   &; 474   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :  210 (   0   ^ 210   !;   0   ?; 210   :)

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

thf(a_type,type,
    a: $i ).

thf(additive_identity_type,type,
    additive_identity: $i ).

thf(b_type,type,
    b: $i ).

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

thf(sum_type,type,
    sum: $i > $i > $i > $o ).

thf(add_type,type,
    add: $i > $i > $i ).

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

thf(additive_inverse_type,type,
    additive_inverse: $i > $i ).

thf(h_type,type,
    h: $i > $i > $i ).

thf(22,axiom,
    ! [A: $i] : ( product @ additive_identity @ A @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).

thf(69,plain,
    ! [A: $i] : ( product @ additive_identity @ A @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(4,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( product @ A @ F @ G )
      | ( sum @ C @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).

thf(37,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( product @ A @ F @ G )
      | ( sum @ C @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).

thf(52,plain,
    ! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ A @ C @ D )
      | ( product @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).

thf(70,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ A @ C @ D )
      | ( product @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

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

thf(65,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(13,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ E )
      | ~ ( sum @ A @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ F @ B @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).

thf(53,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ E )
      | ~ ( sum @ A @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ F @ B @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ A @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).

thf(41,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ A @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( add @ A @ C ) @ ( add @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).

thf(59,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( add @ A @ C ) @ ( add @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( product @ A @ E @ F )
      | ( product @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).

thf(35,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( product @ A @ E @ F )
      | ( product @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( product @ C @ D @ F )
      | ( product @ A @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).

thf(48,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( product @ C @ D @ F )
      | ( product @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ C @ A @ D )
      | ( product @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).

thf(55,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ C @ A @ D )
      | ( product @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ C @ A @ D )
      | ( sum @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).

thf(79,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ C @ A @ D )
      | ( sum @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(30,axiom,
    product @ a @ b @ additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).

thf(83,plain,
    product @ a @ b @ additive_identity,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ C @ D @ A )
      | ( sum @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).

thf(57,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ C @ D @ A )
      | ( sum @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(27,axiom,
    ! [A: $i] : ( product @ A @ additive_identity @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).

thf(78,plain,
    ! [A: $i] : ( product @ A @ additive_identity @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(17,axiom,
    ! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).

thf(61,plain,
    ! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ A @ C @ D )
      | ( sum @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution1) ).

thf(74,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( sum @ A @ C @ D )
      | ( sum @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(2,negated_conjecture,
    ~ ( equalish @ b @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).

thf(32,plain,
    ~ ( equalish @ b @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ E )
      | ~ ( sum @ A @ D @ F )
      | ~ ( product @ F @ B @ G )
      | ( sum @ C @ E @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).

thf(45,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ B @ E )
      | ~ ( sum @ A @ D @ F )
      | ~ ( product @ F @ B @ G )
      | ( sum @ C @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(19,axiom,
    ! [A: $i] : ( sum @ A @ additive_identity @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).

thf(64,plain,
    ! [A: $i] : ( sum @ A @ additive_identity @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(29,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',multiplication_is_well_defined) ).

thf(81,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)],[29]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_substitution) ).

thf(76,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(5,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ A @ E @ F )
      | ( sum @ C @ D @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).

thf(39,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ A @ E @ F )
      | ( sum @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ C @ D @ F )
      | ( sum @ A @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).

thf(50,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ C @ D @ F )
      | ( sum @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution1) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1,negated_conjecture,
    ~ ( equalish @ a @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).

thf(31,plain,
    ~ ( equalish @ a @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equalish @ A @ additive_identity )
      | ( product @ A @ ( h @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_property) ).

thf(72,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equalish @ A @ additive_identity )
      | ( product @ A @ ( h @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ( sum @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ( sum @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(9,axiom,
    ! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).

thf(47,plain,
    ! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ C @ D @ A )
      | ( product @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( product @ C @ D @ A )
      | ( product @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(84,plain,
    $false,
    inference(e,[status(thm)],[69,37,52,70,65,53,41,59,35,48,55,79,83,57,78,61,74,32,45,64,81,76,39,50,67,31,72,43,47,62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : RNG038-2 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat May 18 12:23:39 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.98/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.14  % [INFO] 	 Parsing done (170ms). 
% 1.43/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.96/1.51  % [INFO] 	 eprover registered as external prover. 
% 1.96/1.52  % [INFO] 	 cvc4 registered as external prover. 
% 1.96/1.52  % [INFO] 	 Scanning for conjecture ... 
% 2.12/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ... 
% 2.25/1.67  % [INFO] 	 Axiom selection finished. Selected 28 axioms (removed 0 axioms). 
% 2.39/1.71  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.39/1.72  % [INFO] 	 Type checking passed. 
% 2.39/1.72  % [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 ... 
% 4.05/2.37  % External prover 'e' found a proof!
% 4.05/2.37  % [INFO] 	 Killing All external provers ... 
% 4.05/2.37  % Time passed: 1891ms (effective reasoning time: 1212ms)
% 4.05/2.37  % Axioms used in derivation (28): product_substitution2, addition_is_well_defined, commutativity_of_addition, additive_inverse_substitution, multiplication_is_well_defined, multiplicative_identity1, associativity_of_multiplication2, sum_substitution3, product_substitution1, distributivity1, closure_of_multiplication, associativity_of_addition2, associativity_of_multiplication1, distributivity4, sum_substitution1, closure_of_addition, distributivity3, sum_substitution2, additive_inverse2, multiply_substitution1, product_substitution3, additive_identity2, distributivity2, associativity_of_addition1, add_substitution1, multiplicative_identity2, a_times_b, some_property
% 4.05/2.37  % No. of inferences in proof: 61
% 4.05/2.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1891 ms resp. 1212 ms w/o parsing
% 4.21/2.49  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.21/2.49  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------