TSTP Solution File: TOP053-1 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : TOP053-1 : TPTP v8.1.2. Released v8.1.0.
% 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 : Tue May  7 08:36:35 EDT 2024

% Result   : Unsatisfiable 2.82s 1.88s
% Output   : Refutation 3.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   56 (  39 unt;  17 typ;   0 def)
%            Number of atoms       :   39 (  38 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  150 (   2   ~;   0   |;   0   &; 148   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;  16 con; 0-14 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tuple_type,type,
    tuple: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(a1_type,type,
    a1: $i ).

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

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

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

thf(a5_type,type,
    a5: $i ).

thf(a6_type,type,
    a6: $i ).

thf(a7_type,type,
    a7: $i ).

thf(a8_type,type,
    a8: $i ).

thf(a9_type,type,
    a9: $i ).

thf(a10_type,type,
    a10: $i ).

thf(a11_type,type,
    a11: $i ).

thf(a12_type,type,
    a12: $i ).

thf(a13_type,type,
    a13: $i ).

thf(a14_type,type,
    a14: $i ).

thf(a15_type,type,
    a15: $i ).

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

thf(7,axiom,
    ( ( product @ a5 @ a6 )
    = a7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).

thf(33,plain,
    ( ( product @ a5 @ a6 )
    = a7 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(17,axiom,
    ( ( product @ a8 @ a2 )
    = a9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).

thf(53,plain,
    ( ( product @ a8 @ a2 )
    = a9 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(11,axiom,
    ( ( product @ a9 @ a1 )
    = a10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).

thf(41,plain,
    ( ( product @ a9 @ a1 )
    = a10 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(13,axiom,
    ( ( product @ a13 @ a8 )
    = a6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).

thf(45,plain,
    ( ( product @ a13 @ a8 )
    = a6 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( product @ ( product @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( product @ ( product @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,axiom,
    ( ( product @ a2 @ a12 )
    = a14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).

thf(49,plain,
    ( ( product @ a2 @ a12 )
    = a14 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(10,axiom,
    ( ( product @ a7 @ a3 )
    = a8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).

thf(39,plain,
    ( ( product @ a7 @ a3 )
    = a8 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ( ( product @ a15 @ a8 )
    = a4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).

thf(35,plain,
    ( ( product @ a15 @ a8 )
    = a4 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ( ( product @ a10 @ a11 )
    = a12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).

thf(31,plain,
    ( ( product @ a10 @ a11 )
    = a12 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(12,axiom,
    ( ( product @ a3 @ a4 )
    = a5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).

thf(43,plain,
    ( ( product @ a3 @ a4 )
    = a5 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(16,axiom,
    ( ( product @ a6 @ a7 )
    = a2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).

thf(51,plain,
    ( ( product @ a6 @ a7 )
    = a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(14,axiom,
    ( ( product @ a14 @ a3 )
    = a15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).

thf(47,plain,
    ( ( product @ a14 @ a3 )
    = a15 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9,axiom,
    ( ( product @ a4 @ a7 )
    = a11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).

thf(37,plain,
    ( ( product @ a4 @ a7 )
    = a11 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( product @ ( product @ A @ B ) @ C )
      = ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( product @ ( product @ A @ B ) @ C )
      = ( product @ ( product @ A @ C ) @ ( product @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ( ( tuple @ a1 @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 )
   != ( tuple @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 @ a15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

thf(20,plain,
    ( ( tuple @ a1 @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 )
   != ( tuple @ a2 @ a3 @ a4 @ a5 @ a6 @ a7 @ a8 @ a9 @ a10 @ a11 @ a12 @ a13 @ a14 @ a15 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(19,axiom,
    ( ( product @ a11 @ a10 )
    = a1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).

thf(57,plain,
    ( ( product @ a11 @ a10 )
    = a1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(5,axiom,
    ( ( product @ a12 @ a3 )
    = a13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).

thf(29,plain,
    ( ( product @ a12 @ a3 )
    = a13 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(18,axiom,
    ( ( product @ a1 @ a2 )
    = a3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).

thf(55,plain,
    ( ( product @ a1 @ a2 )
    = a3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( product @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).

thf(23,plain,
    ! [A: $i] :
      ( ( product @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(63,plain,
    $false,
    inference(e,[status(thm)],[33,53,41,45,27,49,39,35,31,43,51,47,37,25,20,57,29,55,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : TOP053-1 : TPTP v8.1.2. Released v8.1.0.
% 0.17/0.18  % Command  : run_Leo-III %s %d
% 0.18/0.39  % Computer : n009.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40  % CPULimit : 300
% 0.18/0.40  % WCLimit  : 300
% 0.18/0.40  % DateTime : Mon May  6 13:49:09 EDT 2024
% 0.18/0.40  % CPUTime  : 
% 1.00/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.10  % [INFO] 	 Parsing done (133ms). 
% 1.29/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.35  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.36  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.42  % [INFO] 	 Found a conjecture and 18 axioms. Running axiom selection ... 
% 2.00/1.46  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.00/1.47  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.00/1.48  % [INFO] 	 Type checking passed. 
% 2.00/1.48  % [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 ... 
% 2.82/1.87  % External prover 'e' found a proof!
% 2.82/1.87  % [INFO] 	 Killing All external provers ... 
% 2.82/1.87  % Time passed: 1321ms (effective reasoning time: 765ms)
% 2.82/1.87  % 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)>
% 2.82/1.88  % Axioms used in derivation (18): knot_07, involutory_quandle, knot_03, knot_12, knot_13, knot_08, involutory_quandle_02, involutory_quandle_01, knot_04, knot_15, knot_10, knot_14, knot_11, knot_06, knot_05, knot_16, knot, knot_09
% 2.82/1.88  % No. of inferences in proof: 39
% 2.82/1.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1321 ms resp. 765 ms w/o parsing
% 3.17/1.95  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------