TSTP Solution File: GRP292-1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP292-1 : TPTP v8.1.2. Released v2.5.0.
% 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 11:13:38 EDT 2023

% Result   : Unsatisfiable 3.52s 1.84s
% Output   : Refutation 3.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   59 (   7 unt;  10 typ;   0 def)
%            Number of atoms       :  105 ( 104 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  264 (  18   ~;  56   |;   0   &; 190   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   18 (   0   ^;  18   !;   0   ?;  18   :)

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

thf(sk_c7_type,type,
    sk_c7: $i ).

thf(sk_c6_type,type,
    sk_c6: $i ).

thf(sk_c5_type,type,
    sk_c5: $i ).

thf(sk_c3_type,type,
    sk_c3: $i ).

thf(sk_c4_type,type,
    sk_c4: $i ).

thf(inverse_type,type,
    inverse: $i > $i ).

thf(sk_c1_type,type,
    sk_c1: $i ).

thf(sk_c2_type,type,
    sk_c2: $i ).

thf(identity_type,type,
    identity: $i ).

thf(22,axiom,
    ! [A: $i] :
      ( ( multiply @ identity @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

thf(89,plain,
    ! [A: $i] :
      ( ( multiply @ identity @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(11,negated_conjecture,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).

thf(41,plain,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(18,negated_conjecture,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).

thf(39,plain,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( multiply @ ( inverse @ A ) @ A )
      = identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

thf(91,plain,
    ! [A: $i] :
      ( ( multiply @ ( inverse @ A ) @ A )
      = identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(17,negated_conjecture,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).

thf(35,plain,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(21,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ sk_c7 @ sk_c6 )
       != sk_c5 )
      | ( ( multiply @ A @ sk_c7 )
       != sk_c6 )
      | ( ( inverse @ A )
       != sk_c7 )
      | ( ( multiply @ B @ sk_c5 )
       != sk_c6 )
      | ( ( inverse @ B )
       != sk_c5 )
      | ( ( multiply @ sk_c5 @ sk_c6 )
       != sk_c7 )
      | ( ( multiply @ C @ D )
       != sk_c6 )
      | ( ( inverse @ C )
       != D )
      | ( ( multiply @ D @ sk_c5 )
       != sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).

thf(31,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( multiply @ sk_c7 @ sk_c6 )
       != sk_c5 )
      | ( ( multiply @ A @ sk_c7 )
       != sk_c6 )
      | ( ( inverse @ A )
       != sk_c7 )
      | ( ( multiply @ B @ sk_c5 )
       != sk_c6 )
      | ( ( inverse @ B )
       != sk_c5 )
      | ( ( multiply @ sk_c5 @ sk_c6 )
       != sk_c7 )
      | ( ( multiply @ C @ D )
       != sk_c6 )
      | ( ( inverse @ C )
       != D )
      | ( ( multiply @ D @ sk_c5 )
       != sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(19,negated_conjecture,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).

thf(43,plain,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(8,negated_conjecture,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).

thf(42,plain,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7,negated_conjecture,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).

thf(37,plain,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,negated_conjecture,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).

thf(25,plain,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ C )
      = ( multiply @ A @ ( multiply @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

thf(93,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ C )
      = ( multiply @ A @ ( multiply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1,negated_conjecture,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).

thf(29,plain,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,negated_conjecture,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).

thf(33,plain,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(20,negated_conjecture,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).

thf(28,plain,
    ( ( ( inverse @ sk_c2 )
      = sk_c5 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(3,negated_conjecture,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).

thf(38,plain,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(15,negated_conjecture,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).

thf(45,plain,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( inverse @ sk_c3 )
      = sk_c4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(9,negated_conjecture,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).

thf(32,plain,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c5 @ sk_c6 )
      = sk_c7 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(2,negated_conjecture,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).

thf(34,plain,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,negated_conjecture,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).

thf(44,plain,
    ( ( ( multiply @ sk_c7 @ sk_c6 )
      = sk_c5 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,negated_conjecture,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).

thf(27,plain,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(16,negated_conjecture,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).

thf(40,plain,
    ( ( ( multiply @ sk_c2 @ sk_c5 )
      = sk_c6 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(10,negated_conjecture,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).

thf(26,plain,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(12,negated_conjecture,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).

thf(36,plain,
    ( ( ( inverse @ sk_c1 )
      = sk_c7 )
    | ( ( multiply @ sk_c4 @ sk_c5 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,negated_conjecture,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).

thf(30,plain,
    ( ( ( multiply @ sk_c1 @ sk_c7 )
      = sk_c6 )
    | ( ( multiply @ sk_c3 @ sk_c4 )
      = sk_c6 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(101,plain,
    $false,
    inference(e,[status(thm)],[89,41,39,91,35,31,43,42,37,25,93,29,33,28,38,45,32,34,44,27,40,26,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP292-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n021.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Fri May 19 02:04:58 EDT 2023
% 0.17/0.38  % CPUTime  : 
% 1.00/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.04  % [INFO] 	 Parsing done (144ms). 
% 1.34/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.01/1.33  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 2.01/1.37  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.23/1.37  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.23/1.38  % [INFO] 	 Type checking passed. 
% 2.23/1.38  % [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 ... 
% 3.52/1.84  % External prover 'e' found a proof!
% 3.52/1.84  % [INFO] 	 Killing All external provers ... 
% 3.52/1.84  % Time passed: 1303ms (effective reasoning time: 785ms)
% 3.52/1.84  % 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)>
% 3.52/1.84  % Axioms used in derivation (3): left_identity, left_inverse, associativity
% 3.52/1.84  % No. of inferences in proof: 49
% 3.52/1.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1303 ms resp. 785 ms w/o parsing
% 3.52/1.88  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/1.88  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------