TSTP Solution File: GRP007-1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP007-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 : Mon May 20 21:02:55 EDT 2024

% Result   : Unsatisfiable 5.64s 2.18s
% Output   : Refutation 5.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   21 (  10 unt;   3 typ;   0 def)
%            Number of atoms       :   35 (  15 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   87 (  17   ~;  13   |;   0   &;  57   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   3 con; 0-3 aty)
%            Number of variables   :   32 (   0   ^  32   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(identity_type,type,
    identity: $i ).

thf(c_type,type,
    c: $i ).

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

thf(10,axiom,
    ! [A: $i] : ( product @ c @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_identity) ).

thf(27,plain,
    ! [A: $i] : ( product @ c @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

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

thf(16,plain,
    ! [A: $i] : ( product @ A @ identity @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

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

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( C = D ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(22,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(328,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ~ ( product @ B @ C @ E )
      | ( ( product @ A @ identity @ A )
       != ( product @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[16,22]) ).

thf(329,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( product @ A @ identity @ B ) ),
    inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity )),bind(D,$thf( A ))]]) ).

thf(366,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( product @ A @ identity @ B ) ),
    inference(simp,[status(thm)],[329]) ).

thf(463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( product @ c @ A @ A )
       != ( product @ B @ identity @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[27,366]) ).

thf(464,plain,
    c = identity,
    inference(pattern_uni,[status(thm)],[463:[bind(A,$thf( identity )),bind(B,$thf( c )),bind(C,$thf( identity ))]]) ).

thf(1,negated_conjecture,
    identity != c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_equals_c) ).

thf(12,plain,
    identity != c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,plain,
    identity != c,
    inference(polarity_switch,[status(thm)],[12]) ).

thf(14,plain,
    c != identity,
    inference(lifteq,[status(thm)],[13]) ).

thf(496,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[464,14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP007-1 : TPTP v8.2.0. Released v1.0.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n014.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun May 19 05:16:09 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.95  % [INFO] 	 Parsing done (99ms). 
% 1.23/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.51/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ... 
% 1.75/1.22  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.86/1.23  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.24  % [INFO] 	 Type checking passed. 
% 1.87/1.24  % [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 ... 
% 5.64/2.17  % [INFO] 	 Killing All external provers ... 
% 5.64/2.18  % Time passed: 1651ms (effective reasoning time: 1211ms)
% 5.64/2.18  % Axioms used in derivation (3): another_left_identity, right_identity, total_function2
% 5.64/2.18  % No. of inferences in proof: 18
% 5.64/2.18  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1651 ms resp. 1211 ms w/o parsing
% 5.66/2.20  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.66/2.20  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------