TSTP Solution File: COL002-1 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : COL002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 07:29:08 EDT 2024

% Result   : Unsatisfiable 2.58s 1.64s
% Output   : Refutation 2.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   17 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   11 (  10 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   74 (   2   ~;   0   |;   0   &;  72   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   22 (   0   ^  22   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(apply_type,type,
    apply: $i > $i > $i ).

thf(fixed_pt_type,type,
    fixed_pt: $i ).

thf(s_type,type,
    s: $i ).

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

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

thf(i_type,type,
    i: $i ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( A
     != ( apply @ fixed_pt @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).

thf(6,plain,
    ! [A: $i] :
      ( A
     != ( apply @ fixed_pt @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ s @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ c @ A ) @ B ) @ C )
      = ( apply @ ( apply @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
      = ( apply @ A @ ( apply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( apply @ i @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).

thf(15,plain,
    ! [A: $i] :
      ( ( apply @ i @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(22,plain,
    $false,
    inference(e,[status(thm)],[6,9,13,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COL002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n007.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 14:04:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/1.04  % [INFO] 	 Parsing done (120ms). 
% 1.21/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.31  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.70/1.33  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.94/1.34  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.94/1.34  % [INFO] 	 Type checking passed. 
% 1.94/1.34  % [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 ... 
% 2.58/1.64  % External prover 'e' found a proof!
% 2.58/1.64  % [INFO] 	 Killing All external provers ... 
% 2.58/1.64  % Time passed: 1112ms (effective reasoning time: 588ms)
% 2.58/1.64  % 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)>
% 2.58/1.64  % Axioms used in derivation (4): s_definition, c_definition, b_definition, i_definition
% 2.58/1.64  % No. of inferences in proof: 11
% 2.58/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1112 ms resp. 588 ms w/o parsing
% 2.89/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.89/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------