TSTP Solution File: COL048-1 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : COL048-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n026.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 Jun 24 04:49:38 EDT 2024

% Result   : Unsatisfiable 277.52s 52.96s
% Output   : Refutation 277.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   24 (  16 unt;   4 typ;   0 def)
%            Number of atoms       :   24 (  23 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  170 (  14   ~;   4   |;   0   &; 152   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  33   !;   0   ?;  33   :)

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

thf(combinator_type,type,
    combinator: $i ).

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

thf(m_type,type,
    m: $i ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
      = ( apply @ A @ ( apply @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).

thf(8,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)],[2]) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
      = ( apply @ A @ ( apply @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( apply @ m @ A )
      = ( apply @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).

thf(12,plain,
    ! [A: $i] :
      ( ( apply @ m @ A )
      = ( apply @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( apply @ m @ A )
      = ( apply @ A @ A ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( apply @ A @ ( apply @ B @ C ) )
        = ( apply @ m @ D ) )
      | ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
       != ( apply @ D @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[9,13]) ).

thf(195,plain,
    ! [B: $i,A: $i] :
      ( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
      = ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( apply @ ( apply @ b @ L ) @ J )),bind(D,$thf( apply @ ( apply @ b @ L ) @ J ))]]) ).

thf(254,plain,
    ! [B: $i,A: $i] :
      ( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
      = ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[195]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( A
     != ( apply @ combinator @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).

thf(5,plain,
    ! [A: $i] :
      ( A
     != ( apply @ combinator @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,plain,
    ! [A: $i] :
      ( A
     != ( apply @ combinator @ A ) ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ! [A: $i] :
      ( ( apply @ combinator @ A )
     != A ),
    inference(lifteq,[status(thm)],[6]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ( ( apply @ A @ A )
       != B )
      | ( ( apply @ m @ A )
       != ( apply @ combinator @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[13,7]) ).

thf(16,plain,
    ! [A: $i] :
      ( ( apply @ m @ A )
     != ( apply @ combinator @ ( apply @ A @ A ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( ( apply @ combinator @ ( apply @ m @ A ) )
       != ( apply @ m @ B ) )
      | ( ( apply @ A @ A )
       != ( apply @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[13,16]) ).

thf(28,plain,
    ! [A: $i] :
      ( ( apply @ combinator @ ( apply @ m @ A ) )
     != ( apply @ m @ A ) ),
    inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(140558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) )
       != ( apply @ m @ C ) )
      | ( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
       != ( apply @ combinator @ ( apply @ m @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[254,28]) ).

thf(140559,plain,
    ( ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) )
   != ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) ) ),
    inference(pattern_uni,[status(thm)],[140558:[bind(A,$thf( m )),bind(B,$thf( combinator )),bind(C,$thf( apply @ ( apply @ b @ combinator ) @ m ))]]) ).

thf(144209,plain,
    $false,
    inference(simp,[status(thm)],[140559]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : COL048-1 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d SAT
% 0.11/0.33  % Computer : n026.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Jun 18 15:36:40 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 1.12/1.05  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.43/1.21  % [INFO] 	 Parsing done (162ms). 
% 1.50/1.23  % [INFO] 	 Running in sequential loop mode. 
% 2.04/1.63  % [INFO] 	 nitpick registered as external prover. 
% 2.04/1.64  % [INFO] 	 Scanning for conjecture ... 
% 2.21/1.72  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.21/1.76  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.21/1.77  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.21/1.77  % [INFO] 	 Type checking passed. 
% 2.39/1.78  % [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 ... 
% 277.52/52.95  % [INFO] 	 Killing All external provers ... 
% 277.52/52.95  % Time passed: 52430ms (effective reasoning time: 51714ms)
% 277.52/52.96  % Axioms used in derivation (2): b_definition, m_definition
% 277.52/52.96  % No. of inferences in proof: 20
% 277.52/52.96  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 52430 ms resp. 51714 ms w/o parsing
% 277.52/52.99  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 277.52/52.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------