TSTP Solution File: ITP019_1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 07:47:01 EDT 2024

% Result   : Theorem 3.14s 1.70s
% Output   : Refutation 3.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   27 (   5 unt;  17 typ;   0 def)
%            Number of atoms       :   17 (  16 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (   8   ~;   0   |;   1   &;  30   @)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :   10 (  10 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    9 (   0   ^   9   !;   0   ?;   9   :)

% Comments : 
%------------------------------------------------------------------------------
thf(u_type,type,
    u: $tType ).

thf(d_type,type,
    d: $tType ).

thf(du_type,type,
    du: $tType ).

thf(mono_2Etyop_2Emin_2Ebool_type,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).

thf(mono_2Etyop_2Enum_2Enum_type,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Enum_2E0_2E0_type,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(1,conjecture,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).

thf(2,negated_conjecture,
    ~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
      = ( mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) ).

thf(11,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
      = ( mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ A )
      = ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) ).

thf(14,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ A )
      = ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
    <=> ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(17,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
       => ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) )
      & ( ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 @ A )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 @ mono_2Ec_2Enum_2E0_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(24,plain,
    $false,
    inference(cvc4,[status(thm)],[6,11,14,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP019_1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n012.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 14:37:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.02/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.38/1.06  % [INFO] 	 Parsing done (175ms). 
% 1.38/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.99/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.99/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.99/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.36  % [INFO] 	 Found a conjecture and 46 axioms. Running axiom selection ... 
% 2.32/1.40  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 43 axioms). 
% 2.32/1.41  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.32/1.41  % [INFO] 	 Type checking passed. 
% 2.32/1.41  % [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 ... 
% 3.14/1.70  % External prover 'cvc4' found a proof!
% 3.14/1.70  % [INFO] 	 Killing All external provers ... 
% 3.14/1.70  % Time passed: 1178ms (effective reasoning time: 625ms)
% 3.14/1.70  % 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)>
% 3.14/1.70  % Axioms used in derivation (3): arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1, arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1, thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 3.14/1.70  % No. of inferences in proof: 10
% 3.14/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1178 ms resp. 625 ms w/o parsing
% 3.14/1.77  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.14/1.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------