TSTP Solution File: ANA009-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA009-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 10:08:45 EDT 2023

% Result   : Unsatisfiable 2.57s 1.61s
% Output   : Refutation 2.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   26 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :   25 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  100 (  12   ~;  10   |;   0   &;  78   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :   18 (   0   ^;  18   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(v_lb_type,type,
    v_lb: $i > $i ).

thf(v_f_type,type,
    v_f: $i > $i ).

thf(t_b_type,type,
    t_b: $i ).

thf(c_0_type,type,
    c_0: $i ).

thf(c_plus_type,type,
    c_plus: $i > $i > $i > $i ).

thf(v_x_type,type,
    v_x: $i ).

thf(c_uminus_type,type,
    c_uminus: $i > $i > $i ).

thf(class_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

thf(class_OrderedGroup_Oab__group__add_type,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

thf(3,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(10,plain,
    class_Ring__and__Field_Oordered__idom @ t_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
        = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
        = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(2,negated_conjecture,
    ~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(9,plain,
    ~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).

thf(17,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).

thf(12,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(8,plain,
    ! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[10,14,9,17,12,8,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA009-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 17:49:51 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.94/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.01  % [INFO] 	 Parsing done (123ms). 
% 1.23/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.57/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.57/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.27  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.85/1.29  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.85/1.30  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.30  % [INFO] 	 Type checking passed. 
% 1.85/1.30  % [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 ... 
% 2.57/1.61  % External prover 'e' found a proof!
% 2.57/1.61  % [INFO] 	 Killing All external provers ... 
% 2.57/1.61  % Time passed: 1097ms (effective reasoning time: 584ms)
% 2.57/1.61  % 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)>
% 2.57/1.61  % Axioms used in derivation (4): cls_OrderedGroup_Oright__minus_0, clsrel_Ring__and__Field_Oordered__idom_37, cls_OrderedGroup_Oadd__le__cancel__right_1, clsrel_Ring__and__Field_Oordered__idom_4
% 2.57/1.61  % No. of inferences in proof: 15
% 2.57/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1097 ms resp. 584 ms w/o parsing
% 2.57/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.57/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------