TSTP Solution File: ANA023-10 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.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 10:08:51 EDT 2023

% Result   : Unsatisfiable 3.04s 1.69s
% Output   : Refutation 3.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   46 (  29 unt;  17 typ;   0 def)
%            Number of atoms       :   29 (  28 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  254 (   2   ~;   0   |;   0   &; 252   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   5 con; 0-4 aty)
%            Number of variables   :   48 (   0   ^;  48   !;   0   ?;  48   :)

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

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

thf(c_minus_type,type,
    c_minus: $i > $i > $i > $i ).

thf(v_k_type,type,
    v_k: $i > $i ).

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

thf(v_g_type,type,
    v_g: $i > $i ).

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

thf(true_type,type,
    true: $i ).

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

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

thf(ifeq2_type,type,
    ifeq2: $i > $i > $i > $i > $i ).

thf(ifeq_type,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $i ).

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

thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $i ).

thf(class_Orderings_Oorder_type,type,
    class_Orderings_Oorder: $i > $i ).

thf(class_Orderings_Olinorder_type,type,
    class_Orderings_Olinorder: $i > $i ).

thf(4,negated_conjecture,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(18,plain,
    ( ( class_Ring__and__Field_Oordered__idom @ t_b )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,negated_conjecture,
    ( ( c_lessequals @ ( v_k @ v_x ) @ ( v_f @ v_x ) @ t_b )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(16,plain,
    ( ( c_lessequals @ ( v_k @ v_x ) @ ( v_f @ v_x ) @ t_b )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    ( ( c_lessequals @ c_0 @ ( c_minus @ ( v_k @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(15,plain,
    ( ( c_lessequals @ c_0 @ ( c_minus @ ( v_k @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).

thf(42,plain,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( class_OrderedGroup_Ocomm__monoid__add @ A ) @ true @ ( c_plus @ c_0 @ B @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( class_OrderedGroup_Ocomm__monoid__add @ A ) @ true @ ( c_plus @ c_0 @ B @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Ocomm__monoid__add @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

thf(38,plain,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Ocomm__monoid__add @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,negated_conjecture,
    ( ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b )
   != true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(17,plain,
    ( ( c_lessequals @ c_0 @ ( c_minus @ ( v_f @ v_x ) @ ( v_g @ v_x ) @ t_b ) @ t_b )
   != true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true @ ( ifeq @ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ D @ A ) @ true @ ( c_lessequals @ B @ ( c_minus @ D @ C @ A ) @ A ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).

thf(32,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true @ ( ifeq @ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ D @ A ) @ true @ ( c_lessequals @ B @ ( c_minus @ D @ C @ A ) @ A ) @ true ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_Orderings_Oorder @ A ) @ true @ ( ifeq @ ( c_lessequals @ B @ C @ A ) @ true @ ( ifeq @ ( c_lessequals @ C @ D @ A ) @ true @ ( c_lessequals @ B @ D @ A ) @ true ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).

thf(34,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_Orderings_Oorder @ A ) @ true @ ( ifeq @ ( c_lessequals @ B @ C @ A ) @ true @ ( ifeq @ ( c_lessequals @ C @ D @ A ) @ true @ ( c_lessequals @ B @ D @ A ) @ true ) @ true ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Orderings_Olinorder @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(40,plain,
    ! [A: $i] :
      ( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Orderings_Olinorder @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( class_Orderings_Olinorder @ A ) @ true @ ( class_Orderings_Oorder @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).

thf(36,plain,
    ! [A: $i] :
      ( ( ifeq @ ( class_Orderings_Olinorder @ A ) @ true @ ( class_Orderings_Oorder @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true @ ( ifeq @ ( c_lessequals @ B @ ( c_minus @ C @ D @ A ) @ A ) @ true @ ( c_lessequals @ ( c_plus @ B @ D @ A ) @ C @ A ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).

thf(30,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ifeq @ ( class_OrderedGroup_Opordered__ab__group__add @ A ) @ true @ ( ifeq @ ( c_lessequals @ B @ ( c_minus @ C @ D @ A ) @ A ) @ true @ ( c_lessequals @ ( c_plus @ B @ D @ A ) @ C @ A ) @ true ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(44,plain,
    $false,
    inference(e,[status(thm)],[18,16,15,42,24,28,38,17,32,34,40,26,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA023-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n001.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 18:26:06 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.92/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.00  % [INFO] 	 Parsing done (131ms). 
% 1.32/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.27  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.95/1.29  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.95/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.95/1.32  % [INFO] 	 Type checking passed. 
% 1.95/1.32  % [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 ... 
% 3.04/1.68  % External prover 'e' found a proof!
% 3.04/1.68  % [INFO] 	 Killing All external provers ... 
% 3.04/1.68  % Time passed: 1174ms (effective reasoning time: 672ms)
% 3.04/1.68  % 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)>
% 3.04/1.69  % Axioms used in derivation (10): ifeq_axiom, cls_OrderedGroup_Ocompare__rls__9_1, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Ocompare__rls__9_0, clsrel_Ring__and__Field_Oordered__idom_23, cls_Orderings_Oorder__class_Oorder__trans_0, ifeq_axiom_001, clsrel_Orderings_Olinorder_4, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Ring__and__Field_Oordered__idom_33
% 3.04/1.69  % No. of inferences in proof: 29
% 3.04/1.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1174 ms resp. 672 ms w/o parsing
% 3.09/1.73  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.09/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------