TSTP Solution File: ANA030-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 10:08:54 EDT 2023

% Result   : Unsatisfiable 3.33s 1.72s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   52 (   7 unt;  19 typ;   0 def)
%            Number of atoms       :   65 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  318 (  34   ~;  32   |;   0   &; 252   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   4 con; 0-3 aty)
%            Number of variables   :   66 (   0   ^;  66   !;   0   ?;  66   :)

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

thf(c_HOL_Oabs_type,type,
    c_HOL_Oabs: $i > $i > $i ).

thf(c_Orderings_Omax_type,type,
    c_Orderings_Omax: $i > $i > $i > $i ).

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

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

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

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

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

thf(c_times_type,type,
    c_times: $i > $i > $i > $i ).

thf(v_c_type,type,
    v_c: $i ).

thf(v_h_type,type,
    v_h: $i > $i ).

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

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

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

thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

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

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

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

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

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_plus @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_minus @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_plus @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_minus @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_minus @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_plus @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_minus @ B @ ( c_uminus @ C @ A ) @ A )
        = ( c_plus @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Omax @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).

thf(41,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Omax @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ ( c_plus @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).

thf(27,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ~ ( c_lessequals @ ( c_minus @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ ( c_plus @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

thf(49,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_minus @ B @ C @ A ) @ A )
        = ( c_minus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_minus @ B @ C @ A ) @ A )
        = ( c_minus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ~ ( c_lessequals @ ( v_f @ ( v_x @ A ) ) @ ( c_plus @ ( v_g @ ( v_x @ A ) ) @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_h @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(18,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( v_f @ ( v_x @ A ) ) @ ( c_plus @ ( v_g @ ( v_x @ A ) ) @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_h @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).

thf(43,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ ( c_Orderings_Omax @ B @ C @ A ) @ D @ A )
      | ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

thf(47,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Orderings_Olinorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ~ ( c_lessequals @ c_0 @ B @ A )
      | ( ( c_HOL_Oabs @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_plus @ B @ C @ A ) @ A )
        = ( c_plus @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_uminus @ ( c_plus @ B @ C @ A ) @ A )
        = ( c_plus @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

thf(45,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ A ) @ ( v_g @ A ) @ t_b ) @ c_0 @ t_b ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ A ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(17,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( c_Orderings_Omax @ ( c_minus @ ( v_f @ A ) @ ( v_g @ A ) @ t_b ) @ c_0 @ t_b ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_h @ A ) @ t_b ) @ t_b ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

thf(51,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(3,negated_conjecture,
    class_Ring__and__Field_Oordered__idom @ t_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

thf(19,plain,
    class_Ring__and__Field_Oordered__idom @ t_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(56,plain,
    $false,
    inference(e,[status(thm)],[24,29,41,27,49,35,18,43,47,38,21,32,45,17,51,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 17:58:55 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.89/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.95  % [INFO] 	 Parsing done (119ms). 
% 1.23/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.57/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.57/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.22  % [INFO] 	 Found a conjecture and 13 axioms. Running axiom selection ... 
% 1.90/1.24  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 1.90/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.90/1.26  % [INFO] 	 Type checking passed. 
% 1.90/1.26  % [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 ... 
% 3.33/1.71  % External prover 'e' found a proof!
% 3.33/1.72  % [INFO] 	 Killing All external provers ... 
% 3.33/1.72  % Time passed: 1202ms (effective reasoning time: 751ms)
% 3.33/1.72  % 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)>
% 3.33/1.72  % Axioms used in derivation (13): cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_OrderedGroup_Ocompare__rls__8_0, cls_OrderedGroup_Ominus__minus_0, cls_OrderedGroup_Ominus__add__distrib_0, cls_OrderedGroup_Ocompare__rls__1_0, clsrel_Ring__and__Field_Oordered__idom_4, cls_OrderedGroup_Oabs__of__nonneg_0, cls_Orderings_Ole__maxI2_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_OrderedGroup_Ominus__diff__eq_0, clsrel_OrderedGroup_Olordered__ab__group__abs_1, cls_OrderedGroup_Odiff__minus__eq__add_0, clsrel_Ring__and__Field_Oordered__idom_33
% 3.33/1.72  % No. of inferences in proof: 33
% 3.33/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1202 ms resp. 751 ms w/o parsing
% 3.33/1.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------