TSTP Solution File: ANA031-2 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA031-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 3.13s 1.73s
% Output   : Refutation 3.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   38 (   7 unt;  15 typ;   0 def)
%            Number of atoms       :   43 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  224 (  22   ~;  20   |;   0   &; 182   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   38 (   0   ^;  38   !;   0   ?;  38   :)

% 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(v_b_type,type,
    v_b: $i > $i ).

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

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

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

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

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

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

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

thf(class_OrderedGroup_Osemigroup__mult_type,type,
    class_OrderedGroup_Osemigroup__mult: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

thf(class_Ring__and__Field_Opordered__semiring_type,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ c_0 @ D @ A )
      | ( c_lessequals @ ( c_times @ D @ B @ A ) @ ( c_times @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).

thf(24,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ c_0 @ D @ A )
      | ( c_lessequals @ ( c_times @ D @ B @ A ) @ ( c_times @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

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

thf(14,plain,
    class_Ring__and__Field_Oordered__idom @ t_b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_times @ ( c_HOL_Oabs @ ( v_b @ ( v_x @ A ) ) @ t_b ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ ( c_times @ A @ ( c_times @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_b ) @ ( c_HOL_Oabs @ ( v_g @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(13,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_times @ ( c_HOL_Oabs @ ( v_b @ ( v_x @ A ) ) @ t_b ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ ( c_times @ A @ ( c_times @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_b ) @ ( c_HOL_Oabs @ ( v_g @ ( v_x @ A ) ) @ t_b ) @ t_b ) @ t_b ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,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(32,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)],[11]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ A ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_b ) @ t_b ) @ t_b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(12,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_b @ A ) @ t_b ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_b ) @ t_b ) @ t_b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
      | ( ( c_times @ ( c_times @ B @ C @ A ) @ D @ A )
        = ( c_times @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).

thf(18,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Osemigroup__mult @ A )
      | ( ( c_times @ ( c_times @ B @ C @ A ) @ D @ A )
        = ( c_times @ B @ ( c_times @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
      | ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

thf(30,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).

thf(28,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_times @ B @ C @ A )
        = ( c_times @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_times @ B @ C @ A )
        = ( c_times @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(37,plain,
    $false,
    inference(cvc4,[status(thm)],[24,14,13,32,12,18,16,26,30,28,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ANA031-2 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 18:13:00 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.96/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.98  % [INFO] 	 Parsing done (124ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.27  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.87/1.30  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.87/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.31  % [INFO] 	 Type checking passed. 
% 1.87/1.32  % [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 ... 
% 3.13/1.73  % External prover 'cvc4' found a proof!
% 3.13/1.73  % [INFO] 	 Killing All external provers ... 
% 3.13/1.73  % Time passed: 1211ms (effective reasoning time: 737ms)
% 3.13/1.73  % 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)>
% 3.13/1.73  % Axioms used in derivation (8): cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_OrderedGroup_Omult__ac__2_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__idom_42, cls_OrderedGroup_Omult__ac__1_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0
% 3.13/1.73  % No. of inferences in proof: 23
% 3.13/1.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1211 ms resp. 737 ms w/o parsing
% 3.41/1.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.41/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------