TSTP Solution File: ANA015-2 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 10:08:47 EDT 2023

% Result   : Unsatisfiable 2.81s 1.61s
% Output   : Refutation 2.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   42 (   7 unt;  17 typ;   0 def)
%            Number of atoms       :   47 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  226 (  24   ~;  22   |;   0   &; 180   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :   40 (   0   ^;  40   !;   0   ?;  40   :)

% 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_g_type,type,
    v_g: $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

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

thf(v_d_type,type,
    v_d: $i ).

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

thf(c_HOL_Oinverse_type,type,
    c_HOL_Oinverse: $i > $i > $i ).

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

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

thf(class_Ring__and__Field_Oordered__field_type,type,
    class_Ring__and__Field_Oordered__field: $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_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

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

thf(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).

thf(25,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(2,negated_conjecture,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( c_HOL_Oinverse @ v_c @ t_a ) @ ( v_g @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(14,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_HOL_Oabs @ ( c_times @ ( c_HOL_Oinverse @ v_c @ t_a ) @ ( v_g @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ ( c_times @ A @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Ofield @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).

thf(29,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Ofield @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).

thf(33,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Opordered__semiring @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_a ) @ ( c_times @ v_d @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_a ) @ t_a ) @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(13,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_g @ A ) @ t_a ) @ ( c_times @ v_d @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_a ) @ t_a ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

thf(17,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(12,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__idom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).

thf(31,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Oordered__idom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).

thf(19,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(3,negated_conjecture,
    class_Ring__and__Field_Oordered__field @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

thf(15,plain,
    class_Ring__and__Field_Oordered__field @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A )
        = ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A )
        = ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(37,plain,
    $false,
    inference(e,[status(thm)],[25,14,29,33,13,17,35,31,19,15,22,27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n003.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 17:59:01 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.84/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.10/0.99  % [INFO] 	 Parsing done (131ms). 
% 1.10/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.25  % [INFO] 	 Found a conjecture and 9 axioms. Running axiom selection ... 
% 1.82/1.28  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 1.82/1.29  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.82/1.30  % [INFO] 	 Type checking passed. 
% 1.82/1.30  % [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 ... 
% 2.81/1.61  % External prover 'e' found a proof!
% 2.81/1.61  % [INFO] 	 Killing All external provers ... 
% 2.81/1.61  % Time passed: 1099ms (effective reasoning time: 611ms)
% 2.81/1.61  % 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)>
% 2.81/1.61  % Axioms used in derivation (9): clsrel_Ring__and__Field_Oordered__field_46, clsrel_Ring__and__Field_Oordered__field_47, cls_Ring__and__Field_Oabs__mult_0, clsrel_Ring__and__Field_Ofield_21, clsrel_Ring__and__Field_Oordered__field_0, cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0, cls_OrderedGroup_Oabs__ge__zero_0, cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0, clsrel_Ring__and__Field_Oordered__field_34
% 2.81/1.61  % No. of inferences in proof: 25
% 2.81/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1099 ms resp. 611 ms w/o parsing
% 2.88/1.64  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.88/1.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------