TSTP Solution File: ANA014-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 10:08:46 EDT 2023

% Result   : Unsatisfiable 2.61s 1.56s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   43 (   7 unt;  16 typ;   0 def)
%            Number of atoms       :   49 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  186 (  24   ~;  22   |;   0   &; 140   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :   38 (   0   ^;  38   !;   0   ?;  38   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_c_type,type,
    v_c: $i ).

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

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_f_type,type,
    v_f: $i > $i ).

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

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

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

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

thf(class_OrderedGroup_Omonoid__mult_type,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

thf(c_1_type,type,
    c_1: $i ).

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

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

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

thf(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

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

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Orderings_Oorder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).

thf(42,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Orderings_Oorder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,negated_conjecture,
    v_c != c_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(14,plain,
    v_c != c_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ c_1 @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_times @ c_1 @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).

thf(34,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Omonoid__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(10,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(36,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( class_OrderedGroup_Osemigroup__mult @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

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

thf(15,plain,
    ! [A: $i] :
      ~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ ( c_times @ A @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ ( v_x @ A ) ) @ t_a ) @ t_a ) @ t_a ) @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,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(28,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)],[7]) ).

thf(11,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(38,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( class_Ring__and__Field_Ofield @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

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

thf(16,plain,
    class_Ring__and__Field_Oordered__field @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
        = c_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B = c_0 )
      | ( ( c_times @ ( c_HOL_Oinverse @ B @ A ) @ B @ A )
        = c_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,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(40,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)],[12]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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(23,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(44,plain,
    $false,
    inference(e,[status(thm)],[42,14,20,34,36,15,28,38,16,31,40,26,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n009.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 17:52:34 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.93/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (103ms). 
% 1.18/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.56/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.56/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.21  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.66/1.23  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.87/1.24  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.24  % [INFO] 	 Type checking passed. 
% 1.87/1.25  % [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 ... 
% 2.61/1.56  % External prover 'e' found a proof!
% 2.61/1.56  % [INFO] 	 Killing All external provers ... 
% 2.61/1.56  % Time passed: 1026ms (effective reasoning time: 589ms)
% 2.61/1.56  % 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)>
% 2.61/1.56  % Axioms used in derivation (10): cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0, clsrel_Ring__and__Field_Oordered__field_58, clsrel_Ring__and__Field_Oordered__field_34, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Ring__and__Field_Oabs__mult_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, clsrel_Ring__and__Field_Ofield_12, clsrel_Ring__and__Field_Ofield_21, clsrel_Ring__and__Field_Oordered__field_0
% 2.61/1.56  % No. of inferences in proof: 27
% 2.61/1.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1026 ms resp. 589 ms w/o parsing
% 2.80/1.59  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.80/1.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------