TSTP Solution File: ANA003-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ANA003-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 10:08:43 EDT 2023

% Result   : Unsatisfiable 3.71s 1.84s
% Output   : Refutation 3.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   52 (   9 unt;  17 typ;   0 def)
%            Number of atoms       :   75 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  358 (  44   ~;  40   |;   0   &; 274   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  17 usr;   6 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^;  54   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(n0_type,type,
    n0: $i ).

thf(fp31_type,type,
    fp31: $i > $i ).

thf(absolute_type,type,
    absolute: $i > $i ).

thf(add_type,type,
    add: $i > $i > $i ).

thf(minus_type,type,
    minus: $i > $i ).

thf(a_type,type,
    a: $i ).

thf(f_type,type,
    f: $i > $i ).

thf(l1_type,type,
    l1: $i ).

thf(fp32_type,type,
    fp32: $i > $i ).

thf(g_type,type,
    g: $i > $i ).

thf(l2_type,type,
    l2: $i ).

thf(b_type,type,
    b: $i ).

thf(fp33_type,type,
    fp33: $i > $i ).

thf(equalish_type,type,
    equalish: $i > $i > $o ).

thf(minimum_type,type,
    minimum: $i > $i > $i ).

thf(half_type,type,
    half: $i > $i ).

thf(6,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).

thf(20,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_3) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(7,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).

thf(22,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_2) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ ( minimum @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ B )
      | ~ ( less_than @ B @ C )
      | ( less_than @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(5,negated_conjecture,
    less_than @ n0 @ b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).

thf(18,plain,
    less_than @ n0 @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

thf(31,plain,
    ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ ( half @ B ) )
      | ~ ( less_than @ C @ ( half @ B ) )
      | ( less_than @ ( add @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ A @ ( half @ B ) )
      | ~ ( less_than @ C @ ( half @ B ) )
      | ( less_than @ ( add @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp32 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp32 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp31 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( fp31 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(47,plain,
    ! [A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ( less_than @ n0 @ ( half @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(4,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_1) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ n0 @ B )
      | ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(2,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_than @ n0 @ A )
      | ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
      | ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(33,plain,
    ! [A: $i] :
      ~ ( less_than @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    ! [A: $i] : ( equalish @ ( add @ n0 @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

thf(32,plain,
    ! [A: $i] : ( equalish @ ( add @ n0 @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
      | ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).

thf(45,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
      | ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(52,plain,
    $false,
    inference(e,[status(thm)],[20,41,22,39,35,18,31,43,23,19,47,24,37,21,33,32,45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n026.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 18:13:51 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.99/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.37/1.01  % [INFO] 	 Parsing done (129ms). 
% 1.37/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.31  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 2.08/1.34  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 2.08/1.35  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.08/1.36  % [INFO] 	 Type checking passed. 
% 2.08/1.36  % [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 ... 
% 3.71/1.84  % External prover 'e' found a proof!
% 3.71/1.84  % [INFO] 	 Killing All external provers ... 
% 3.71/1.84  % Time passed: 1296ms (effective reasoning time: 821ms)
% 3.71/1.84  % 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)>
% 3.71/1.84  % Axioms used in derivation (10): axiom_7, axiom_2_2, left_identity, axiom_3, right_identity, transitivity_of_less_than, axiom_2_1, c_17, reflexivity_of_less_than, axiom_2_3
% 3.71/1.84  % No. of inferences in proof: 35
% 3.71/1.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1296 ms resp. 821 ms w/o parsing
% 3.71/1.88  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/1.88  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------