TSTP Solution File: SYO633-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 12:36:44 EDT 2023

% Result   : Unsatisfiable 3.03s 1.76s
% Output   : Refutation 3.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   33 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   93 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  808 (  68   ~;  66   |;   0   &; 674   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  15 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   94 (   0   ^;  94   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
    '\'E\'': $i > $i > $o ).

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

thf(s_type,type,
    s: $i > $i ).

thf('\'0\'_type',type,
    '\'0\'': $i ).

thf('\'LEQ\'_type',type,
    '\'LEQ\'': $i > $i > $o ).

thf('\'AP\'_type',type,
    '\'AP\'': $i > $i > $i ).

thf(8,axiom,
    ! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_08) ).

thf(25,plain,
    ! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ D ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_01) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ '\'0\'' ) ) @ D ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,axiom,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_04) ).

thf(20,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_06) ).

thf(22,plain,
    ! [B: $i,A: $i] : ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_03) ).

thf(18,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ '\'0\'' )
      | ~ ( '\'E\'' @ ( f @ F ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(2,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ E ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_02) ).

thf(16,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ '\'0\'' ) @ E ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_11) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_10) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(5,axiom,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_05) ).

thf(21,plain,
    ! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_12) ).

thf(32,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ D ) ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(13,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ F ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_13) ).

thf(34,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'LEQ\'' @ ( '\'AP\'' @ '\'0\'' @ F ) @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(9,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_09) ).

thf(26,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ E ) ) @ ( s @ '\'0\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_07) ).

thf(23,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'E\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
      | ~ ( '\'E\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
      | ~ ( '\'E\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
      | ~ ( '\'E\'' @ ( f @ D ) @ ( s @ '\'0\'' ) )
      | ~ ( '\'E\'' @ ( f @ E ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
      | ( '\'E\'' @ ( f @ ( '\'AP\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ) @ F ) ) @ '\'0\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(36,plain,
    $false,
    inference(e,[status(thm)],[25,14,20,22,18,16,30,28,21,32,34,26,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n006.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 18:04:37 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/1.02  % [INFO] 	 Parsing done (141ms). 
% 1.35/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.27  % [INFO] 	 13 axioms and no conjecture found. 
% 1.99/1.32  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.99/1.33  % [INFO] 	 Type checking passed. 
% 1.99/1.33  % [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 ... 
% 3.03/1.75  % External prover 'e' found a proof!
% 3.03/1.76  % [INFO] 	 Killing All external provers ... 
% 3.03/1.76  % Time passed: 1246ms (effective reasoning time: 726ms)
% 3.03/1.76  % Axioms used in derivation (13): clause_12_09, clause_0_02, clause_4_12, clause_5_03, clause_2_07, clause_3_01, clause_6_04, clause_1_10, clause_10_13, clause_9_11, clause_7_08, clause_11_06, clause_8_05
% 3.03/1.76  % No. of inferences in proof: 27
% 3.03/1.76  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1246 ms resp. 726 ms w/o parsing
% 3.61/1.81  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/1.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------