TSTP Solution File: SYN592-1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYN592-1 : TPTP v8.2.0. Released v2.5.0.
% 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 : Tue May 21 08:12:52 EDT 2024

% Result   : Unsatisfiable 3.22s 1.84s
% Output   : Refutation 3.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   72 (  27 unt;  17 typ;   0 def)
%            Number of atoms       :  109 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  376 (  58   ~;  54   |;   0   &; 264   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :   80 (   0   ^  80   !;   0   ?;  80   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p9_type,type,
    p9: $i > $o ).

thf(c14_type,type,
    c14: $i ).

thf(p8_type,type,
    p8: $i > $o ).

thf(c13_type,type,
    c13: $i ).

thf(p7_type,type,
    p7: $i > $i > $o ).

thf(p2_type,type,
    p2: $i > $i > $o ).

thf(p3_type,type,
    p3: $i > $i > $o ).

thf(p10_type,type,
    p10: $i > $i > $o ).

thf(c15_type,type,
    c15: $i ).

thf(c17_type,type,
    c17: $i ).

thf(c16_type,type,
    c16: $i ).

thf(p12_type,type,
    p12: $i > $i > $o ).

thf(f4_type,type,
    f4: $i > $i > $i ).

thf(c18_type,type,
    c18: $i ).

thf(p11_type,type,
    p11: $i > $i > $o ).

thf(f5_type,type,
    f5: $i > $i ).

thf(f6_type,type,
    f6: $i > $i ).

thf(27,negated_conjecture,
    ! [A: $i] :
      ( ( p11 @ c13 @ ( f4 @ c17 @ ( f6 @ A ) ) )
      | ( p11 @ c13 @ ( f4 @ ( f6 @ A ) @ c17 ) )
      | ~ ( p12 @ c14 @ ( f4 @ A @ c17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_27) ).

thf(52,plain,
    ! [A: $i] :
      ( ( p11 @ c13 @ ( f4 @ c17 @ ( f6 @ A ) ) )
      | ( p11 @ c13 @ ( f4 @ ( f6 @ A ) @ c17 ) )
      | ~ ( p12 @ c14 @ ( f4 @ A @ c17 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(26,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f4 @ A @ B ) @ ( f4 @ C @ D ) )
      | ~ ( p2 @ A @ C )
      | ~ ( p2 @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_26) ).

thf(53,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f4 @ A @ B ) @ ( f4 @ C @ D ) )
      | ~ ( p2 @ A @ C )
      | ~ ( p2 @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(3,negated_conjecture,
    ! [A: $i] : ( p7 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_3) ).

thf(41,plain,
    ! [A: $i] : ( p7 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,negated_conjecture,
    p12 @ c14 @ ( f4 @ c18 @ c17 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_11) ).

thf(44,plain,
    p12 @ c14 @ ( f4 @ c18 @ c17 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,negated_conjecture,
    ~ ( p11 @ c13 @ ( f4 @ c17 @ ( f5 @ c18 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_12) ).

thf(39,plain,
    ~ ( p11 @ c13 @ ( f4 @ c17 @ ( f5 @ c18 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(9,negated_conjecture,
    p10 @ c13 @ c16,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_9) ).

thf(35,plain,
    p10 @ c13 @ c16,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p9 @ A )
      | ~ ( p9 @ B )
      | ~ ( p7 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_15) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ( p9 @ A )
      | ~ ( p9 @ B )
      | ~ ( p7 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(16,negated_conjecture,
    ! [A: $i] :
      ( ( p11 @ c14 @ ( f4 @ c15 @ A ) )
      | ~ ( p10 @ c13 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_16) ).

thf(43,plain,
    ! [A: $i] :
      ( ( p11 @ c14 @ ( f4 @ c15 @ A ) )
      | ~ ( p10 @ c13 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(7,negated_conjecture,
    p10 @ c13 @ c15,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_7) ).

thf(40,plain,
    p10 @ c13 @ c15,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,negated_conjecture,
    ! [A: $i] : ( p2 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).

thf(47,plain,
    ! [A: $i] : ( p2 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(18,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f6 @ A ) @ ( f6 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_18) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f6 @ A ) @ ( f6 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(2,negated_conjecture,
    p8 @ c13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13_is_p8_2) ).

thf(37,plain,
    p8 @ c13,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(19,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p7 @ A @ B )
      | ~ ( p7 @ C @ A )
      | ~ ( p7 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_19) ).

thf(46,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p7 @ A @ B )
      | ~ ( p7 @ C @ A )
      | ~ ( p7 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(10,negated_conjecture,
    ~ ( p2 @ c17 @ c15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_10) ).

thf(29,plain,
    ~ ( p2 @ c17 @ c15 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,negated_conjecture,
    ! [A: $i] : ( p10 @ c14 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_6) ).

thf(33,plain,
    ! [A: $i] : ( p10 @ c14 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,negated_conjecture,
    ! [A: $i] : ( p3 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).

thf(28,plain,
    ! [A: $i] : ( p3 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f5 @ A ) @ ( f5 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f5 @ A ) @ ( f5 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(8,negated_conjecture,
    p10 @ c13 @ c17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_8) ).

thf(45,plain,
    p10 @ c13 @ c17,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,negated_conjecture,
    p9 @ c14,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c14_is_p9_1) ).

thf(32,plain,
    p9 @ c14,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(21,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_21) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(23,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p10 @ A @ B )
      | ~ ( p2 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p10 @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10_23) ).

thf(54,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p10 @ A @ B )
      | ~ ( p2 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p10 @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(24,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p12 @ A @ B )
      | ~ ( p3 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p12 @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_24) ).

thf(49,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p12 @ A @ B )
      | ~ ( p3 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p12 @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(25,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p11 @ A @ B )
      | ~ ( p3 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p11 @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11_25) ).

thf(50,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p11 @ A @ B )
      | ~ ( p3 @ C @ B )
      | ~ ( p7 @ D @ A )
      | ~ ( p11 @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(20,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B )
      | ~ ( p2 @ C @ A )
      | ~ ( p2 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_20) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B )
      | ~ ( p2 @ C @ A )
      | ~ ( p2 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(13,negated_conjecture,
    ~ ( p11 @ c13 @ ( f4 @ ( f5 @ c18 ) @ c17 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p11_13) ).

thf(36,plain,
    ~ ( p11 @ c13 @ ( f4 @ ( f5 @ c18 ) @ c17 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(14,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p8 @ A )
      | ~ ( p8 @ B )
      | ~ ( p7 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_14) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( p8 @ A )
      | ~ ( p8 @ B )
      | ~ ( p7 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(22,negated_conjecture,
    ! [A: $i] :
      ( ( p2 @ ( f6 @ A ) @ ( f5 @ A ) )
      | ~ ( p12 @ c14 @ ( f4 @ A @ c17 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_22) ).

thf(51,plain,
    ! [A: $i] :
      ( ( p2 @ ( f6 @ A ) @ ( f5 @ A ) )
      | ~ ( p12 @ c14 @ ( f4 @ A @ c17 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(72,plain,
    $false,
    inference(cvc4,[status(thm)],[52,53,41,44,39,35,48,43,40,47,42,37,46,29,33,28,38,45,32,34,54,49,50,31,36,30,51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN592-1 : TPTP v8.2.0. Released v2.5.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n003.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 : Mon May 20 15:46:08 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.01/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/1.02  % [INFO] 	 Parsing done (121ms). 
% 1.32/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.75/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.98/1.38  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.98/1.38  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.98/1.39  % [INFO] 	 Type checking passed. 
% 1.98/1.39  % [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 ... 
% 3.22/1.83  % External prover 'cvc4' found a proof!
% 3.22/1.83  % [INFO] 	 Killing All external provers ... 
% 3.22/1.83  % Time passed: 1315ms (effective reasoning time: 805ms)
% 3.22/1.84  % Axioms used in derivation (0): 
% 3.22/1.84  % No. of inferences in proof: 55
% 3.22/1.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1315 ms resp. 805 ms w/o parsing
% 3.52/1.93  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/1.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------