TSTP Solution File: KRS003-1 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : KRS003-1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  7 07:51:43 EDT 2024

% Result   : Unsatisfiable 2.61s 1.58s
% Output   : Refutation 2.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   46 (   5 unt;  13 typ;   0 def)
%            Number of atoms       :   69 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  176 (  32   ~;  36   |;   0   &; 108   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(e_type,type,
    e: $i > $o ).

thf(exist_type,type,
    exist: $i ).

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

thf(s2least_type,type,
    s2least: $i > $o ).

thf(c_type,type,
    c: $i > $o ).

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

thf(u1r2_type,type,
    u1r2: $i > $i ).

thf(u1r1_type,type,
    u1r1: $i > $i ).

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

thf(s1most_type,type,
    s1most: $i > $o ).

thf(d_type,type,
    d: $i > $o ).

thf(u3r2_type,type,
    u3r2: $i > $i ).

thf(u3r1_type,type,
    u3r1: $i > $i ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( s2least @ A )
      | ( equalish @ B @ C )
      | ~ ( s @ A @ B )
      | ~ ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( s2least @ A )
      | ( equalish @ B @ C )
      | ~ ( s @ A @ B )
      | ~ ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( s1most @ A )
      | ( s @ A @ ( u3r2 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).

thf(41,plain,
    ! [A: $i] :
      ( ( s1most @ A )
      | ( s @ A @ ( u3r2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( s @ A @ ( u1r2 @ A ) )
      | ~ ( s2least @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).

thf(27,plain,
    ! [A: $i] :
      ( ( s @ A @ ( u1r2 @ A ) )
      | ~ ( s2least @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( s1most @ A )
      | ( s @ A @ ( u3r1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).

thf(39,plain,
    ! [A: $i] :
      ( ( s1most @ A )
      | ( s @ A @ ( u3r1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ A @ B )
      | ~ ( s1most @ C )
      | ~ ( s @ C @ A )
      | ~ ( s @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ A @ B )
      | ~ ( s1most @ C )
      | ~ ( s @ C @ A )
      | ~ ( s @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(2,negated_conjecture,
    f @ exist,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).

thf(18,plain,
    f @ exist,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( s1most @ A )
      | ~ ( d @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).

thf(31,plain,
    ! [A: $i] :
      ( ( s1most @ A )
      | ~ ( d @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( c @ A )
      | ~ ( e @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).

thf(43,plain,
    ! [A: $i] :
      ( ( c @ A )
      | ~ ( e @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ~ ( s2least @ A )
      | ~ ( equalish @ ( u1r2 @ A ) @ ( u1r1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( s2least @ A )
      | ~ ( equalish @ ( u1r2 @ A ) @ ( u1r1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( s2least @ A )
      | ~ ( c @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).

thf(19,plain,
    ! [A: $i] :
      ( ( s2least @ A )
      | ~ ( c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( s1most @ A )
      | ~ ( equalish @ ( u3r2 @ A ) @ ( u3r1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).

thf(37,plain,
    ! [A: $i] :
      ( ( s1most @ A )
      | ~ ( equalish @ ( u3r2 @ A ) @ ( u3r1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( s @ A @ ( u1r1 @ A ) )
      | ~ ( s2least @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).

thf(25,plain,
    ! [A: $i] :
      ( ( s @ A @ ( u1r1 @ A ) )
      | ~ ( s2least @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( c @ A )
      | ~ ( s2least @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).

thf(21,plain,
    ! [A: $i] :
      ( ( c @ A )
      | ~ ( s2least @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( d @ A )
      | ~ ( s1most @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).

thf(33,plain,
    ! [A: $i] :
      ( ( d @ A )
      | ~ ( s1most @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( d @ A )
      | ~ ( f @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).

thf(45,plain,
    ! [A: $i] :
      ( ( d @ A )
      | ~ ( f @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1,negated_conjecture,
    e @ exist,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).

thf(17,plain,
    e @ exist,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(47,plain,
    $false,
    inference(e,[status(thm)],[29,41,27,39,35,18,31,43,23,19,37,25,21,33,45,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS003-1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n028.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  6 15:20:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.87/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (114ms). 
% 1.19/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.50/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.50/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.22  % [INFO] 	 Found a conjecture and 14 axioms. Running axiom selection ... 
% 1.85/1.24  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 1.85/1.25  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.25  % [INFO] 	 Type checking passed. 
% 1.85/1.26  % [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 ... 
% 2.61/1.58  % External prover 'e' found a proof!
% 2.61/1.58  % [INFO] 	 Killing All external provers ... 
% 2.61/1.58  % Time passed: 1059ms (effective reasoning time: 608ms)
% 2.61/1.58  % 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)>
% 2.61/1.58  % Axioms used in derivation (14): clause_5, clause_16, clause_9, clause_14, clause_4, clause_13, clause_6, clause_12, clause_8, clause_15, clause_7, clause_10, clause_11, clause_3
% 2.61/1.58  % No. of inferences in proof: 33
% 2.61/1.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1059 ms resp. 608 ms w/o parsing
% 2.87/1.62  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.87/1.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------