TSTP Solution File: KRS125+1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : KRS125+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : Tue May  7 10:38:21 EDT 2024

% Result   : Unsatisfiable 4.05s 2.05s
% Output   : Refutation 4.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   49 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :  100 (   7 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  179 (  22   ~;  14   |;  11   &; 111   @)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :   44 (   0   ^  34   !;  10   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
    cUnsatisfiable: $i > $o ).

thf(ce3_type,type,
    ce3: $i > $o ).

thf(cf_type,type,
    cf: $i > $o ).

thf(cc_type,type,
    cc: $i > $o ).

thf(cdxcomp_type,type,
    cdxcomp: $i > $o ).

thf(cd_type,type,
    cd: $i > $o ).

thf(ra_Px1_type,type,
    ra_Px1: $i > $i > $o ).

thf(i2003_11_14_17_22_17947_type,type,
    i2003_11_14_17_22_17947: $i ).

thf(sk2_type,type,
    sk2: $i > $i ).

thf(13,axiom,
    cUnsatisfiable @ i2003_11_14_17_22_17947,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).

thf(60,plain,
    cUnsatisfiable @ i2003_11_14_17_22_17947,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( cUnsatisfiable @ A )
    <=> ( ( ce3 @ A )
        & ( cf @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(24,plain,
    ! [A: $i] :
      ( ( ( cUnsatisfiable @ A )
       => ( ( ce3 @ A )
          & ( cf @ A ) ) )
      & ( ( ( ce3 @ A )
          & ( cf @ A ) )
       => ( cUnsatisfiable @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(25,plain,
    ( ! [A: $i] :
        ( ( cUnsatisfiable @ A )
       => ( ( ce3 @ A )
          & ( cf @ A ) ) )
    & ! [A: $i] :
        ( ( ( ce3 @ A )
          & ( cf @ A ) )
       => ( cUnsatisfiable @ A ) ) ),
    inference(miniscope,[status(thm)],[24]) ).

thf(28,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( cf @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(65,plain,
    ! [A: $i] :
      ( ( cf @ A )
      | ( ( cUnsatisfiable @ i2003_11_14_17_22_17947 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[60,28]) ).

thf(66,plain,
    cf @ i2003_11_14_17_22_17947,
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( cf @ A )
     => ( cd @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).

thf(58,plain,
    ! [A: $i] :
      ( ( cf @ A )
     => ( cd @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(59,plain,
    ! [A: $i] :
      ( ~ ( cf @ A )
      | ( cd @ A ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(110,plain,
    ! [A: $i] :
      ( ( cd @ A )
      | ( ( cf @ i2003_11_14_17_22_17947 )
       != ( cf @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[66,59]) ).

thf(111,plain,
    cd @ i2003_11_14_17_22_17947,
    inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( ce3 @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(63,plain,
    ! [A: $i] :
      ( ( ce3 @ A )
      | ( ( cUnsatisfiable @ i2003_11_14_17_22_17947 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[60,27]) ).

thf(64,plain,
    ce3 @ i2003_11_14_17_22_17947,
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ce3 @ A )
     => ( cc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).

thf(56,plain,
    ! [A: $i] :
      ( ( ce3 @ A )
     => ( cc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(57,plain,
    ! [A: $i] :
      ( ~ ( ce3 @ A )
      | ( cc @ A ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(91,plain,
    ! [A: $i] :
      ( ( cc @ A )
      | ( ( ce3 @ i2003_11_14_17_22_17947 )
       != ( ce3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64,57]) ).

thf(92,plain,
    cc @ i2003_11_14_17_22_17947,
    inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( cc @ A )
     => ( cdxcomp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

thf(30,plain,
    ! [A: $i] :
      ( ( cc @ A )
     => ( cdxcomp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(31,plain,
    ! [A: $i] :
      ( ~ ( cc @ A )
      | ( cdxcomp @ A ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(95,plain,
    ! [A: $i] :
      ( ( cdxcomp @ A )
      | ( ( cc @ i2003_11_14_17_22_17947 )
       != ( cc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[92,31]) ).

thf(96,plain,
    cdxcomp @ i2003_11_14_17_22_17947,
    inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( cdxcomp @ A )
    <=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

thf(41,plain,
    ! [A: $i] :
      ( ( ( cdxcomp @ A )
       => ? [B: $i] : ( ra_Px1 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cdxcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(42,plain,
    ( ! [A: $i] :
        ( ( cdxcomp @ A )
       => ? [B: $i] : ( ra_Px1 @ A @ B ) )
    & ! [A: $i] :
        ( ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cdxcomp @ A ) ) ),
    inference(miniscope,[status(thm)],[41]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( cdxcomp @ A )
      | ( ra_Px1 @ A @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(97,plain,
    ! [A: $i] :
      ( ( ra_Px1 @ A @ ( sk2 @ A ) )
      | ( ( cdxcomp @ i2003_11_14_17_22_17947 )
       != ( cdxcomp @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[96,44]) ).

thf(98,plain,
    ra_Px1 @ i2003_11_14_17_22_17947 @ ( sk2 @ i2003_11_14_17_22_17947 ),
    inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( i2003_11_14_17_22_17947 ))]]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( cd @ A )
    <=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

thf(36,plain,
    ! [A: $i] :
      ( ( ( cd @ A )
       => ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cd @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(37,plain,
    ( ! [A: $i] :
        ( ( cd @ A )
       => ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
    & ! [A: $i] :
        ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cd @ A ) ) ),
    inference(miniscope,[status(thm)],[36]) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cd @ A )
      | ~ ( ra_Px1 @ A @ B ) ),
    inference(cnf,[status(esa)],[37]) ).

thf(99,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cd @ A )
      | ( ( ra_Px1 @ i2003_11_14_17_22_17947 @ ( sk2 @ i2003_11_14_17_22_17947 ) )
       != ( ra_Px1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[98,39]) ).

thf(100,plain,
    ~ ( cd @ i2003_11_14_17_22_17947 ),
    inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( i2003_11_14_17_22_17947 )),bind(B,$thf( sk2 @ i2003_11_14_17_22_17947 ))]]) ).

thf(121,plain,
    $false,
    inference(rewrite,[status(thm)],[111,100]) ).

thf(122,plain,
    $false,
    inference(simp,[status(thm)],[121]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KRS125+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n009.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 22:56:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 1.01/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.04  % [INFO] 	 Parsing done (135ms). 
% 1.25/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.70/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.30  % [INFO] 	 13 axioms and no conjecture found. 
% 1.94/1.34  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.94/1.34  % [INFO] 	 Type checking passed. 
% 1.94/1.35  % [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 ... 
% 4.05/2.05  % [INFO] 	 Killing All external provers ... 
% 4.05/2.05  % Time passed: 1527ms (effective reasoning time: 993ms)
% 4.05/2.05  % Axioms used in derivation (7): axiom_7, axiom_10, axiom_2, axiom_6, axiom_3, axiom_11, axiom_12
% 4.05/2.05  % No. of inferences in proof: 40
% 4.05/2.05  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1527 ms resp. 993 ms w/o parsing
% 4.14/2.09  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.14/2.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------