TSTP Solution File: KRS075+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : KRS075+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 : Mon May 20 23:19:08 EDT 2024

% Result   : Unsatisfiable 11.99s 3.28s
% Output   : Refutation 12.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   64 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :  155 (  26 equ;   0 cnn)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  382 (  52   ~;  37   |;  31   &; 249   @)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :   82 (   0   ^  67   !;  15   ?;  82   :)

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

thf(cowlThing_type,type,
    cowlThing: $i > $o ).

thf(cp_type,type,
    cp: $i > $o ).

thf(rf_type,type,
    rf: $i > $i > $o ).

thf(rf1_type,type,
    rf1: $i > $i > $o ).

thf(rs_type,type,
    rs: $i > $i > $o ).

thf(i2003_11_14_17_19_02584_type,type,
    i2003_11_14_17_19_02584: $i ).

thf(sk1_type,type,
    sk1: $i > $i ).

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

thf(sk3_type,type,
    sk3: $i > $i ).

thf(28,axiom,
    cUnsatisfiable @ i2003_11_14_17_19_02584,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

thf(147,plain,
    cUnsatisfiable @ i2003_11_14_17_19_02584,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( cUnsatisfiable @ A )
    <=> ( ? [B: $i] :
            ( ( rf1 @ A @ B )
            & ~ ( cp @ B ) )
        & ? [B: $i] :
            ( ( rs @ A @ B )
            & ( cowlThing @ B ) )
        & ? [B: $i] :
            ( ( rf @ A @ B )
            & ( cp @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(113,plain,
    ! [A: $i] :
      ( ( ( cUnsatisfiable @ A )
       => ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ~ ( cp @ B ) )
          & ? [B: $i] :
              ( ( rs @ A @ B )
              & ( cowlThing @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) ) )
      & ( ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ~ ( cp @ B ) )
          & ? [B: $i] :
              ( ( rs @ A @ B )
              & ( cowlThing @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) )
       => ( cUnsatisfiable @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(114,plain,
    ( ! [A: $i] :
        ( ( cUnsatisfiable @ A )
       => ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ~ ( cp @ B ) )
          & ? [B: $i] :
              ( ( rs @ A @ B )
              & ( cowlThing @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) ) )
    & ! [A: $i] :
        ( ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ~ ( cp @ B ) )
          & ? [B: $i] :
              ( ( rs @ A @ B )
              & ( cowlThing @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) )
       => ( cUnsatisfiable @ A ) ) ),
    inference(miniscope,[status(thm)],[113]) ).

thf(119,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( rf1 @ A @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(178,plain,
    ! [A: $i] :
      ( ( rf1 @ A @ ( sk1 @ A ) )
      | ( ( cUnsatisfiable @ i2003_11_14_17_19_02584 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,119]) ).

thf(179,plain,
    rf1 @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf1 @ A @ B )
        & ( rf1 @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(126,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf1 @ A @ B )
        & ( rf1 @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rf1 @ A @ B )
      | ~ ( rf1 @ A @ C )
      | ( B = C ) ),
    inference(cnf,[status(esa)],[126]) ).

thf(128,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( rf1 @ A @ B )
      | ~ ( rf1 @ A @ C ) ),
    inference(lifteq,[status(thm)],[127]) ).

thf(617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( rf1 @ A @ C )
      | ( ( rf1 @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) )
       != ( rf1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[179,128]) ).

thf(618,plain,
    ! [A: $i] :
      ( ( ( sk1 @ i2003_11_14_17_19_02584 )
        = A )
      | ~ ( rf1 @ i2003_11_14_17_19_02584 @ A ) ),
    inference(pattern_uni,[status(thm)],[617:[bind(A,$thf( i2003_11_14_17_19_02584 )),bind(B,$thf( sk1 @ i2003_11_14_17_19_02584 )),bind(C,$thf( C ))]]) ).

thf(785,plain,
    ! [A: $i] :
      ( ( ( sk1 @ i2003_11_14_17_19_02584 )
        = A )
      | ~ ( rf1 @ i2003_11_14_17_19_02584 @ A ) ),
    inference(simp,[status(thm)],[618]) ).

thf(120,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( rs @ A @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(180,plain,
    ! [A: $i] :
      ( ( rs @ A @ ( sk2 @ A ) )
      | ( ( cUnsatisfiable @ i2003_11_14_17_19_02584 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,120]) ).

thf(181,plain,
    rs @ i2003_11_14_17_19_02584 @ ( sk2 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(966,plain,
    ! [A: $i] :
      ( ~ ( rf1 @ i2003_11_14_17_19_02584 @ A )
      | ( rs @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) )
      | ( A
       != ( sk2 @ i2003_11_14_17_19_02584 ) ) ),
    inference(paramod_ordered,[status(thm)],[785,181]) ).

thf(967,plain,
    ( ~ ( rf1 @ i2003_11_14_17_19_02584 @ ( sk2 @ i2003_11_14_17_19_02584 ) )
    | ( rs @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) ) ),
    inference(pattern_uni,[status(thm)],[966:[bind(A,$thf( sk2 @ i2003_11_14_17_19_02584 ))]]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

thf(148,plain,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rs @ A @ B )
      | ( rf1 @ A @ B ) ),
    inference(cnf,[status(esa)],[148]) ).

thf(2818,plain,
    ! [B: $i,A: $i] :
      ( ( rf1 @ A @ B )
      | ( ( rs @ i2003_11_14_17_19_02584 @ ( sk2 @ i2003_11_14_17_19_02584 ) )
       != ( rs @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[181,149]) ).

thf(2819,plain,
    rf1 @ i2003_11_14_17_19_02584 @ ( sk2 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[2818:[bind(A,$thf( i2003_11_14_17_19_02584 )),bind(B,$thf( sk2 @ i2003_11_14_17_19_02584 ))]]) ).

thf(2829,plain,
    ( ~ $true
    | ( rs @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) ) ),
    inference(rewrite,[status(thm)],[967,2819]) ).

thf(2830,plain,
    rs @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ),
    inference(simp,[status(thm)],[2829]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

thf(150,plain,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(151,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rs @ A @ B )
      | ( rf @ A @ B ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(3342,plain,
    ! [B: $i,A: $i] :
      ( ( rf @ A @ B )
      | ( ( rs @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) )
       != ( rs @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2830,151]) ).

thf(3343,plain,
    rf @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[3342:[bind(A,$thf( i2003_11_14_17_19_02584 )),bind(B,$thf( sk1 @ i2003_11_14_17_19_02584 ))]]) ).

thf(115,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( rf @ A @ ( sk3 @ A ) ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(163,plain,
    ! [A: $i] :
      ( ( rf @ A @ ( sk3 @ A ) )
      | ( ( cUnsatisfiable @ i2003_11_14_17_19_02584 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,115]) ).

thf(164,plain,
    rf @ i2003_11_14_17_19_02584 @ ( sk3 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf @ A @ B )
        & ( rf @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(123,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf @ A @ B )
        & ( rf @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(124,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rf @ A @ B )
      | ~ ( rf @ A @ C )
      | ( B = C ) ),
    inference(cnf,[status(esa)],[123]) ).

thf(125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( rf @ A @ B )
      | ~ ( rf @ A @ C ) ),
    inference(lifteq,[status(thm)],[124]) ).

thf(121,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ( cp @ ( sk3 @ A ) ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( cp @ ( sk3 @ A ) )
      | ( ( cUnsatisfiable @ i2003_11_14_17_19_02584 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,121]) ).

thf(159,plain,
    cp @ ( sk3 @ i2003_11_14_17_19_02584 ),
    inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(118,plain,
    ! [A: $i] :
      ( ~ ( cUnsatisfiable @ A )
      | ~ ( cp @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[114]) ).

thf(152,plain,
    ! [A: $i] :
      ( ~ ( cp @ ( sk1 @ A ) )
      | ( ( cUnsatisfiable @ i2003_11_14_17_19_02584 )
       != ( cUnsatisfiable @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,118]) ).

thf(153,plain,
    ~ ( cp @ ( sk1 @ i2003_11_14_17_19_02584 ) ),
    inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(165,plain,
    ( ( cp @ ( sk3 @ i2003_11_14_17_19_02584 ) )
   != ( cp @ ( sk1 @ i2003_11_14_17_19_02584 ) ) ),
    inference(paramod_ordered,[status(thm)],[159,153]) ).

thf(167,plain,
    ( ( sk3 @ i2003_11_14_17_19_02584 )
   != ( sk1 @ i2003_11_14_17_19_02584 ) ),
    inference(simp,[status(thm)],[165]) ).

thf(229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rf @ A @ B )
      | ~ ( rf @ A @ C )
      | ( C
       != ( sk1 @ i2003_11_14_17_19_02584 ) )
      | ( B
       != ( sk3 @ i2003_11_14_17_19_02584 ) ) ),
    inference(paramod_ordered,[status(thm)],[125,167]) ).

thf(230,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rf @ A @ ( sk3 @ i2003_11_14_17_19_02584 ) )
      | ~ ( rf @ A @ B )
      | ( B
       != ( sk1 @ i2003_11_14_17_19_02584 ) ) ),
    inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( A )),bind(B,$thf( sk3 @ i2003_11_14_17_19_02584 )),bind(C,$thf( C ))]]) ).

thf(378,plain,
    ! [A: $i] :
      ( ~ ( rf @ A @ ( sk3 @ i2003_11_14_17_19_02584 ) )
      | ~ ( rf @ A @ ( sk1 @ i2003_11_14_17_19_02584 ) ) ),
    inference(simp,[status(thm)],[230]) ).

thf(409,plain,
    ! [A: $i] :
      ( ~ ( rf @ A @ ( sk1 @ i2003_11_14_17_19_02584 ) )
      | ( ( rf @ i2003_11_14_17_19_02584 @ ( sk3 @ i2003_11_14_17_19_02584 ) )
       != ( rf @ A @ ( sk3 @ i2003_11_14_17_19_02584 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[164,378]) ).

thf(410,plain,
    ~ ( rf @ i2003_11_14_17_19_02584 @ ( sk1 @ i2003_11_14_17_19_02584 ) ),
    inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( i2003_11_14_17_19_02584 ))]]) ).

thf(3523,plain,
    $false,
    inference(rewrite,[status(thm)],[3343,410]) ).

thf(3524,plain,
    $false,
    inference(simp,[status(thm)],[3523]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KRS075+1 : TPTP v8.2.0. Released v3.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n025.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 : Sat May 18 22:28:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.93/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.12/0.98  % [INFO] 	 Parsing done (114ms). 
% 1.12/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.26  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.30  % [INFO] 	 30 axioms and no conjecture found. 
% 2.08/1.38  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.08/1.38  % [INFO] 	 Type checking passed. 
% 2.08/1.39  % [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 ... 
% 11.99/3.25  % [INFO] 	 Killing All external provers ... 
% 11.99/3.27  % Time passed: 2718ms (effective reasoning time: 2259ms)
% 11.99/3.28  % Axioms used in derivation (6): axiom_10, axiom_2, axiom_3, axiom_11, axiom_9, axiom_4
% 11.99/3.28  % No. of inferences in proof: 54
% 11.99/3.28  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2718 ms resp. 2259 ms w/o parsing
% 12.13/3.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.13/3.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------