TSTP Solution File: KRS112+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 07:51:54 EDT 2024

% Result   : Unsatisfiable 3.67s 2.04s
% Output   : Refutation 3.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   96 (   3 unt;  17 typ;   0 def)
%            Number of atoms       :  243 (  52 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  474 (   8   ~;   0   |;  78   &; 302   @)
%                                         (   9 <=>;  77  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   2 con; 0-2 aty)
%            Number of variables   :  190 (   0   ^ 175   !;  15   ?; 190   :)

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

thf(ca_Ax2_type,type,
    ca_Ax2: $i > $o ).

thf(ca_Vx3_type,type,
    ca_Vx3: $i > $o ).

thf(cowlNothing_type,type,
    cowlNothing: $i > $o ).

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

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

thf(cpxcomp_type,type,
    cpxcomp: $i > $o ).

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

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

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

thf(rinvF_type,type,
    rinvF: $i > $i > $o ).

thf(rinvF1_type,type,
    rinvF1: $i > $i > $o ).

thf(rinvS_type,type,
    rinvS: $i > $i > $o ).

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

thf(xsd_integer_type,type,
    xsd_integer: $i > $o ).

thf(xsd_string_type,type,
    xsd_string: $i > $o ).

thf(i2003_11_14_17_21_19256_type,type,
    i2003_11_14_17_21_19256: $i ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ C @ A ) )
     => ( rf1 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_2) ).

thf(88,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ C @ A ) )
     => ( rf1 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ C @ A ) )
     => ( rs @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_2) ).

thf(120,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ C @ A ) )
     => ( rs @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).

thf(52,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ A @ C ) )
     => ( rf1 @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_1) ).

thf(84,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ A @ C ) )
     => ( rf1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ A @ C ) )
     => ( rinvF @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_1) ).

thf(92,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ A @ C ) )
     => ( rinvF @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_string @ A ) )
     => ( xsd_string @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).

thf(128,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_string @ A ) )
     => ( xsd_string @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(2,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( ca_Ax2 @ A ) )
     => ( ca_Ax2 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Ax2_substitution_1) ).

thf(44,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( ca_Ax2 @ A ) )
     => ( ca_Ax2 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ A @ C ) )
     => ( rf @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_1) ).

thf(76,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ A @ C ) )
     => ( rf @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ C @ A ) )
     => ( rf @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_2) ).

thf(80,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ C @ A ) )
     => ( rf @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ C @ A ) )
     => ( rinvS @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_2) ).

thf(112,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ C @ A ) )
     => ( rinvS @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( ra_Px1 @ C @ A ) )
     => ( ra_Px1 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).

thf(72,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( ra_Px1 @ C @ A ) )
     => ( ra_Px1 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ C @ A ) )
     => ( rinvF1 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_2) ).

thf(104,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ C @ A ) )
     => ( rinvF1 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cUnsatisfiable @ A ) )
     => ( cUnsatisfiable @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).

thf(40,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cUnsatisfiable @ A ) )
     => ( cUnsatisfiable @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rs @ A @ B )
        & ( rs @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).

thf(195,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rs @ A @ B )
        & ( rs @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( ra_Px1 @ A @ C ) )
     => ( ra_Px1 @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).

thf(68,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( ra_Px1 @ A @ C ) )
     => ( ra_Px1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ A @ C ) )
     => ( rinvF1 @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_1) ).

thf(100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ A @ C ) )
     => ( rinvF1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlThing @ A ) )
     => ( cowlThing @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).

thf(56,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlThing @ A ) )
     => ( cowlThing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( cUnsatisfiable @ A )
    <=> ( ? [B: $i] :
            ( ( rf1 @ A @ B )
            & ( ca_Ax2 @ B ) )
        & ? [B: $i] :
            ( ( rf @ A @ B )
            & ( cp @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(142,plain,
    ! [A: $i] :
      ( ( ( cUnsatisfiable @ A )
       => ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ( ca_Ax2 @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) ) )
      & ( ( ? [B: $i] :
              ( ( rf1 @ A @ B )
              & ( ca_Ax2 @ B ) )
          & ? [B: $i] :
              ( ( rf @ A @ B )
              & ( cp @ B ) ) )
       => ( cUnsatisfiable @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf @ A @ B )
        & ( rf @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(174,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf @ A @ B )
        & ( rf @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvF1 @ A @ B )
    <=> ( rf1 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

thf(185,plain,
    ! [A: $i,B: $i] :
      ( ( ( rinvF1 @ A @ B )
       => ( rf1 @ B @ A ) )
      & ( ( rf1 @ B @ A )
       => ( rinvF1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

thf(132,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ A @ C ) )
     => ( rs @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_1) ).

thf(116,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ A @ C ) )
     => ( rs @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cp @ A ) )
     => ( cp @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp_substitution_1) ).

thf(60,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cp @ A ) )
     => ( cp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).

thf(201,plain,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( ca_Ax2 @ A )
    <=> ( ( cpxcomp @ A )
        & ! [B: $i] :
            ( ( rinvF1 @ A @ B )
           => ( ca_Vx3 @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(160,plain,
    ! [A: $i] :
      ( ( ( ca_Ax2 @ A )
       => ( ( cpxcomp @ A )
          & ! [B: $i] :
              ( ( rinvF1 @ A @ B )
             => ( ca_Vx3 @ B ) ) ) )
      & ( ( ( cpxcomp @ A )
          & ! [B: $i] :
              ( ( rinvF1 @ A @ B )
             => ( ca_Vx3 @ B ) ) )
       => ( ca_Ax2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(137,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_integer @ A ) )
     => ( xsd_integer @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).

thf(124,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_integer @ A ) )
     => ( xsd_integer @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ C @ A ) )
     => ( rinvF @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_2) ).

thf(96,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ C @ A ) )
     => ( rinvF @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cpxcomp @ A ) )
     => ( cpxcomp @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cpxcomp_substitution_1) ).

thf(64,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cpxcomp @ A ) )
     => ( cpxcomp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvF @ A @ B )
    <=> ( rf @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

thf(180,plain,
    ! [A: $i,B: $i] :
      ( ( ( rinvF @ A @ B )
       => ( rf @ B @ A ) )
      & ( ( rf @ B @ A )
       => ( rinvF @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( cpxcomp @ A )
    <=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(155,plain,
    ! [A: $i] :
      ( ( ( cpxcomp @ A )
       => ? [B: $i] : ( ra_Px1 @ A @ B ) )
      & ( ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cpxcomp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(37,axiom,
    cUnsatisfiable @ i2003_11_14_17_21_19256,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).

thf(198,plain,
    cUnsatisfiable @ i2003_11_14_17_21_19256,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ A @ C ) )
     => ( rinvS @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_1) ).

thf(108,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ A @ C ) )
     => ( rinvS @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( ca_Vx3 @ A ) )
     => ( ca_Vx3 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Vx3_substitution_1) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( ca_Vx3 @ A ) )
     => ( ca_Vx3 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( cp @ A )
    <=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(150,plain,
    ! [A: $i] :
      ( ( ( cp @ A )
       => ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
      & ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
       => ( cp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).

thf(199,plain,
    ! [A: $i,B: $i] :
      ( ( rs @ A @ B )
     => ( rf @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf1 @ A @ B )
        & ( rf1 @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(177,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rf1 @ A @ B )
        & ( rf1 @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( ca_Vx3 @ A )
    <=> ? [B: $i] :
          ( ( rs @ A @ B )
          & ( cowlThing @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(168,plain,
    ! [A: $i] :
      ( ( ( ca_Vx3 @ A )
       => ? [B: $i] :
            ( ( rs @ A @ B )
            & ( cowlThing @ B ) ) )
      & ( ? [B: $i] :
            ( ( rs @ A @ B )
            & ( cowlThing @ B ) )
       => ( ca_Vx3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvS @ A @ B )
    <=> ( rs @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

thf(190,plain,
    ! [A: $i,B: $i] :
      ( ( ( rinvS @ A @ B )
       => ( rs @ B @ A ) )
      & ( ( rs @ B @ A )
       => ( rinvS @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(203,plain,
    $false,
    inference(e,[status(thm)],[88,120,52,84,92,128,44,76,80,112,72,104,40,195,68,100,56,142,174,185,132,116,60,201,160,137,124,96,64,180,155,198,108,48,150,199,177,168,190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% 0.15/0.17  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n019.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 15:17:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.86/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/1.06  % [INFO] 	 Parsing done (148ms). 
% 1.24/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.30  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.30  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.30  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.34  % [INFO] 	 39 axioms and no conjecture found. 
% 1.87/1.41  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.87/1.41  % [INFO] 	 Type checking passed. 
% 1.87/1.42  % [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 ... 
% 3.67/2.03  % External prover 'e' found a proof!
% 3.67/2.03  % [INFO] 	 Killing All external provers ... 
% 3.67/2.03  % Time passed: 1514ms (effective reasoning time: 959ms)
% 3.67/2.04  % Axioms used in derivation (39): axiom_15, rinvF1_substitution_1, ca_Ax2_substitution_1, axiom_2, rinvS_substitution_2, cowlThing_substitution_1, axiom_3, rinvS_substitution_1, axiom_11, rf_substitution_1, axiom_12, axiom_7, cowlNothing_substitution_1, rinvF_substitution_2, axiom_10, cpxcomp_substitution_1, xsd_string_substitution_1, rf1_substitution_2, axiom_6, ra_Px1_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_8, rs_substitution_2, axiom_5, axiom_13, rinvF1_substitution_2, rinvF_substitution_1, rf_substitution_2, axiom_0, axiom_9, rs_substitution_1, axiom_14, cp_substitution_1, ca_Vx3_substitution_1, axiom_4
% 3.67/2.04  % No. of inferences in proof: 79
% 3.67/2.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1514 ms resp. 959 ms w/o parsing
% 3.97/2.09  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.97/2.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------