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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---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 : 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 : Mon May 20 23:18:18 EDT 2024

% Result   : Unsatisfiable 3.86s 1.95s
% Output   : Refutation 4.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   74 (   3 unt;  13 typ;   0 def)
%            Number of atoms       :  186 (  42 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  371 (   8   ~;   0   |;  64   &; 238   @)
%                                         (   5 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :  149 (   0   ^ 140   !;   9   ?; 149   :)

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

thf(cowlNothing_type,type,
    cowlNothing: $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(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_19_02584_type,type,
    i2003_11_14_17_19_02584: $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(24,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvF @ A @ B )
    <=> ( rf @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(129,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)],[24]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvF1 @ A @ B )
    <=> ( rf1 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(134,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)],[25]) ).

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(8,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(59,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ C @ A ) )
     => ( rf1 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).

thf(35,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlNothing @ A ) )
     => ( cowlNothing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(43,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cp @ A ) )
     => ( cp @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,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(75,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ C @ A ) )
     => ( rinvF1 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,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(51,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ C @ A ) )
     => ( rf @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,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(47,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf @ A @ C ) )
     => ( rf @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,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(83,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ C @ A ) )
     => ( rinvS @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(11,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(71,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF1 @ A @ C ) )
     => ( rinvF1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rs @ A @ B )
        & ( rs @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(144,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rs @ A @ B )
        & ( rs @ A @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

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

thf(39,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cowlThing @ A ) )
     => ( cowlThing @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

thf(103,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(16,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(91,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ C @ A ) )
     => ( rs @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(108,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(9,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(63,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ A @ C ) )
     => ( rinvF @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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(17,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(95,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_integer @ A ) )
     => ( xsd_integer @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(10,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(67,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvF @ C @ A ) )
     => ( rinvF @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

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

thf(31,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( cUnsatisfiable @ A ) )
     => ( cUnsatisfiable @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(18,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(99,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        & ( xsd_string @ A ) )
     => ( xsd_string @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(15,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(87,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rs @ A @ C ) )
     => ( rs @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(7,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(55,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rf1 @ A @ C ) )
     => ( rf1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( rinvS @ A @ B )
    <=> ( rs @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(139,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)],[26]) ).

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(13,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(79,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = B )
        & ( rinvS @ A @ C ) )
     => ( rinvS @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(152,plain,
    $false,
    inference(e,[status(thm)],[147,129,134,148,59,35,123,43,75,51,47,83,71,144,113,39,103,91,108,63,150,95,67,31,99,87,55,139,126,79]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KRS075+1 : TPTP v8.2.0. Released v3.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n003.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 : Sat May 18 22:28:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.07/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/1.06  % [INFO] 	 Parsing done (133ms). 
% 1.32/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.28  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.75/1.29  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.32  % [INFO] 	 30 axioms and no conjecture found. 
% 2.13/1.38  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.13/1.39  % [INFO] 	 Type checking passed. 
% 2.13/1.39  % [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 ... 
% 3.86/1.95  % External prover 'e' found a proof!
% 3.86/1.95  % [INFO] 	 Killing All external provers ... 
% 3.86/1.95  % Time passed: 1416ms (effective reasoning time: 875ms)
% 3.86/1.95  % Axioms used in derivation (30): rinvF1_substitution_1, axiom_2, axiom_6, rinvS_substitution_2, cowlThing_substitution_1, axiom_3, cUnsatisfiable_substitution_1, rinvS_substitution_1, axiom_5, axiom_11, rf_substitution_1, cp_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, rinvF_substitution_2, axiom_10, xsd_string_substitution_1, rf1_substitution_2, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_8, rs_substitution_2, rinvF1_substitution_2, rinvF_substitution_1, rf_substitution_2, axiom_0, axiom_9, rs_substitution_1
% 3.86/1.95  % No. of inferences in proof: 61
% 3.86/1.95  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1416 ms resp. 875 ms w/o parsing
% 4.01/2.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.01/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------