TSTP Solution File: SEV091^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV091^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 Jun 24 15:59:30 EDT 2024

% Result   : Theorem 13.21s 3.37s
% Output   : Refutation 13.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   48 (  10 unt;   0 typ;   0 def)
%            Number of atoms       :  155 (  13 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  408 (  51   ~;  54   |;  15   &; 276   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :  108 (   0   ^ 108   !;   0   ?; 108   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cQ_type,type,
    cQ: $i > $i > $o ).

thf(cP_type,type,
    cP: $i > $i > $o ).

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

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

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

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( cP @ A @ B )
            & ( cP @ B @ C ) )
         => ( cP @ A @ C ) )
      & ! [A: $i,B: $i,C: $i] :
          ( ( ( cQ @ A @ B )
            & ( cQ @ B @ C ) )
         => ( cQ @ A @ C ) )
      & ! [A: $i,B: $i] :
          ( ( cQ @ A @ B )
         => ( cQ @ B @ A ) )
      & ! [A: $i,B: $i] :
          ( ( cP @ A @ B )
          | ( cQ @ A @ B ) ) )
   => ( ! [A: $i,B: $i] : ( cP @ A @ B )
      | ! [A: $i,B: $i] : ( cQ @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCADE13_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i,B: $i,C: $i] :
            ( ( ( cP @ A @ B )
              & ( cP @ B @ C ) )
           => ( cP @ A @ C ) )
        & ! [A: $i,B: $i,C: $i] :
            ( ( ( cQ @ A @ B )
              & ( cQ @ B @ C ) )
           => ( cQ @ A @ C ) )
        & ! [A: $i,B: $i] :
            ( ( cQ @ A @ B )
           => ( cQ @ B @ A ) )
        & ! [A: $i,B: $i] :
            ( ( cP @ A @ B )
            | ( cQ @ A @ B ) ) )
     => ( ! [A: $i,B: $i] : ( cP @ A @ B )
        | ! [A: $i,B: $i] : ( cQ @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i,B: $i,C: $i] :
            ( ( ( cP @ A @ B )
              & ( cP @ B @ C ) )
           => ( cP @ A @ C ) )
        & ! [A: $i,B: $i,C: $i] :
            ( ( ( cQ @ A @ B )
              & ( cQ @ B @ C ) )
           => ( cQ @ A @ C ) )
        & ! [A: $i,B: $i] :
            ( ( cQ @ A @ B )
           => ( cQ @ B @ A ) )
        & ! [A: $i,B: $i] :
            ( ( cP @ A @ B )
            | ( cQ @ A @ B ) ) )
     => ( ! [A: $i,B: $i] : ( cP @ A @ B )
        | ! [A: $i,B: $i] : ( cQ @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ B )
      | ( cQ @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A @ B )
      | ( cQ @ A @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cP @ A @ B )
      | ~ ( cP @ B @ C )
      | ( cP @ A @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( cP @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cP @ A @ B )
      | ~ ( cP @ B @ C )
      | ( ( cP @ A @ C )
       != ( cP @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[7,4]) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( cP @ sk1 @ A )
      | ~ ( cP @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).

thf(32,plain,
    ! [A: $i] :
      ( ~ ( cP @ sk1 @ A )
      | ~ ( cP @ A @ sk2 ) ),
    inference(simp,[status(thm)],[27]) ).

thf(40,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cQ @ A @ B )
      | ~ ( cP @ sk1 @ C )
      | ( ( cP @ A @ B )
       != ( cP @ C @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,32]) ).

thf(41,plain,
    ! [A: $i] :
      ( ( cQ @ A @ sk2 )
      | ~ ( cP @ sk1 @ A ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).

thf(99,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cQ @ A @ B )
      | ( cQ @ C @ sk2 )
      | ( ( cP @ A @ B )
       != ( cP @ sk1 @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,41]) ).

thf(100,plain,
    ! [A: $i] :
      ( ( cQ @ sk1 @ A )
      | ( cQ @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(102,plain,
    ! [A: $i] :
      ( ( cQ @ sk1 @ A )
      | ( cQ @ A @ sk2 ) ),
    inference(simp,[status(thm)],[100]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ( cQ @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ( cQ @ B @ A ) ),
    inference(simp,[status(thm)],[5]) ).

thf(137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cQ @ sk1 @ A )
      | ( cQ @ C @ B )
      | ( ( cQ @ A @ sk2 )
       != ( cQ @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[102,10]) ).

thf(138,plain,
    ! [A: $i] :
      ( ( cQ @ sk1 @ A )
      | ( cQ @ sk2 @ A ) ),
    inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ~ ( cQ @ B @ C )
      | ( cQ @ A @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ~ ( cQ @ B @ C )
      | ( cQ @ A @ C ) ),
    inference(simp,[status(thm)],[9]) ).

thf(8,plain,
    ~ ( cQ @ sk3 @ sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(62,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ~ ( cQ @ B @ C )
      | ( ( cQ @ A @ C )
       != ( cQ @ sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,8]) ).

thf(63,plain,
    ! [A: $i] :
      ( ~ ( cQ @ sk3 @ A )
      | ~ ( cQ @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).

thf(83,plain,
    ! [A: $i] :
      ( ~ ( cQ @ sk3 @ A )
      | ~ ( cQ @ A @ sk4 ) ),
    inference(simp,[status(thm)],[63]) ).

thf(535,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ sk1 @ A )
      | ~ ( cQ @ sk3 @ B )
      | ( ( cQ @ sk2 @ A )
       != ( cQ @ B @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[138,83]) ).

thf(536,plain,
    ( ( cQ @ sk1 @ sk4 )
    | ~ ( cQ @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[535:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cQ @ A @ sk2 )
      | ( cQ @ C @ B )
      | ( ( cQ @ sk1 @ A )
       != ( cQ @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[102,10]) ).

thf(136,plain,
    ! [A: $i] :
      ( ( cQ @ A @ sk2 )
      | ( cQ @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ A @ B )
      | ( ( cP @ A @ B )
       != ( cP @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,4]) ).

thf(17,plain,
    cQ @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ B @ A )
      | ( ( cQ @ sk1 @ sk2 )
       != ( cQ @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[17,10]) ).

thf(49,plain,
    cQ @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(74,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ( cQ @ A @ C )
      | ( ( cQ @ sk2 @ sk1 )
       != ( cQ @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[49,12]) ).

thf(75,plain,
    ! [A: $i] :
      ( ~ ( cQ @ A @ sk2 )
      | ( cQ @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(2203,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ A @ sk1 )
      | ( cQ @ B @ sk1 )
      | ( ( cQ @ A @ sk2 )
       != ( cQ @ B @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[136,75]) ).

thf(2204,plain,
    ! [A: $i] :
      ( ( cQ @ A @ sk1 )
      | ( cQ @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[2203:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(2221,plain,
    ! [A: $i] : ( cQ @ A @ sk1 ),
    inference(simp,[status(thm)],[2204]) ).

thf(2279,plain,
    ! [B: $i,A: $i] :
      ( ~ ( cQ @ B @ sk4 )
      | ( ( cQ @ A @ sk1 )
       != ( cQ @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2221,83]) ).

thf(2280,plain,
    ~ ( cQ @ sk1 @ sk4 ),
    inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).

thf(2318,plain,
    ( $false
    | ~ ( cQ @ sk3 @ sk2 ) ),
    inference(rewrite,[status(thm)],[536,2280]) ).

thf(2319,plain,
    ~ ( cQ @ sk3 @ sk2 ),
    inference(simp,[status(thm)],[2318]) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( cQ @ A @ B )
      | ( cQ @ A @ C )
      | ( ( cQ @ sk1 @ sk2 )
       != ( cQ @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[17,12]) ).

thf(67,plain,
    ! [A: $i] :
      ( ~ ( cQ @ A @ sk1 )
      | ( cQ @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).

thf(2273,plain,
    ! [A: $i] :
      ( ~ $true
      | ( cQ @ A @ sk2 ) ),
    inference(rewrite,[status(thm)],[67,2221]) ).

thf(2274,plain,
    ! [A: $i] : ( cQ @ A @ sk2 ),
    inference(simp,[status(thm)],[2273]) ).

thf(2495,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[2319,2274]) ).

thf(2496,plain,
    $false,
    inference(simp,[status(thm)],[2495]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV091^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d SAT
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Jun 21 18:16:25 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.04/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.37/1.09  % [INFO] 	 Parsing done (127ms). 
% 1.37/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.35  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.42  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.00/1.44  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.44  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.44  % [INFO] 	 Type checking passed. 
% 2.00/1.44  % [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 ... 
% 13.21/3.37  % [INFO] 	 Killing All external provers ... 
% 13.21/3.37  % Time passed: 2831ms (effective reasoning time: 2265ms)
% 13.21/3.37  % 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)>
% 13.21/3.37  % Axioms used in derivation (0): 
% 13.21/3.37  % No. of inferences in proof: 48
% 13.21/3.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2831 ms resp. 2265 ms w/o parsing
% 13.21/3.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.21/3.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------