TSTP Solution File: SEV191^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% 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 21 04:11:05 EDT 2024

% Result   : Theorem 8.97s 2.70s
% Output   : Refutation 8.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   81 (  10 unt;  16 typ;   0 def)
%            Number of atoms       :  221 ( 118 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  578 (  98   ~; 108   |;  54   &; 304   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;  14 con; 0-3 aty)
%            Number of variables   :  131 (   0   ^  83   !;  48   ?; 131   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cP_type,type,
    cP: a > a > a ).

thf(c0_type,type,
    c0: a ).

thf(sk1_type,type,
    sk1: a > a > a > $o ).

thf(sk2_type,type,
    sk2: a > a > a > $o ).

thf(sk3_type,type,
    sk3: a ).

thf(sk4_type,type,
    sk4: a ).

thf(sk5_type,type,
    sk5: a ).

thf(sk6_type,type,
    sk6: $o ).

thf(sk7_type,type,
    sk7: $o ).

thf(sk8_type,type,
    sk8: a ).

thf(sk9_type,type,
    sk9: a ).

thf(sk10_type,type,
    sk10: a ).

thf(sk11_type,type,
    sk11: a ).

thf(sk12_type,type,
    sk12: a ).

thf(sk13_type,type,
    sk13: a ).

thf(1,conjecture,
    ( ! [A: a > a > a > $o] :
        ( $true
       => $true )
    & ! [A: a > a > a > $o,B: a > a > a > $o] :
        ( ( $true
          & $true
          & ! [C: a,D: a,E: a] :
              ( ( A @ C @ D @ E )
             => ( B @ C @ D @ E ) ) )
       => ! [C: a,D: a,E: a] :
            ( ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ( D
                    = ( cP @ H @ I ) )
                  & ( E
                    = ( cP @ J @ K ) )
                  & ( A @ F @ H @ J )
                  & ( A @ G @ I @ K ) ) )
           => ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ( D
                    = ( cP @ H @ I ) )
                  & ( E
                    = ( cP @ J @ K ) )
                  & ( B @ F @ H @ J )
                  & ( B @ G @ I @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_JOINFN_MONOTONE_pme) ).

thf(2,negated_conjecture,
    ~ ( ! [A: a > a > a > $o] :
          ( $true
         => $true )
      & ! [A: a > a > a > $o,B: a > a > a > $o] :
          ( ( $true
            & $true
            & ! [C: a,D: a,E: a] :
                ( ( A @ C @ D @ E )
               => ( B @ C @ D @ E ) ) )
         => ! [C: a,D: a,E: a] :
              ( ( ( ( C = c0 )
                  & ( D = E ) )
                | ( ( D = c0 )
                  & ( C = E ) )
                | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                    ( ( C
                      = ( cP @ F @ G ) )
                    & ( D
                      = ( cP @ H @ I ) )
                    & ( E
                      = ( cP @ J @ K ) )
                    & ( A @ F @ H @ J )
                    & ( A @ G @ I @ K ) ) )
             => ( ( ( C = c0 )
                  & ( D = E ) )
                | ( ( D = c0 )
                  & ( C = E ) )
                | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                    ( ( C
                      = ( cP @ F @ G ) )
                    & ( D
                      = ( cP @ H @ I ) )
                    & ( E
                      = ( cP @ J @ K ) )
                    & ( B @ F @ H @ J )
                    & ( B @ G @ I @ K ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > a > a > $o,B: a > a > a > $o] :
        ( ! [C: a,D: a,E: a] :
            ( ( A @ C @ D @ E )
           => ( B @ C @ D @ E ) )
       => ! [C: a,D: a,E: a] :
            ( ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ( D
                    = ( cP @ H @ I ) )
                  & ( E
                    = ( cP @ J @ K ) )
                  & ( A @ F @ H @ J )
                  & ( A @ G @ I @ K ) ) )
           => ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a,H: a,I: a,J: a,K: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ( D
                    = ( cP @ H @ I ) )
                  & ( E
                    = ( cP @ J @ K ) )
                  & ( B @ F @ H @ J )
                  & ( B @ G @ I @ K ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ! [A: a > a > a > $o,B: a > a > a > $o] :
        ( ! [C: a,D: a,E: a] :
            ( ( A @ C @ D @ E )
           => ( B @ C @ D @ E ) )
       => ! [C: a,D: a,E: a] :
            ( ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ? [H: a,I: a] :
                      ( ( D
                        = ( cP @ H @ I ) )
                      & ? [J: a,K: a] :
                          ( ( E
                            = ( cP @ J @ K ) )
                          & ( A @ F @ H @ J )
                          & ( A @ G @ I @ K ) ) ) ) )
           => ( ( ( C = c0 )
                & ( D = E ) )
              | ( ( D = c0 )
                & ( C = E ) )
              | ? [F: a,G: a] :
                  ( ( C
                    = ( cP @ F @ G ) )
                  & ? [H: a,I: a] :
                      ( ( D
                        = ( cP @ H @ I ) )
                      & ? [J: a,K: a] :
                          ( ( E
                            = ( cP @ J @ K ) )
                          & ( B @ F @ H @ J )
                          & ( B @ G @ I @ K ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(12,plain,
    ( ~ sk6
    | ~ sk7
    | ( sk4
      = ( cP @ sk10 @ sk11 ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(25,plain,
    ( ( ( cP @ sk10 @ sk11 )
      = sk4 )
    | ~ sk6
    | ~ sk7 ),
    inference(lifteq,[status(thm)],[12]) ).

thf(8,plain,
    ( ~ sk6
    | ( sk4 = c0 )
    | sk7 ),
    inference(cnf,[status(esa)],[4]) ).

thf(28,plain,
    ( ( sk4 = c0 )
    | ~ sk6
    | sk7 ),
    inference(lifteq,[status(thm)],[8]) ).

thf(11,plain,
    ( ( sk4 = sk5 )
    | sk6 ),
    inference(cnf,[status(esa)],[4]) ).

thf(27,plain,
    ( ( sk5 = sk4 )
    | sk6 ),
    inference(lifteq,[status(thm)],[11]) ).

thf(17,plain,
    ( ( sk3 = c0 )
    | sk6 ),
    inference(cnf,[status(esa)],[4]) ).

thf(24,plain,
    ( ( sk3 = c0 )
    | sk6 ),
    inference(lifteq,[status(thm)],[17]) ).

thf(13,plain,
    ( ( sk3 != c0 )
    | ( sk4 != sk5 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(23,plain,
    ( ( sk3 != c0 )
    | ( sk5 != sk4 ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(31,plain,
    ( sk6
    | ( sk5 != sk4 )
    | ( sk3 != sk3 ) ),
    inference(paramod_ordered,[status(thm)],[24,23]) ).

thf(32,plain,
    ( sk6
    | ( sk5 != sk4 ) ),
    inference(pattern_uni,[status(thm)],[31:[]]) ).

thf(54,plain,
    ( sk6
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[27,32]) ).

thf(55,plain,
    sk6,
    inference(pattern_uni,[status(thm)],[54:[]]) ).

thf(83,plain,
    ( ( sk4 = c0 )
    | ~ $true
    | sk7 ),
    inference(rewrite,[status(thm)],[28,55]) ).

thf(84,plain,
    ( ( sk4 = c0 )
    | sk7 ),
    inference(simp,[status(thm)],[83]) ).

thf(5,plain,
    ( ~ sk6
    | ( sk3 = sk5 )
    | sk7 ),
    inference(cnf,[status(esa)],[4]) ).

thf(18,plain,
    ( ( sk5 = sk3 )
    | ~ sk6
    | sk7 ),
    inference(lifteq,[status(thm)],[5]) ).

thf(56,plain,
    ( ( sk5 = sk3 )
    | ~ $true
    | sk7 ),
    inference(rewrite,[status(thm)],[18,55]) ).

thf(57,plain,
    ( ( sk5 = sk3 )
    | sk7 ),
    inference(simp,[status(thm)],[56]) ).

thf(6,plain,
    ( ( sk4 != c0 )
    | ( sk3 != sk5 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(22,plain,
    ( ( sk4 != c0 )
    | ( sk5 != sk3 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(61,plain,
    ( sk7
    | ( sk4 != c0 )
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[57,22]) ).

thf(62,plain,
    ( sk7
    | ( sk4 != c0 ) ),
    inference(pattern_uni,[status(thm)],[61:[]]) ).

thf(85,plain,
    ( sk7
    | ( sk4 != sk4 ) ),
    inference(paramod_ordered,[status(thm)],[84,62]) ).

thf(86,plain,
    sk7,
    inference(pattern_uni,[status(thm)],[85:[]]) ).

thf(164,plain,
    ( ( ( cP @ sk10 @ sk11 )
      = sk4 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[25,86,55]) ).

thf(165,plain,
    ( ( cP @ sk10 @ sk11 )
    = sk4 ),
    inference(simp,[status(thm)],[164]) ).

thf(16,plain,
    ( ~ sk6
    | ~ sk7
    | ( sk5
      = ( cP @ sk12 @ sk13 ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(26,plain,
    ( ( ( cP @ sk12 @ sk13 )
      = sk5 )
    | ~ sk6
    | ~ sk7 ),
    inference(lifteq,[status(thm)],[16]) ).

thf(199,plain,
    ( ( ( cP @ sk12 @ sk13 )
      = sk5 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[26,86,55]) ).

thf(200,plain,
    ( ( cP @ sk12 @ sk13 )
    = sk5 ),
    inference(simp,[status(thm)],[199]) ).

thf(10,plain,
    ( ~ sk6
    | ~ sk7
    | ( sk3
      = ( cP @ sk8 @ sk9 ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ( ( ( cP @ sk8 @ sk9 )
      = sk3 )
    | ~ sk6
    | ~ sk7 ),
    inference(lifteq,[status(thm)],[10]) ).

thf(104,plain,
    ( ( ( cP @ sk8 @ sk9 )
      = sk3 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[19,86,55]) ).

thf(105,plain,
    ( ( cP @ sk8 @ sk9 )
    = sk3 ),
    inference(simp,[status(thm)],[104]) ).

thf(14,plain,
    ! [F: a,E: a,D: a,C: a,B: a,A: a] :
      ( ( sk3
       != ( cP @ A @ B ) )
      | ( sk4
       != ( cP @ C @ D ) )
      | ( sk5
       != ( cP @ E @ F ) )
      | ~ ( sk2 @ A @ C @ E )
      | ~ ( sk2 @ B @ D @ F ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(20,plain,
    ! [F: a,E: a,D: a,C: a,B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk3 )
      | ( ( cP @ C @ D )
       != sk4 )
      | ( ( cP @ E @ F )
       != sk5 )
      | ~ ( sk2 @ A @ C @ E )
      | ~ ( sk2 @ B @ D @ F ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(21,plain,
    ! [F: a,E: a,D: a,C: a,B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk3 )
      | ( ( cP @ C @ D )
       != sk4 )
      | ( ( cP @ E @ F )
       != sk5 )
      | ~ ( sk2 @ A @ C @ E )
      | ~ ( sk2 @ B @ D @ F ) ),
    inference(simp,[status(thm)],[20]) ).

thf(109,plain,
    ! [F: a,E: a,D: a,C: a,B: a,A: a] :
      ( ( ( cP @ C @ D )
       != sk4 )
      | ( ( cP @ E @ F )
       != sk5 )
      | ~ ( sk2 @ A @ C @ E )
      | ~ ( sk2 @ B @ D @ F )
      | ( ( cP @ sk8 @ sk9 )
       != ( cP @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[105,21]) ).

thf(110,plain,
    ! [D: a,C: a,B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk4 )
      | ( ( cP @ C @ D )
       != sk5 )
      | ~ ( sk2 @ sk8 @ A @ C )
      | ~ ( sk2 @ sk9 @ B @ D ) ),
    inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).

thf(122,plain,
    ! [D: a,C: a,B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk4 )
      | ( ( cP @ C @ D )
       != sk5 )
      | ~ ( sk2 @ sk8 @ A @ C )
      | ~ ( sk2 @ sk9 @ B @ D ) ),
    inference(simp,[status(thm)],[110]) ).

thf(660,plain,
    ! [D: a,C: a,B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk4 )
      | ~ ( sk2 @ sk8 @ A @ C )
      | ~ ( sk2 @ sk9 @ B @ D )
      | ( ( cP @ sk12 @ sk13 )
       != ( cP @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[200,122]) ).

thf(661,plain,
    ! [B: a,A: a] :
      ( ( ( cP @ A @ B )
       != sk4 )
      | ~ ( sk2 @ sk8 @ A @ sk12 )
      | ~ ( sk2 @ sk9 @ B @ sk13 ) ),
    inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk12 )),bind(D,$thf( sk13 ))]]) ).

thf(685,plain,
    ! [B: a,A: a] :
      ( ~ ( sk2 @ sk8 @ A @ sk12 )
      | ~ ( sk2 @ sk9 @ B @ sk13 )
      | ( ( cP @ sk10 @ sk11 )
       != ( cP @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[165,661]) ).

thf(686,plain,
    ( ~ ( sk2 @ sk8 @ sk10 @ sk12 )
    | ~ ( sk2 @ sk9 @ sk11 @ sk13 ) ),
    inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( sk10 )),bind(B,$thf( sk11 ))]]) ).

thf(9,plain,
    ( ~ sk6
    | ~ sk7
    | ( sk1 @ sk9 @ sk11 @ sk13 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(95,plain,
    ( ~ $true
    | ~ $true
    | ( sk1 @ sk9 @ sk11 @ sk13 ) ),
    inference(rewrite,[status(thm)],[9,86,55]) ).

thf(96,plain,
    sk1 @ sk9 @ sk11 @ sk13,
    inference(simp,[status(thm)],[95]) ).

thf(15,plain,
    ! [C: a,B: a,A: a] :
      ( ~ ( sk1 @ A @ B @ C )
      | ( sk2 @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(129,plain,
    ! [C: a,B: a,A: a] :
      ( ( sk2 @ A @ B @ C )
      | ( ( sk1 @ sk9 @ sk11 @ sk13 )
       != ( sk1 @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[96,15]) ).

thf(130,plain,
    sk2 @ sk9 @ sk11 @ sk13,
    inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( sk9 )),bind(B,$thf( sk11 )),bind(C,$thf( sk13 ))]]) ).

thf(7,plain,
    ( ~ sk6
    | ~ sk7
    | ( sk1 @ sk8 @ sk10 @ sk12 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(58,plain,
    ( ~ $true
    | ~ sk7
    | ( sk1 @ sk8 @ sk10 @ sk12 ) ),
    inference(rewrite,[status(thm)],[7,55]) ).

thf(59,plain,
    ( ~ sk7
    | ( sk1 @ sk8 @ sk10 @ sk12 ) ),
    inference(simp,[status(thm)],[58]) ).

thf(93,plain,
    ( ~ $true
    | ( sk1 @ sk8 @ sk10 @ sk12 ) ),
    inference(rewrite,[status(thm)],[59,86]) ).

thf(94,plain,
    sk1 @ sk8 @ sk10 @ sk12,
    inference(simp,[status(thm)],[93]) ).

thf(131,plain,
    ! [C: a,B: a,A: a] :
      ( ( sk2 @ A @ B @ C )
      | ( ( sk1 @ sk8 @ sk10 @ sk12 )
       != ( sk1 @ A @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[94,15]) ).

thf(132,plain,
    sk2 @ sk8 @ sk10 @ sk12,
    inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( sk8 )),bind(B,$thf( sk10 )),bind(C,$thf( sk12 ))]]) ).

thf(704,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[686,130,132]) ).

thf(705,plain,
    $false,
    inference(simp,[status(thm)],[704]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 18:59:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.03  % [INFO] 	 Parsing done (121ms). 
% 1.31/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.06/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.06/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.06/1.36  % [INFO] 	 Type checking passed. 
% 2.06/1.36  % [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 ... 
% 8.97/2.69  % [INFO] 	 Killing All external provers ... 
% 8.97/2.70  % Time passed: 2168ms (effective reasoning time: 1656ms)
% 8.97/2.70  % 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)>
% 8.97/2.70  % Axioms used in derivation (0): 
% 8.97/2.70  % No. of inferences in proof: 65
% 8.97/2.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2168 ms resp. 1656 ms w/o parsing
% 8.97/2.74  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.97/2.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------