TSTP Solution File: SEU933^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU933^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 03:44:17 EDT 2024

% Result   : Theorem 77.50s 13.86s
% Output   : Refutation 77.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   51 (  16 unt;   6 typ;   0 def)
%            Number of atoms       :  141 (  78 equ;   8 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  469 (  93   ~;  79   |;   6   &; 273   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  117 ( 117   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   7 usr;   8 con; 0-4 aty)
%            Number of variables   :  167 (  82   ^  85   !;   0   ?; 167   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $i ).

thf(a_type,type,
    a: $i ).

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

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

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

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

thf(1,conjecture,
    ( ( a != b )
   => ~ ! [A: $i > $i,B: $i > $i] :
          ( ! [C: ( $i > $i ) > $o] :
              ( ( ( C @ A )
                & ! [D: $i > $i] :
                    ( ( C @ D )
                   => ( C
                      @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
             => ( C
                @ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
         => ! [C: ( $i > $i ) > $o] :
              ( ( ( C @ A )
                & ! [D: $i > $i] :
                    ( ( C @ D )
                   => ( C
                      @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
             => ( C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196B_pme) ).

thf(2,negated_conjecture,
    ~ ( ( a != b )
     => ~ ! [A: $i > $i,B: $i > $i] :
            ( ! [C: ( $i > $i ) > $o] :
                ( ( ( C @ A )
                  & ! [D: $i > $i] :
                      ( ( C @ D )
                     => ( C
                        @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
               => ( C
                  @ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
           => ! [C: ( $i > $i ) > $o] :
                ( ( ( C @ A )
                  & ! [D: $i > $i] :
                      ( ( C @ D )
                     => ( C
                        @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
               => ( C @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( a != b )
     => ~ ! [A: $i > $i,B: $i > $i] :
            ( ! [C: ( $i > $i ) > $o] :
                ( ( ( C @ A )
                  & ! [D: $i > $i] :
                      ( ( C @ D )
                     => ( C
                        @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
               => ( C
                  @ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
           => ! [C: ( $i > $i ) > $o] :
                ( ( ( C @ A )
                  & ! [D: $i > $i] :
                      ( ( C @ D )
                     => ( C
                        @ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
               => ( C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( sk2 @ B @ A @ A )
      | ( sk1 @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ~ ( sk2 @ B @ A
          @ ^ [C: $i] : ( B @ ( A @ C ) ) )
      | ( sk1 @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(19,plain,
    ! [D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
      ( ( sk1 @ A @ B )
      | ( sk1 @ C @ D )
      | ( ( sk2 @ B @ A @ A )
       != ( sk2 @ D @ C
          @ ^ [E: $i] : ( D @ ( C @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4,9]) ).

thf(20,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( sk1 @ A @ B )
      | ( sk1 @ A @ B )
      | ( A
       != ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[19:[bind(A,$thf( C )),bind(B,$thf( D ))]]) ).

thf(21,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( sk1 @ A @ B )
      | ( sk1 @ A @ B )
      | ( A
       != ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[20:[]]) ).

thf(22,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( sk1 @ A @ B )
      | ( A
       != ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
    inference(simp,[status(thm)],[21]) ).

thf(24,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( ( B @ ( A @ ( sk4 @ B @ A ) ) )
       != ( A @ ( sk4 @ B @ A ) ) )
      | ( sk1 @ A @ B ) ),
    inference(func_ext,[status(esa)],[22]) ).

thf(5,plain,
    ! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( C @ A )
      | ~ ( C
          @ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
      | ( C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( C @ A )
      | ~ ( C
          @ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
      | ( C @ B ) ),
    inference(simp,[status(thm)],[5]) ).

thf(40,plain,
    ! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( C @ A )
      | ( C @ B )
      | ( ( C
          @ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
       != ( sk1 @ A @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[12]) ).

thf(58,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ( A != A )
      | ( A = B )
      | ( ( A
          = ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
       != ( sk1 @ A @ B ) )
      | ~ $true ),
    inference(replace_leibeq,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ ( $i > $i ) @ A ))]]) ).

thf(67,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A != A )
      | ( A = B )
      | ~ ( sk1 @ A @ B )
      | ( ( A
          = ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
       != ( sk1 @ A @ B ) )
      | ~ $true ),
    inference(lifteq,[status(thm)],[58]) ).

thf(99,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A = B )
      | ~ ( sk1 @ A @ B )
      | ( ( A
          = ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
       != ( sk1 @ A @ B ) ) ),
    inference(simp,[status(thm)],[67]) ).

thf(8,plain,
    ! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( C @ A )
      | ( C @ ( sk3 @ C @ B @ A ) )
      | ( C @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ( A != A )
      | ( A
        = ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
      | ( A = B ) ),
    inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( (=) @ ( $i > $i ) @ (@) ))]]) ).

thf(16,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A != A )
      | ( A
        = ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
      | ( A = B )
      | ~ ( sk1 @ A @ B ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(17,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A
        = ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
      | ( A = B )
      | ~ ( sk1 @ A @ B ) ),
    inference(simp,[status(thm)],[16]) ).

thf(209,plain,
    ! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
      ( ( A = B )
      | ~ ( sk1 @ A @ B )
      | ~ ( sk1 @ C @ D )
      | ~ ( E @ C )
      | ~ ( E @ A )
      | ( E @ D )
      | ( ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A )
       != ( ^ [F: $i] : ( C @ ( sk3 @ E @ D @ C @ F ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[17,12]) ).

thf(253,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( ( ^ [C: $i] : C )
        = A )
      | ~ ( sk1
          @ ^ [C: $i] : C
          @ A )
      | ~ ( sk1
          @ ^ [C: $i] : C
          @ B )
      | ( ( ^ [C: $i] : C )
       != ( ^ [C: $i] : C ) )
      | ( ( ^ [C: $i] : C )
       != ( ^ [C: $i] : C ) )
      | ( ( ^ [C: $i] : C )
        = B )
      | ( ( ^ [C: $i] : A )
       != ( ^ [C: $i] : B ) ) ),
    inference(pre_uni,[status(thm)],[209:[bind(A,$thf( ^ [F: $i] : F )),bind(B,$thf( B )),bind(C,$thf( ^ [F: $i] : F )),bind(D,$thf( D )),bind(E,$thf( (=) @ ( $i > $i ) @ ^ [F: $i] : F ))]]) ).

thf(254,plain,
    ! [A: $i > $i] :
      ( ( ( ^ [B: $i] : B )
        = A )
      | ( ( ^ [B: $i] : B )
       != ( ^ [B: $i] : B ) )
      | ( ( ^ [B: $i] : B )
       != ( ^ [B: $i] : B ) )
      | ~ ( sk1
          @ ^ [B: $i] : B
          @ A )
      | ~ ( sk1
          @ ^ [B: $i] : B
          @ A )
      | ( ( ^ [B: $i] : B )
        = A ) ),
    inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( (@) )),bind(B,$thf( (@) ))]]) ).

thf(281,plain,
    ! [A: $i > $i] :
      ( ( ( ^ [B: $i] : B )
        = A )
      | ( ( ^ [B: $i] : B )
       != ( ^ [B: $i] : B ) )
      | ( ( ^ [B: $i] : B )
       != ( ^ [B: $i] : B ) )
      | ~ ( sk1
          @ ^ [B: $i] : B
          @ A )
      | ~ ( sk1
          @ ^ [B: $i] : B
          @ A )
      | ( ( ^ [B: $i] : B )
        = A ) ),
    inference(lifteq,[status(thm)],[254]) ).

thf(282,plain,
    ! [A: $i > $i] :
      ( ( ( ^ [B: $i] : B )
        = A )
      | ~ ( sk1
          @ ^ [B: $i] : B
          @ A ) ),
    inference(simp,[status(thm)],[281]) ).

thf(283,plain,
    ! [B: $i,A: $i > $i] :
      ( ( ( A @ B )
        = B )
      | ~ ( sk1
          @ ^ [C: $i] : C
          @ A ) ),
    inference(func_ext,[status(esa)],[282]) ).

thf(7,plain,
    a != b,
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    a != b,
    inference(lifteq,[status(thm)],[7]) ).

thf(754,plain,
    ! [B: $i,A: $i > $i] :
      ( ~ ( sk1
          @ ^ [C: $i] : C
          @ A )
      | ( B != b )
      | ( ( A @ B )
       != a ) ),
    inference(paramod_ordered,[status(thm)],[283,15]) ).

thf(774,plain,
    ! [A: $i] :
      ( ~ ( sk1
          @ ^ [B: $i] : B
          @ ^ [B: $i] : a )
      | ( A != b ) ),
    inference(pre_uni,[status(thm)],[754:[bind(A,$thf( ^ [C: $i] : a ))]]) ).

thf(776,plain,
    ~ ( sk1
      @ ^ [A: $i] : A
      @ ^ [A: $i] : a ),
    inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( b ))]]) ).

thf(796,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A
       != ( ^ [C: $i] : ( B @ ( A @ C ) ) ) )
      | ( ( sk1 @ A @ B )
       != ( sk1
          @ ^ [C: $i] : C
          @ ^ [C: $i] : a ) ) ),
    inference(paramod_ordered,[status(thm)],[22,776]) ).

thf(797,plain,
    ( ( ^ [A: $i] : A )
   != ( ^ [A: $i] : a ) ),
    inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( ^ [C: $i] : C )),bind(B,$thf( ^ [C: $i] : a ))]]) ).

thf(826,plain,
    sk7 != a,
    inference(func_ext,[status(esa)],[797]) ).

thf(857,plain,
    ! [B: $i,A: $i > $i] :
      ( ~ ( sk1
          @ ^ [C: $i] : C
          @ A )
      | ( B != a )
      | ( ( A @ B )
       != sk7 ) ),
    inference(paramod_ordered,[status(thm)],[283,826]) ).

thf(858,plain,
    ! [A: $i] :
      ( ~ ( sk1
          @ ^ [B: $i] : B
          @ ^ [B: $i] : sk7 )
      | ( A != a ) ),
    inference(pre_uni,[status(thm)],[857:[bind(A,$thf( ^ [C: $i] : sk7 ))]]) ).

thf(860,plain,
    ~ ( sk1
      @ ^ [A: $i] : A
      @ ^ [A: $i] : sk7 ),
    inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( a ))]]) ).

thf(956,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( A
       != ( ^ [C: $i] : ( B @ ( A @ C ) ) ) )
      | ( ( sk1 @ A @ B )
       != ( sk1
          @ ^ [C: $i] : C
          @ ^ [C: $i] : sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[22,860]) ).

thf(957,plain,
    ( ( ^ [A: $i] : A )
   != ( ^ [A: $i] : sk7 ) ),
    inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( ^ [C: $i] : C )),bind(B,$thf( ^ [C: $i] : sk7 ))]]) ).

thf(4123,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ~ ( sk1 @ A @ B )
      | ( ( A
          = ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
       != ( sk1 @ A @ B ) )
      | ( B
       != ( ^ [C: $i] : C ) )
      | ( A
       != ( ^ [C: $i] : sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[99,957]) ).

thf(4124,plain,
    ! [A: $i > $i] :
      ( ~ ( sk1
          @ ^ [B: $i] : sk7
          @ A )
      | ( ( sk1
          @ ^ [B: $i] : sk7
          @ A )
       != ( ( ^ [B: $i] : sk7 )
          = ( ^ [B: $i] : sk7 ) ) )
      | ( A
       != ( ^ [B: $i] : B ) ) ),
    inference(pattern_uni,[status(thm)],[4123:[bind(A,$thf( ^ [C: $i] : sk7 ))]]) ).

thf(4708,plain,
    ~ ( sk1
      @ ^ [A: $i] : sk7
      @ ^ [A: $i] : A ),
    inference(simp,[status(thm)],[4124]) ).

thf(5023,plain,
    ! [B: $i > $i,A: $i > $i] :
      ( ( ( B @ ( A @ ( sk4 @ B @ A ) ) )
       != ( A @ ( sk4 @ B @ A ) ) )
      | ( ( sk1 @ A @ B )
       != ( sk1
          @ ^ [C: $i] : sk7
          @ ^ [C: $i] : C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,4708]) ).

thf(5024,plain,
    sk7 != sk7,
    inference(pattern_uni,[status(thm)],[5023:[bind(A,$thf( ^ [C: $i] : sk7 )),bind(B,$thf( ^ [C: $i] : C ))]]) ).

thf(5059,plain,
    $false,
    inference(simp,[status(thm)],[5024]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SEU933^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_Leo-III %s %d
% 0.11/0.33  % Computer : n012.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Sun May 19 17:05:09 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.97/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.09  % [INFO] 	 Parsing done (156ms). 
% 1.28/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.44  % [INFO] 	 nitpick registered as external prover. 
% 1.83/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.03/1.58  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.03/1.58  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.03/1.59  % [INFO] 	 Type checking passed. 
% 2.03/1.59  % [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 ... 
% 77.50/13.85  % [INFO] 	 Killing All external provers ... 
% 77.50/13.86  % Time passed: 13383ms (effective reasoning time: 12751ms)
% 77.50/13.86  % 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)>
% 77.50/13.86  % Axioms used in derivation (0): 
% 77.50/13.86  % No. of inferences in proof: 45
% 77.50/13.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13383 ms resp. 12751 ms w/o parsing
% 77.50/13.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.50/13.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------