TSTP Solution File: SEV087^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n028.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 11.28s 2.98s
% Output   : Refutation 11.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   34 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :  377 ( 186 equ; 112 cnn)
%            Maximal formula atoms :    8 (  11 avg)
%            Number of connectives :  476 (  49   ~;  62   |;  15   &; 344   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  166 ( 166   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   69 (  42   ^  24   !;   3   ?;  69   :)

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

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

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

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

thf(sk5_type,type,
    sk5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

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

thf(1,conjecture,
    ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ~ ( A
          @ ^ [B: $i] : $true
          @ ^ [B: $i] : $false )
      & ! [B: $i > $o] : ( A @ B @ B )
      & ! [B: $i > $o,C: $i > $o,D: $i > $o] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) )
      & ! [B: $i > $o,C: $i > $o] :
          ( ( ( A @ B @ C )
            & ( A @ C @ B ) )
         => ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme) ).

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

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

thf(7,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
      | ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(18,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[7:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(34,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(35,plain,
    ( ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[34]) ).

thf(10,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
      | ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
     != ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[10:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(23,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(24,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[23]) ).

thf(6,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
      | ( ( sk5 @ A )
       != ( sk6 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
     != ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
     != ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(41,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[15]) ).

thf(42,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[41]) ).

thf(62,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
     != ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,42]) ).

thf(63,plain,
    ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
   != ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(pattern_uni,[status(thm)],[62:[]]) ).

thf(8,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
      | ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(20,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[8:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(25,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(26,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
      = ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[25]) ).

thf(5,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk3 @ A ) @ ( sk4 @ A ) )
      | ( ( sk5 @ A )
       != ( sk6 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
     != ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(30,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(31,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[30]) ).

thf(57,plain,
    ( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,31]) ).

thf(58,plain,
    ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
    = ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(pattern_uni,[status(thm)],[57:[]]) ).

thf(65,plain,
    ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
   != ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(rewrite,[status(thm)],[63,58]) ).

thf(4,plain,
    ! [A: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( A
        @ ^ [B: $i] : $true
        @ ^ [B: $i] : $false )
      | ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
      | ( A @ ( sk2 @ A ) @ ( sk3 @ A ) )
      | ( ( sk5 @ A )
       != ( sk6 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(21,plain,
    ( ( ( ^ [A: $i] : $true )
      = ( ^ [A: $i] : $false ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
      = ( sk3 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk5 @ ( (=) @ ( $i > $o ) ) )
     != ( sk6 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(replace_andrewseq,[status(thm)],[4:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).

thf(28,plain,
    ( ( ( ^ [A: $i] : $false )
      = ( ^ [A: $i] : $true ) )
    | ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
     != ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(29,plain,
    ( ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
      = ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
    | ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
     != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
    inference(simp,[status(thm)],[28]) ).

thf(67,plain,
    ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
   != ( sk5 @ ( (=) @ ( $i > $o ) ) ) ),
    inference(simplifyReflect,[status(thm)],[29,65]) ).

thf(387,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[35,65,67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jun 21 19:17:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.04/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.03  % [INFO] 	 Parsing done (116ms). 
% 1.30/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.95/1.30  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.95/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.31  % [INFO] 	 Type checking passed. 
% 1.95/1.31  % [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 ... 
% 11.28/2.98  % [INFO] 	 Killing All external provers ... 
% 11.28/2.98  % Time passed: 2456ms (effective reasoning time: 1941ms)
% 11.28/2.98  % 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)>
% 11.28/2.98  % Axioms used in derivation (0): 
% 11.28/2.98  % No. of inferences in proof: 34
% 11.28/2.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2456 ms resp. 1941 ms w/o parsing
% 11.28/3.06  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.28/3.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------