TSTP Solution File: SYO048^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO048^1 : 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 08:59:06 EDT 2024

% Result   : Theorem 4.39s 2.14s
% Output   : Refutation 4.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   75 (  12 unt;  18 typ;   5 def)
%            Number of atoms       :  166 (  14 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  411 ( 103   ~;  91   |;   0   &; 217   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   62 (  62   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;  11 con; 0-3 aty)
%            Number of variables   :   57 (  13   ^  44   !;   0   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mforall_prop_def,definition,
    ( mforall_prop
    = ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
        ! [C: $i > $o] : ( A @ C @ B ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

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

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

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

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

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

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

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

thf(sk8_type,type,
    sk8: $i > $i > $o ).

thf(sk9_type,type,
    sk9: $i ).

thf(sk10_type,type,
    sk10: $i > $o ).

thf(sk11_type,type,
    sk11: $i > $o ).

thf(sk12_type,type,
    sk12: $i ).

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( mvalid
      @ ( mforall_prop
        @ ^ [B: $i > $o] :
            ( mforall_prop
            @ ^ [C: $i > $o] : ( mequiv @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( mvalid
        @ ( mforall_prop
          @ ^ [B: $i > $o] :
              ( mforall_prop
              @ ^ [C: $i > $o] : ( mequiv @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ A @ C ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ~ ~ ( ~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
              ( ~ ! [E: $i] :
                    ( ~ ( A @ B @ E )
                    | ~ ( ~ ( C @ E )
                        | ~ ( D @ E ) ) )
              | ~ ( ~ ! [E: $i] :
                        ( ~ ( A @ B @ E )
                        | ( C @ E ) )
                  | ~ ! [E: $i] :
                        ( ~ ( A @ B @ E )
                        | ( D @ E ) ) ) )
        | ~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
              ( ~ ! [E: $i] :
                    ( ~ ( A @ B @ E )
                    | ( C @ E ) )
              | ~ ! [E: $i] :
                    ( ~ ( A @ B @ E )
                    | ( D @ E ) )
              | ! [E: $i] :
                  ( ~ ( A @ B @ E )
                  | ~ ( ~ ( C @ E )
                      | ~ ( D @ E ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(5,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ( sk2 @ sk3 @ sk7 )
    | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ( ~ sk1
    | ( sk8 @ sk9 @ sk12 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( sk8 @ sk9 @ A )
      | ( sk11 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( sk8 @ sk9 @ A )
      | ( sk11 @ A ) ),
    inference(simp,[status(thm)],[14]) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( sk11 @ A )
      | ( ( sk8 @ sk9 @ sk12 )
       != ( sk8 @ sk9 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,16]) ).

thf(20,plain,
    ( ~ sk1
    | ( sk11 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( sk12 ))]]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( sk8 @ sk9 @ A )
      | ( sk10 @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( sk8 @ sk9 @ A )
      | ( sk10 @ A ) ),
    inference(simp,[status(thm)],[10]) ).

thf(17,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( sk10 @ A )
      | ( ( sk8 @ sk9 @ sk12 )
       != ( sk8 @ sk9 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,15]) ).

thf(18,plain,
    ( ~ sk1
    | ( sk10 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk12 ))]]) ).

thf(11,plain,
    ( ~ sk1
    | ~ ( sk10 @ sk12 )
    | ~ ( sk11 @ sk12 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(25,plain,
    ( ~ sk1
    | ~ ( sk11 @ sk12 )
    | ( ( sk10 @ sk12 )
     != ( sk10 @ sk12 ) ) ),
    inference(paramod_ordered,[status(thm)],[18,11]) ).

thf(26,plain,
    ( ~ sk1
    | ~ ( sk11 @ sk12 ) ),
    inference(pattern_uni,[status(thm)],[25:[]]) ).

thf(33,plain,
    ( ~ sk1
    | ( ( sk11 @ sk12 )
     != ( sk11 @ sk12 ) ) ),
    inference(paramod_ordered,[status(thm)],[20,26]) ).

thf(34,plain,
    ~ sk1,
    inference(pattern_uni,[status(thm)],[33:[]]) ).

thf(35,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ( sk2 @ sk3 @ sk7 )
    | $false ),
    inference(rewrite,[status(thm)],[5,34]) ).

thf(36,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ( sk2 @ sk3 @ sk7 ) ),
    inference(simp,[status(thm)],[35]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk5 @ A )
      | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(55,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk5 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[12,34]) ).

thf(56,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk5 @ A ) ),
    inference(simp,[status(thm)],[55]) ).

thf(85,plain,
    ! [A: $i] :
      ( ( sk2 @ sk3 @ sk6 )
      | ( sk5 @ A )
      | ( ( sk2 @ sk3 @ sk7 )
       != ( sk2 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[36,56]) ).

thf(86,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ( sk5 @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( sk7 ))]]) ).

thf(6,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ~ ( sk5 @ sk7 )
    | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(37,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ~ ( sk5 @ sk7 )
    | $false ),
    inference(rewrite,[status(thm)],[6,34]) ).

thf(38,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | ~ ( sk5 @ sk7 ) ),
    inference(simp,[status(thm)],[37]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk4 @ A )
      | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(41,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk4 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[8,34]) ).

thf(42,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 @ A )
      | ( sk4 @ A ) ),
    inference(simp,[status(thm)],[41]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( sk5 @ sk7 )
      | ( sk4 @ A )
      | ( ( sk2 @ sk3 @ sk6 )
       != ( sk2 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[38,42]) ).

thf(45,plain,
    ( ~ ( sk5 @ sk7 )
    | ( sk4 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( sk6 ))]]) ).

thf(13,plain,
    ( ~ ( sk4 @ sk6 )
    | ( sk2 @ sk3 @ sk7 )
    | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(96,plain,
    ( ~ ( sk4 @ sk6 )
    | ( sk2 @ sk3 @ sk7 )
    | $false ),
    inference(rewrite,[status(thm)],[13,34]) ).

thf(97,plain,
    ( ~ ( sk4 @ sk6 )
    | ( sk2 @ sk3 @ sk7 ) ),
    inference(simp,[status(thm)],[96]) ).

thf(98,plain,
    ! [A: $i] :
      ( ~ ( sk4 @ sk6 )
      | ( sk5 @ A )
      | ( ( sk2 @ sk3 @ sk7 )
       != ( sk2 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[97,56]) ).

thf(99,plain,
    ( ~ ( sk4 @ sk6 )
    | ( sk5 @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( sk7 ))]]) ).

thf(7,plain,
    ( ~ ( sk4 @ sk6 )
    | ~ ( sk5 @ sk7 )
    | sk1 ),
    inference(cnf,[status(esa)],[4]) ).

thf(39,plain,
    ( ~ ( sk4 @ sk6 )
    | ~ ( sk5 @ sk7 )
    | $false ),
    inference(rewrite,[status(thm)],[7,34]) ).

thf(40,plain,
    ( ~ ( sk4 @ sk6 )
    | ~ ( sk5 @ sk7 ) ),
    inference(simp,[status(thm)],[39]) ).

thf(112,plain,
    ( ~ ( sk4 @ sk6 )
    | ( ( sk5 @ sk7 )
     != ( sk5 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[99,40]) ).

thf(113,plain,
    ~ ( sk4 @ sk6 ),
    inference(pattern_uni,[status(thm)],[112:[]]) ).

thf(126,plain,
    ( ~ ( sk5 @ sk7 )
    | $false ),
    inference(rewrite,[status(thm)],[45,113]) ).

thf(127,plain,
    ~ ( sk5 @ sk7 ),
    inference(simp,[status(thm)],[126]) ).

thf(155,plain,
    ( ( sk2 @ sk3 @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[86,127]) ).

thf(156,plain,
    sk2 @ sk3 @ sk6,
    inference(simp,[status(thm)],[155]) ).

thf(159,plain,
    ! [A: $i] :
      ( ( sk4 @ A )
      | ( ( sk2 @ sk3 @ sk6 )
       != ( sk2 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[156,42]) ).

thf(160,plain,
    sk4 @ sk6,
    inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( sk6 ))]]) ).

thf(166,plain,
    $false,
    inference(rewrite,[status(thm)],[160,113]) ).

thf(167,plain,
    $false,
    inference(simp,[status(thm)],[166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n012.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May 20 08:40:54 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.95/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.04  % [INFO] 	 Parsing done (148ms). 
% 1.28/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.98/1.28  % [INFO] 	 nitpick registered as external prover. 
% 1.98/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.25/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.43/1.42  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.43/1.42  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.43/1.43  % [INFO] 	 Type checking passed. 
% 2.43/1.43  % [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 ... 
% 4.39/2.13  % [INFO] 	 Killing All external provers ... 
% 4.39/2.13  % Time passed: 1589ms (effective reasoning time: 1080ms)
% 4.39/2.13  % 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)>
% 4.39/2.14  % Axioms used in derivation (0): 
% 4.39/2.14  % No. of inferences in proof: 52
% 4.39/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1589 ms resp. 1080 ms w/o parsing
% 4.57/2.19  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.57/2.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------