TSTP Solution File: SWV270-2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWV270-2 : TPTP v8.2.0. Released v3.2.0.
% 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 05:51:02 EDT 2024

% Result   : Unsatisfiable 83.64s 15.44s
% Output   : Refutation 83.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   53 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :  104 (   7 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  544 (  35   ~;  46   |;   0   &; 463   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   92 (   0   ^  92   !;   0   ?;  92   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(c_Message_Omsg_OMPair_type,type,
    c_Message_Omsg_OMPair: $i > $i > $i ).

thf(v_X_type,type,
    v_X: $i ).

thf(v_Y_type,type,
    v_Y: $i ).

thf(c_union_type,type,
    c_union: $i > $i > $i > $i ).

thf(c_Message_Oparts_type,type,
    c_Message_Oparts: $i > $i ).

thf(v_H_type,type,
    v_H: $i ).

thf(c_Message_Osynth_type,type,
    c_Message_Osynth: $i > $i ).

thf(tc_Message_Omsg_type,type,
    tc_Message_Omsg: $i ).

thf(1,negated_conjecture,
    c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(9,plain,
    c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

thf(18,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(19,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(232,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg )
       != ( c_in @ A @ ( c_union @ B @ C @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[9,19]) ).

thf(233,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg )
    | ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) ),
    inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( c_Message_Omsg_OMPair @ v_X @ v_Y )),bind(B,$thf( c_Message_Oparts @ v_H )),bind(C,$thf( c_Message_Osynth @ v_H )),bind(D,$thf( tc_Message_Omsg ))]]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg )
       != ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[233,15]) ).

thf(295,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
    | ( c_in @ v_X @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg )
    | ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg ) ),
    inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( v_X )),bind(B,$thf( v_Y )),bind(C,$thf( v_H ))]]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

thf(22,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(23,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(2,negated_conjecture,
    ~ ( c_in @ v_X @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(10,plain,
    ~ ( c_in @ v_X @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ~ ( c_in @ v_X @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_in @ A @ ( c_union @ D @ B @ C ) @ C )
       != ( c_in @ v_X @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[23,11]) ).

thf(634,plain,
    ~ ( c_in @ v_X @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ),
    inference(pattern_uni,[status(thm)],[633:[bind(A,$thf( v_X )),bind(B,$thf( c_Message_Osynth @ v_H )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( c_Message_Oparts @ v_H ))]]) ).

thf(13242,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
    | $false
    | ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg ) ),
    inference(rewrite,[status(thm)],[295,634]) ).

thf(13243,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
    | ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg ) ),
    inference(simp,[status(thm)],[13242]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(13262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
       != ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[13243,13]) ).

thf(13263,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg )
    | ( c_in @ v_X @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) ),
    inference(pattern_uni,[status(thm)],[13262:[bind(A,$thf( v_X )),bind(B,$thf( v_Y )),bind(C,$thf( v_H ))]]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

thf(20,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(382,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( ( c_in @ A @ ( c_union @ B @ D @ C ) @ C )
       != ( c_in @ v_X @ ( c_union @ ( c_Message_Oparts @ v_H ) @ ( c_Message_Osynth @ v_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[21,11]) ).

thf(383,plain,
    ~ ( c_in @ v_X @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ),
    inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( v_X )),bind(B,$thf( c_Message_Oparts @ v_H )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( c_Message_Osynth @ v_H ))]]) ).

thf(13382,plain,
    ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg )
    | $false ),
    inference(rewrite,[status(thm)],[13263,383]) ).

thf(13383,plain,
    c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg,
    inference(simp,[status(thm)],[13382]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(66,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ C @ ( c_Message_Oparts @ E ) @ tc_Message_Omsg )
      | ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
       != ( c_in @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Message_Oparts @ E ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[17,13]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ B @ C ) @ A @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( c_Message_Omsg_OMPair @ F @ G )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).

thf(75,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ B @ C ) @ A @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    inference(simp,[status(thm)],[67]) ).

thf(13425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( ( c_in @ ( c_Message_Omsg_OMPair @ v_X @ v_Y ) @ v_H @ tc_Message_Omsg )
       != ( c_in @ ( c_Message_Omsg_OMPair @ B @ C ) @ A @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[13383,75]) ).

thf(13426,plain,
    c_in @ v_X @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg,
    inference(pattern_uni,[status(thm)],[13425:[bind(A,$thf( v_H )),bind(B,$thf( v_X )),bind(C,$thf( v_Y ))]]) ).

thf(13519,plain,
    $false,
    inference(rewrite,[status(thm)],[13426,383]) ).

thf(13520,plain,
    $false,
    inference(simp,[status(thm)],[13519]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWV270-2 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n019.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sun May 19 08:13:39 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.95/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/0.99  % [INFO] 	 Parsing done (106ms). 
% 1.17/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.57/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 1.81/1.29  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.81/1.30  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.81/1.30  % [INFO] 	 Type checking passed. 
% 1.81/1.30  % [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 ... 
% 83.64/15.43  % [INFO] 	 Killing All external provers ... 
% 83.64/15.44  % Time passed: 14892ms (effective reasoning time: 14436ms)
% 83.64/15.44  % Axioms used in derivation (6): cls_Message_Oparts_OInj_0, cls_Set_OUn__iff_0, cls_Message_OMPair__parts_1, cls_Set_OUn__iff_1, cls_Message_OMPair__synth_1, cls_Set_OUn__iff_2
% 83.64/15.44  % No. of inferences in proof: 44
% 83.64/15.44  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14892 ms resp. 14436 ms w/o parsing
% 83.64/15.48  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.64/15.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------