TSTP Solution File: SET063+3 by CSE---1.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE---1.6
% Problem  : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d

% Computer : n024.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 : Thu Aug 31 14:28:20 EDT 2023

% Result   : Theorem 0.18s 0.60s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33  % Computer : n024.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   : Sat Aug 26 14:03:24 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.18/0.55  start to proof:theBenchmark
% 0.18/0.60  %-------------------------------------------
% 0.18/0.60  % File        :CSE---1.6
% 0.18/0.60  % Problem     :theBenchmark
% 0.18/0.60  % Transform   :cnf
% 0.18/0.60  % Format      :tptp:raw
% 0.18/0.60  % Command     :java -jar mcs_scs.jar %d %s
% 0.18/0.60  
% 0.18/0.60  % Result      :Theorem 0.000000s
% 0.18/0.60  % Output      :CNFRefutation 0.000000s
% 0.18/0.60  %-------------------------------------------
% 0.18/0.60  %--------------------------------------------------------------------------
% 0.18/0.60  % File     : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.18/0.60  % Domain   : Set Theory
% 0.18/0.60  % Problem  : If X is a subset of the empty set, then X is the empty set
% 0.18/0.60  % Version  : [Try90] axioms : Reduced > Incomplete.
% 0.18/0.60  % English  :
% 0.18/0.60  
% 0.18/0.60  % Refs     : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.18/0.60  %          : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.18/0.60  %          : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.18/0.60  % Source   : [ILF]
% 0.18/0.60  % Names    : BOOLE (30) [TS89]
% 0.18/0.60  
% 0.18/0.60  % Status   : Theorem
% 0.18/0.60  % Rating   : 0.00 v6.1.0, 0.03 v6.0.0, 0.00 v5.3.0, 0.07 v5.2.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1
% 0.18/0.60  % Syntax   : Number of formulae    :    7 (   3 unt;   0 def)
% 0.18/0.60  %            Number of atoms       :   13 (   2 equ)
% 0.18/0.60  %            Maximal formula atoms :    3 (   1 avg)
% 0.18/0.60  %            Number of connectives :    8 (   2   ~;   0   |;   1   &)
% 0.18/0.60  %                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
% 0.18/0.60  %            Maximal formula depth :    6 (   4 avg)
% 0.18/0.60  %            Maximal term depth    :    1 (   1 avg)
% 0.18/0.60  %            Number of predicates  :    4 (   3 usr;   0 prp; 1-2 aty)
% 0.18/0.60  %            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
% 0.18/0.60  %            Number of variables   :   11 (  11   !;   0   ?)
% 0.18/0.60  % SPC      : FOF_THM_RFO_SEQ
% 0.18/0.60  
% 0.18/0.60  % Comments :
% 0.18/0.60  %--------------------------------------------------------------------------
% 0.18/0.60  %---- line(boole - th(27),1833153)
% 0.18/0.60  fof(empty_set_subset,axiom,
% 0.18/0.60      ! [B] : subset(empty_set,B) ).
% 0.18/0.60  
% 0.18/0.60  %---- line(hidden - axiom31,1832636)
% 0.18/0.60  fof(empty_set_defn,axiom,
% 0.18/0.60      ! [B] : ~ member(B,empty_set) ).
% 0.18/0.60  
% 0.18/0.60  %---- line(tarski - df(3),1832749)
% 0.18/0.60  fof(subset_defn,axiom,
% 0.18/0.60      ! [B,C] :
% 0.18/0.60        ( subset(B,C)
% 0.18/0.60      <=> ! [D] :
% 0.18/0.60            ( member(D,B)
% 0.18/0.60           => member(D,C) ) ) ).
% 0.18/0.60  
% 0.18/0.60  %---- line(boole - df(8),1833103)
% 0.18/0.60  fof(equal_defn,axiom,
% 0.18/0.60      ! [B,C] :
% 0.18/0.60        ( B = C
% 0.18/0.60      <=> ( subset(B,C)
% 0.18/0.60          & subset(C,B) ) ) ).
% 0.18/0.60  
% 0.18/0.60  %---- property(reflexivity,op(subset,2,predicate))
% 0.18/0.60  fof(reflexivity_of_subset,axiom,
% 0.18/0.60      ! [B] : subset(B,B) ).
% 0.18/0.60  
% 0.18/0.60  %---- line(hidden - axiom33,1832628)
% 0.18/0.60  fof(empty_defn,axiom,
% 0.18/0.60      ! [B] :
% 0.18/0.60        ( empty(B)
% 0.18/0.60      <=> ! [C] : ~ member(C,B) ) ).
% 0.18/0.60  
% 0.18/0.60  %---- line(boole - th(30),1833179)
% 0.18/0.60  fof(prove_subset_of_empty_set_is_empty_set,conjecture,
% 0.18/0.60      ! [B] :
% 0.18/0.60        ( subset(B,empty_set)
% 0.18/0.60       => B = empty_set ) ).
% 0.18/0.60  
% 0.18/0.60  %--------------------------------------------------------------------------
% 0.18/0.60  %-------------------------------------------
% 0.18/0.60  % Proof found
% 0.18/0.60  % SZS status Theorem for theBenchmark
% 0.18/0.60  % SZS output start Proof
% 0.18/0.60  %ClaNum:24(EqnAxiom:11)
% 0.18/0.60  %VarNum:36(SingletonVarNum:17)
% 0.18/0.60  %MaxLitNum:3
% 0.18/0.60  %MaxfuncDepth:1
% 0.18/0.60  %SharedTerms:4
% 0.18/0.60  %goalClause: 12 15
% 0.18/0.60  %singleGoalClaCount:2
% 0.18/0.60  [12]P1(a1,a2)
% 0.18/0.60  [15]~E(a1,a2)
% 0.18/0.60  [13]P1(a2,x131)
% 0.18/0.60  [14]P1(x141,x141)
% 0.18/0.60  [16]~P2(x161,a2)
% 0.18/0.60  [19]P3(x191)+P2(f3(x191),x191)
% 0.18/0.60  [18]~E(x181,x182)+P1(x181,x182)
% 0.18/0.60  [20]~P3(x201)+~P2(x202,x201)
% 0.18/0.60  [22]P1(x221,x222)+P2(f4(x221,x222),x221)
% 0.18/0.60  [24]P1(x241,x242)+~P2(f4(x241,x242),x242)
% 0.18/0.60  [21]~P1(x212,x211)+~P1(x211,x212)+E(x211,x212)
% 0.18/0.60  [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232)
% 0.18/0.60  %EqnAxiom
% 0.18/0.60  [1]E(x11,x11)
% 0.18/0.60  [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.60  [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.60  [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.18/0.60  [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 0.18/0.60  [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 0.18/0.60  [7]P1(x72,x73)+~E(x71,x72)+~P1(x71,x73)
% 0.18/0.60  [8]P1(x83,x82)+~E(x81,x82)+~P1(x83,x81)
% 0.18/0.60  [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 0.18/0.60  [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 0.18/0.60  [11]~P3(x111)+P3(x112)+~E(x111,x112)
% 0.18/0.60  
% 0.18/0.60  %-------------------------------------------
% 0.18/0.61  cnf(26,plain,
% 0.18/0.61     (~P2(x261,a2)),
% 0.18/0.61     inference(rename_variables,[],[16])).
% 0.18/0.61  cnf(29,plain,
% 0.18/0.61     ($false),
% 0.18/0.61     inference(scs_inference,[],[12,13,16,26,15,19,23,21]),
% 0.18/0.61     ['proof']).
% 0.18/0.61  % SZS output end Proof
% 0.18/0.61  % Total time :0.000000s
%------------------------------------------------------------------------------