TSTP Solution File: SET604+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n022.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 14:30:20 EDT 2023
% Result : Theorem 0.22s 0.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 12:32:55 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.59 start to proof:theBenchmark
% 0.22/0.64 %-------------------------------------------
% 0.22/0.64 % File :CSE---1.6
% 0.22/0.64 % Problem :theBenchmark
% 0.22/0.64 % Transform :cnf
% 0.22/0.64 % Format :tptp:raw
% 0.22/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.22/0.64
% 0.22/0.64 % Result :Theorem 0.000000s
% 0.22/0.64 % Output :CNFRefutation 0.000000s
% 0.22/0.64 %-------------------------------------------
% 0.22/0.64 %--------------------------------------------------------------------------
% 0.22/0.64 % File : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 0.22/0.64 % Domain : Set Theory
% 0.22/0.64 % Problem : The difference of the empty set and X is the empty set
% 0.22/0.64 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.22/0.64 % English :
% 0.22/0.64
% 0.22/0.64 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.22/0.64 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.22/0.64 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.22/0.64 % Source : [ILF]
% 0.22/0.64 % Names : BOOLE (75) [TS89]
% 0.22/0.64
% 0.22/0.64 % Status : Theorem
% 0.22/0.64 % Rating : 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.00 v5.3.0, 0.07 v5.2.0, 0.00 v4.0.1, 0.04 v3.7.0, 0.00 v2.3.0, 0.33 v2.2.1
% 0.22/0.64 % Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% 0.22/0.64 % Number of atoms : 17 ( 3 equ)
% 0.22/0.64 % Maximal formula atoms : 3 ( 1 avg)
% 0.22/0.64 % Number of connectives : 11 ( 3 ~; 0 |; 2 &)
% 0.22/0.64 % ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.64 % Maximal formula depth : 7 ( 4 avg)
% 0.22/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.22/0.64 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.22/0.64 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.22/0.64 % Number of variables : 16 ( 16 !; 0 ?)
% 0.22/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.22/0.64
% 0.22/0.64 % Comments :
% 0.22/0.64 %--------------------------------------------------------------------------
% 0.22/0.64 %---- line(boole - th(27),1833153)
% 0.22/0.64 fof(empty_set_subset,axiom,
% 0.22/0.64 ! [B] : subset(empty_set,B) ).
% 0.22/0.64
% 0.22/0.64 %---- line(boole - th(45),1833405)
% 0.22/0.64 fof(difference_empty_set,axiom,
% 0.22/0.64 ! [B,C] :
% 0.22/0.64 ( difference(B,C) = empty_set
% 0.22/0.64 <=> subset(B,C) ) ).
% 0.22/0.64
% 0.22/0.64 %---- line(hidden - axiom126,1832636)
% 0.22/0.64 fof(empty_set_defn,axiom,
% 0.22/0.64 ! [B] : ~ member(B,empty_set) ).
% 0.22/0.64
% 0.22/0.64 %---- line(boole - df(4),1833078)
% 0.22/0.64 fof(difference_defn,axiom,
% 0.22/0.64 ! [B,C,D] :
% 0.22/0.64 ( member(D,difference(B,C))
% 0.22/0.64 <=> ( member(D,B)
% 0.22/0.64 & ~ member(D,C) ) ) ).
% 0.22/0.64
% 0.22/0.64 %---- line(boole - df(8),1833103)
% 0.22/0.64 fof(equal_defn,axiom,
% 0.22/0.64 ! [B,C] :
% 0.22/0.64 ( B = C
% 0.22/0.64 <=> ( subset(B,C)
% 0.22/0.64 & subset(C,B) ) ) ).
% 0.22/0.64
% 0.22/0.64 %---- line(tarski - df(3),1832749)
% 0.22/0.64 fof(subset_defn,axiom,
% 0.22/0.64 ! [B,C] :
% 0.22/0.65 ( subset(B,C)
% 0.22/0.65 <=> ! [D] :
% 0.22/0.65 ( member(D,B)
% 0.22/0.65 => member(D,C) ) ) ).
% 0.22/0.65
% 0.22/0.65 %---- property(reflexivity,op(subset,2,predicate))
% 0.22/0.65 fof(reflexivity_of_subset,axiom,
% 0.22/0.65 ! [B] : subset(B,B) ).
% 0.22/0.65
% 0.22/0.65 %---- line(hidden - axiom128,1832628)
% 0.22/0.65 fof(empty_defn,axiom,
% 0.22/0.65 ! [B] :
% 0.22/0.65 ( empty(B)
% 0.22/0.65 <=> ! [C] : ~ member(C,B) ) ).
% 0.22/0.65
% 0.22/0.65 %---- line(boole - th(75),1833864)
% 0.22/0.65 fof(prove_no_difference_with_empty_set,conjecture,
% 0.22/0.65 ! [B] : difference(empty_set,B) = empty_set ).
% 0.22/0.65
% 0.22/0.65 %--------------------------------------------------------------------------
% 0.22/0.65 %-------------------------------------------
% 0.22/0.65 % Proof found
% 0.22/0.65 % SZS status Theorem for theBenchmark
% 0.22/0.65 % SZS output start Proof
% 0.22/0.65 %ClaNum:30(EqnAxiom:13)
% 0.22/0.65 %VarNum:61(SingletonVarNum:30)
% 0.22/0.65 %MaxLitNum:3
% 0.22/0.65 %MaxfuncDepth:1
% 0.22/0.65 %SharedTerms:4
% 0.22/0.65 %goalClause: 16
% 0.22/0.65 %singleGoalClaCount:1
% 0.22/0.65 [16]~E(f2(a1,a3),a1)
% 0.22/0.65 [14]P1(a1,x141)
% 0.22/0.65 [15]P1(x151,x151)
% 0.22/0.65 [17]~P2(x171,a1)
% 0.22/0.65 [20]P3(x201)+P2(f4(x201),x201)
% 0.22/0.65 [19]~E(x191,x192)+P1(x191,x192)
% 0.22/0.65 [21]~P3(x211)+~P2(x212,x211)
% 0.22/0.65 [22]~P1(x221,x222)+E(f2(x221,x222),a1)
% 0.22/0.65 [23]P1(x231,x232)+~E(f2(x231,x232),a1)
% 0.22/0.65 [25]P1(x251,x252)+P2(f5(x251,x252),x251)
% 0.22/0.65 [29]P1(x291,x292)+~P2(f5(x291,x292),x292)
% 0.22/0.65 [28]P2(x281,x282)+~P2(x281,f2(x282,x283))
% 0.22/0.65 [30]~P2(x301,x302)+~P2(x301,f2(x303,x302))
% 0.22/0.65 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242)
% 0.22/0.65 [26]~P2(x261,x263)+P2(x261,x262)+~P1(x263,x262)
% 0.22/0.65 [27]~P2(x271,x273)+P2(x271,x272)+P2(x271,f2(x273,x272))
% 0.22/0.65 %EqnAxiom
% 0.22/0.65 [1]E(x11,x11)
% 0.22/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.22/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.22/0.65 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.22/0.65 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.22/0.65 [6]~E(x61,x62)+E(f4(x61),f4(x62))
% 0.22/0.65 [7]~E(x71,x72)+E(f5(x71,x73),f5(x72,x73))
% 0.22/0.65 [8]~E(x81,x82)+E(f5(x83,x81),f5(x83,x82))
% 0.22/0.65 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.22/0.65 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.22/0.65 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113)
% 0.22/0.65 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121)
% 0.22/0.65 [13]~P3(x131)+P3(x132)+~E(x131,x132)
% 0.22/0.65
% 0.22/0.65 %-------------------------------------------
% 0.22/0.65 cnf(33,plain,
% 0.22/0.65 ($false),
% 0.22/0.65 inference(scs_inference,[],[16,14,17,20,22]),
% 0.22/0.65 ['proof']).
% 0.22/0.65 % SZS output end Proof
% 0.22/0.65 % Total time :0.000000s
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