TSTP Solution File: SET605+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET605+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 : n013.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 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:49:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 % File : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.62 % Domain : Set Theory
% 0.19/0.62 % Problem : The difference of X and the union of X and Y is the empty set
% 0.19/0.62 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.62 % Source : [ILF]
% 0.19/0.62 % Names : BOOLE (76) [TS89]
% 0.19/0.62
% 0.19/0.62 % Status : Theorem
% 0.19/0.63 % Rating : 0.03 v8.1.0, 0.06 v7.4.0, 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.05 v3.3.0, 0.14 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.3.0, 0.33 v2.2.1
% 0.19/0.63 % Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% 0.19/0.63 % Number of atoms : 24 ( 5 equ)
% 0.19/0.63 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.63 % Number of connectives : 15 ( 3 ~; 1 |; 2 &)
% 0.19/0.63 % ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.63 % Maximal formula depth : 7 ( 4 avg)
% 0.19/0.63 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.63 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.19/0.63 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.63 % Number of variables : 26 ( 26 !; 0 ?)
% 0.19/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.63
% 0.19/0.63 % Comments :
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %---- line(boole - th(31),1833190)
% 0.19/0.63 fof(subset_of_union,axiom,
% 0.19/0.63 ! [B,C] : subset(B,union(B,C)) ).
% 0.19/0.63
% 0.19/0.63 %---- line(boole - th(45),1833405)
% 0.19/0.63 fof(difference_empty_set,axiom,
% 0.19/0.63 ! [B,C] :
% 0.19/0.63 ( difference(B,C) = empty_set
% 0.19/0.63 <=> subset(B,C) ) ).
% 0.19/0.63
% 0.19/0.63 %---- line(boole - df(2),1833042)
% 0.19/0.63 fof(union_defn,axiom,
% 0.19/0.63 ! [B,C,D] :
% 0.19/0.63 ( member(D,union(B,C))
% 0.19/0.63 <=> ( member(D,B)
% 0.19/0.63 | member(D,C) ) ) ).
% 0.19/0.63
% 0.19/0.63 %---- line(hidden - axiom129,1832636)
% 0.19/0.63 fof(empty_set_defn,axiom,
% 0.19/0.63 ! [B] : ~ member(B,empty_set) ).
% 0.19/0.63
% 0.19/0.63 %---- line(boole - df(4),1833078)
% 0.19/0.63 fof(difference_defn,axiom,
% 0.19/0.63 ! [B,C,D] :
% 0.19/0.63 ( member(D,difference(B,C))
% 0.19/0.63 <=> ( member(D,B)
% 0.19/0.63 & ~ member(D,C) ) ) ).
% 0.19/0.63
% 0.19/0.63 %---- line(boole - df(8),1833103)
% 0.19/0.63 fof(equal_defn,axiom,
% 0.19/0.63 ! [B,C] :
% 0.19/0.63 ( B = C
% 0.19/0.63 <=> ( subset(B,C)
% 0.19/0.63 & subset(C,B) ) ) ).
% 0.19/0.63
% 0.19/0.63 %---- property(commutativity,op(union,2,function))
% 0.19/0.63 fof(commutativity_of_union,axiom,
% 0.19/0.63 ! [B,C] : union(B,C) = union(C,B) ).
% 0.19/0.63
% 0.19/0.63 %---- line(tarski - df(3),1832749)
% 0.19/0.63 fof(subset_defn,axiom,
% 0.19/0.63 ! [B,C] :
% 0.19/0.63 ( subset(B,C)
% 0.19/0.63 <=> ! [D] :
% 0.19/0.63 ( member(D,B)
% 0.19/0.63 => member(D,C) ) ) ).
% 0.19/0.63
% 0.19/0.63 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.63 fof(reflexivity_of_subset,axiom,
% 0.19/0.63 ! [B] : subset(B,B) ).
% 0.19/0.63
% 0.19/0.63 %---- line(hidden - axiom131,1832628)
% 0.19/0.63 fof(empty_defn,axiom,
% 0.19/0.63 ! [B] :
% 0.19/0.63 ( empty(B)
% 0.19/0.63 <=> ! [C] : ~ member(C,B) ) ).
% 0.19/0.63
% 0.19/0.63 %---- line(hidden - axiom132,1832615)
% 0.19/0.63 fof(equal_member_defn,axiom,
% 0.19/0.63 ! [B,C] :
% 0.19/0.63 ( B = C
% 0.19/0.63 <=> ! [D] :
% 0.19/0.63 ( member(D,B)
% 0.19/0.63 <=> member(D,C) ) ) ).
% 0.19/0.63
% 0.19/0.63 %---- line(boole - th(76),1833872)
% 0.19/0.63 fof(prove_th76,conjecture,
% 0.19/0.63 ! [B,C] : difference(B,union(B,C)) = empty_set ).
% 0.19/0.63
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:40(EqnAxiom:17)
% 0.19/0.63 %VarNum:100(SingletonVarNum:46)
% 0.19/0.63 %MaxLitNum:3
% 0.19/0.63 %MaxfuncDepth:2
% 0.19/0.63 %SharedTerms:6
% 0.19/0.63 %goalClause: 22
% 0.19/0.63 %singleGoalClaCount:1
% 0.19/0.63 [22]~E(f3(a4,f1(a4,a8)),a2)
% 0.19/0.63 [18]P1(x181,x181)
% 0.19/0.63 [21]~P2(x211,a2)
% 0.19/0.63 [19]E(f1(x191,x192),f1(x192,x191))
% 0.19/0.63 [20]P1(x201,f1(x201,x202))
% 0.19/0.63 [25]P3(x251)+P2(f5(x251),x251)
% 0.19/0.63 [24]~E(x241,x242)+P1(x241,x242)
% 0.19/0.63 [26]~P3(x261)+~P2(x262,x261)
% 0.19/0.63 [27]~P1(x271,x272)+E(f3(x271,x272),a2)
% 0.19/0.63 [28]P1(x281,x282)+~E(f3(x281,x282),a2)
% 0.19/0.63 [30]P1(x301,x302)+P2(f6(x301,x302),x301)
% 0.19/0.63 [36]P1(x361,x362)+~P2(f6(x361,x362),x362)
% 0.19/0.63 [32]~P2(x321,x323)+P2(x321,f1(x322,x323))
% 0.19/0.63 [33]~P2(x331,x332)+P2(x331,f1(x332,x333))
% 0.19/0.63 [35]P2(x351,x352)+~P2(x351,f3(x352,x353))
% 0.19/0.63 [38]~P2(x381,x382)+~P2(x381,f3(x383,x382))
% 0.19/0.63 [29]~P1(x292,x291)+~P1(x291,x292)+E(x291,x292)
% 0.19/0.63 [37]E(x371,x372)+P2(f7(x371,x372),x372)+P2(f7(x371,x372),x371)
% 0.19/0.63 [40]E(x401,x402)+~P2(f7(x401,x402),x402)+~P2(f7(x401,x402),x401)
% 0.19/0.63 [31]~P2(x311,x313)+P2(x311,x312)+~P1(x313,x312)
% 0.19/0.63 [34]~P2(x341,x343)+P2(x341,x342)+P2(x341,f3(x343,x342))
% 0.19/0.63 [39]P2(x391,x392)+P2(x391,x393)+~P2(x391,f1(x393,x392))
% 0.19/0.63 %EqnAxiom
% 0.19/0.63 [1]E(x11,x11)
% 0.19/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.63 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.63 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.63 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.19/0.63 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.19/0.63 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.19/0.63 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.19/0.63 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103))
% 0.19/0.63 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112))
% 0.19/0.63 [12]~E(x121,x122)+E(f5(x121),f5(x122))
% 0.19/0.63 [13]P1(x132,x133)+~E(x131,x132)+~P1(x131,x133)
% 0.19/0.63 [14]P1(x143,x142)+~E(x141,x142)+~P1(x143,x141)
% 0.19/0.63 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.19/0.63 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.19/0.63 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(42,plain,
% 0.19/0.63 (~P2(x421,a2)),
% 0.19/0.63 inference(rename_variables,[],[21])).
% 0.19/0.63 cnf(46,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[22,21,42,20,25,30,27]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------