TSTP Solution File: SET596+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET596+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 : n003.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 14:30:17 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET596+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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 13:37:54 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.59 %-------------------------------------------
% 0.20/0.59 % File :CSE---1.6
% 0.20/0.59 % Problem :theBenchmark
% 0.20/0.59 % Transform :cnf
% 0.20/0.59 % Format :tptp:raw
% 0.20/0.59 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.59
% 0.20/0.59 % Result :Theorem 0.000000s
% 0.20/0.59 % Output :CNFRefutation 0.000000s
% 0.20/0.59 %-------------------------------------------
% 0.20/0.59 %--------------------------------------------------------------------------
% 0.20/0.59 % File : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.59 % Domain : Set Theory
% 0.20/0.59 % Problem : If X (= Y and Y ^ Z = the empty set, then X ^ Z = the empty set
% 0.20/0.59 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.59 % English : If X is a subset of Y and the intersection of Y and Z is the
% 0.20/0.59 % empty set, then the intersection of X and Z is the empty set.
% 0.20/0.59
% 0.20/0.59 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.59 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.59 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.59 % Source : [ILF]
% 0.20/0.59 % Names : BOOLE (55) [TS89]
% 0.20/0.59
% 0.20/0.59 % Status : Theorem
% 0.20/0.59 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.20/0.59 % Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% 0.20/0.59 % Number of atoms : 24 ( 6 equ)
% 0.20/0.59 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.59 % Number of connectives : 15 ( 2 ~; 0 |; 3 &)
% 0.20/0.59 % ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.59 % Maximal formula depth : 6 ( 5 avg)
% 0.20/0.59 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.59 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.59 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.20/0.59 % Number of variables : 24 ( 24 !; 0 ?)
% 0.20/0.59 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.59
% 0.20/0.59 % Comments :
% 0.20/0.59 %--------------------------------------------------------------------------
% 0.20/0.59 %---- line(boole - th(30),1833179)
% 0.20/0.59 fof(subset_of_empty_set_is_empty_set,axiom,
% 0.20/0.59 ! [B] :
% 0.20/0.59 ( subset(B,empty_set)
% 0.20/0.59 => B = empty_set ) ).
% 0.20/0.59
% 0.20/0.59 %---- line(boole - th(40),1833318)
% 0.20/0.59 fof(intersection_of_subset,axiom,
% 0.20/0.59 ! [B,C,D] :
% 0.20/0.59 ( subset(B,C)
% 0.20/0.59 => subset(intersection(B,D),intersection(C,D)) ) ).
% 0.20/0.59
% 0.20/0.59 %---- line(hidden - axiom79,1832636)
% 0.20/0.59 fof(empty_set_defn,axiom,
% 0.20/0.59 ! [B] : ~ member(B,empty_set) ).
% 0.20/0.59
% 0.20/0.59 %---- line(boole - df(3),1833060)
% 0.20/0.59 fof(intersection_defn,axiom,
% 0.20/0.59 ! [B,C,D] :
% 0.20/0.59 ( member(D,intersection(B,C))
% 0.20/0.59 <=> ( member(D,B)
% 0.20/0.59 & member(D,C) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- line(tarski - df(3),1832749)
% 0.20/0.60 fof(subset_defn,axiom,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( subset(B,C)
% 0.20/0.60 <=> ! [D] :
% 0.20/0.60 ( member(D,B)
% 0.20/0.60 => member(D,C) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- line(boole - df(8),1833103)
% 0.20/0.60 fof(equal_defn,axiom,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( B = C
% 0.20/0.60 <=> ( subset(B,C)
% 0.20/0.60 & subset(C,B) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- property(commutativity,op(intersection,2,function))
% 0.20/0.60 fof(commutativity_of_intersection,axiom,
% 0.20/0.60 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.20/0.60
% 0.20/0.60 %---- property(reflexivity,op(subset,2,predicate))
% 0.20/0.60 fof(reflexivity_of_subset,axiom,
% 0.20/0.60 ! [B] : subset(B,B) ).
% 0.20/0.60
% 0.20/0.60 %---- line(hidden - axiom81,1832628)
% 0.20/0.60 fof(empty_defn,axiom,
% 0.20/0.60 ! [B] :
% 0.20/0.60 ( empty(B)
% 0.20/0.60 <=> ! [C] : ~ member(C,B) ) ).
% 0.20/0.60
% 0.20/0.60 %---- line(hidden - axiom82,1832615)
% 0.20/0.60 fof(equal_member_defn,axiom,
% 0.20/0.60 ! [B,C] :
% 0.20/0.60 ( B = C
% 0.20/0.60 <=> ! [D] :
% 0.20/0.60 ( member(D,B)
% 0.20/0.60 <=> member(D,C) ) ) ).
% 0.20/0.60
% 0.20/0.60 %---- line(boole - th(55),1833564)
% 0.20/0.60 fof(prove_th55,conjecture,
% 0.20/0.60 ! [B,C,D] :
% 0.20/0.60 ( ( subset(B,C)
% 0.20/0.60 & intersection(C,D) = empty_set )
% 0.20/0.60 => intersection(B,D) = empty_set ) ).
% 0.20/0.60
% 0.20/0.60 %--------------------------------------------------------------------------
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 %ClaNum:36(EqnAxiom:15)
% 0.20/0.60 %VarNum:80(SingletonVarNum:35)
% 0.20/0.60 %MaxLitNum:3
% 0.20/0.60 %MaxfuncDepth:1
% 0.20/0.60 %SharedTerms:9
% 0.20/0.60 %goalClause: 16 17 20
% 0.20/0.60 %singleGoalClaCount:3
% 0.20/0.60 [17]P1(a3,a1)
% 0.20/0.60 [16]E(f8(a1,a7),a2)
% 0.20/0.60 [20]~E(f8(a3,a7),a2)
% 0.20/0.60 [18]P1(x181,x181)
% 0.20/0.60 [21]~P2(x211,a2)
% 0.20/0.60 [19]E(f8(x191,x192),f8(x192,x191))
% 0.20/0.60 [24]~P1(x241,a2)+E(x241,a2)
% 0.20/0.60 [25]P3(x251)+P2(f4(x251),x251)
% 0.20/0.60 [23]~E(x231,x232)+P1(x231,x232)
% 0.20/0.60 [26]~P3(x261)+~P2(x262,x261)
% 0.20/0.60 [28]P1(x281,x282)+P2(f5(x281,x282),x281)
% 0.20/0.60 [32]P1(x321,x322)+~P2(f5(x321,x322),x322)
% 0.20/0.60 [30]P2(x301,x302)+~P2(x301,f8(x303,x302))
% 0.20/0.60 [31]P2(x311,x312)+~P2(x311,f8(x312,x313))
% 0.20/0.60 [35]~P1(x351,x353)+P1(f8(x351,x352),f8(x353,x352))
% 0.20/0.60 [27]~P1(x272,x271)+~P1(x271,x272)+E(x271,x272)
% 0.20/0.60 [33]E(x331,x332)+P2(f6(x331,x332),x332)+P2(f6(x331,x332),x331)
% 0.20/0.60 [36]E(x361,x362)+~P2(f6(x361,x362),x362)+~P2(f6(x361,x362),x361)
% 0.20/0.60 [29]~P2(x291,x293)+P2(x291,x292)+~P1(x293,x292)
% 0.20/0.60 [34]~P2(x341,x343)+~P2(x341,x342)+P2(x341,f8(x342,x343))
% 0.20/0.60 %EqnAxiom
% 0.20/0.60 [1]E(x11,x11)
% 0.20/0.60 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.60 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43))
% 0.20/0.60 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52))
% 0.20/0.60 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.20/0.60 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.20/0.60 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.20/0.60 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.20/0.60 [10]~E(x101,x102)+E(f4(x101),f4(x102))
% 0.20/0.60 [11]P1(x112,x113)+~E(x111,x112)+~P1(x111,x113)
% 0.20/0.60 [12]P1(x123,x122)+~E(x121,x122)+~P1(x123,x121)
% 0.20/0.60 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.20/0.60 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.20/0.60 [15]~P3(x151)+P3(x152)+~E(x151,x152)
% 0.20/0.60
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 cnf(41,plain,
% 0.20/0.60 (~P2(x411,a2)),
% 0.20/0.60 inference(rename_variables,[],[21])).
% 0.20/0.60 cnf(44,plain,
% 0.20/0.60 (~P2(x441,a2)),
% 0.20/0.60 inference(rename_variables,[],[21])).
% 0.20/0.60 cnf(66,plain,
% 0.20/0.60 ($false),
% 0.20/0.60 inference(scs_inference,[],[16,18,21,41,44,17,20,2,24,25,28,15,11,3,23,31,30,10,9,8,7,6,5,4,35,14,12]),
% 0.20/0.60 ['proof']).
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time :0.000000s
%------------------------------------------------------------------------------