TSTP Solution File: SET638+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET638+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 : n027.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 14:30:32 EDT 2023
% Result : Theorem 0.21s 0.69s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 14:51:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof:theBenchmark
% 0.21/0.68 %-------------------------------------------
% 0.21/0.68 % File :CSE---1.6
% 0.21/0.68 % Problem :theBenchmark
% 0.21/0.68 % Transform :cnf
% 0.21/0.68 % Format :tptp:raw
% 0.21/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.68
% 0.21/0.68 % Result :Theorem 0.030000s
% 0.21/0.68 % Output :CNFRefutation 0.030000s
% 0.21/0.68 %-------------------------------------------
% 0.21/0.69 %--------------------------------------------------------------------------
% 0.21/0.69 % File : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.21/0.69 % Domain : Set Theory
% 0.21/0.69 % Problem : If X (= Y U Z and X ^ Z = the empty set , then X (= Y
% 0.21/0.69 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.21/0.69 % English : If X is a subset of the union of Y and Z and the intersection
% 0.21/0.69 % of X and Z is the empty set, then X is a subset of Y.
% 0.21/0.69
% 0.21/0.69 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.21/0.69 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.21/0.69 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.69 % Source : [ILF]
% 0.21/0.69 % Names : BOOLE (120) [TS89]
% 0.21/0.69
% 0.21/0.69 % Status : Theorem
% 0.21/0.69 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.13 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.14 v2.5.0, 0.00 v2.3.0, 0.33 v2.2.1
% 0.21/0.69 % Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% 0.21/0.69 % Number of atoms : 29 ( 8 equ)
% 0.21/0.69 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.69 % Number of connectives : 16 ( 2 ~; 1 |; 3 &)
% 0.21/0.69 % ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.69 % Maximal formula depth : 6 ( 4 avg)
% 0.21/0.69 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.69 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.21/0.69 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.21/0.69 % Number of variables : 33 ( 33 !; 0 ?)
% 0.21/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.69
% 0.21/0.69 % Comments :
% 0.21/0.69 %--------------------------------------------------------------------------
% 0.21/0.69 %---- line(boole - th(37),1833277)
% 0.21/0.69 fof(intersection_is_subset,axiom,
% 0.21/0.69 ! [B,C] : subset(intersection(B,C),B) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - th(42),1833351)
% 0.21/0.69 fof(subset_intersection,axiom,
% 0.21/0.69 ! [B,C] :
% 0.21/0.69 ( subset(B,C)
% 0.21/0.69 => intersection(B,C) = B ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - th(60),1833665)
% 0.21/0.69 fof(union_empty_set,axiom,
% 0.21/0.69 ! [B] : union(B,empty_set) = B ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - th(70),1833813)
% 0.21/0.69 fof(intersection_distributes_over_union,axiom,
% 0.21/0.69 ! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - df(2),1833042)
% 0.21/0.69 fof(union_defn,axiom,
% 0.21/0.69 ! [B,C,D] :
% 0.21/0.69 ( member(D,union(B,C))
% 0.21/0.69 <=> ( member(D,B)
% 0.21/0.69 | member(D,C) ) ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(hidden - axiom228,1832636)
% 0.21/0.69 fof(empty_set_defn,axiom,
% 0.21/0.69 ! [B] : ~ member(B,empty_set) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - df(3),1833060)
% 0.21/0.69 fof(intersection_defn,axiom,
% 0.21/0.69 ! [B,C,D] :
% 0.21/0.69 ( member(D,intersection(B,C))
% 0.21/0.69 <=> ( member(D,B)
% 0.21/0.69 & member(D,C) ) ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(tarski - df(3),1832749)
% 0.21/0.69 fof(subset_defn,axiom,
% 0.21/0.69 ! [B,C] :
% 0.21/0.69 ( subset(B,C)
% 0.21/0.69 <=> ! [D] :
% 0.21/0.69 ( member(D,B)
% 0.21/0.69 => member(D,C) ) ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - df(8),1833103)
% 0.21/0.69 fof(equal_defn,axiom,
% 0.21/0.69 ! [B,C] :
% 0.21/0.69 ( B = C
% 0.21/0.69 <=> ( subset(B,C)
% 0.21/0.69 & subset(C,B) ) ) ).
% 0.21/0.69
% 0.21/0.69 %---- property(commutativity,op(union,2,function))
% 0.21/0.69 fof(commutativity_of_union,axiom,
% 0.21/0.69 ! [B,C] : union(B,C) = union(C,B) ).
% 0.21/0.69
% 0.21/0.69 %---- property(commutativity,op(intersection,2,function))
% 0.21/0.69 fof(commutativity_of_intersection,axiom,
% 0.21/0.69 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.21/0.69
% 0.21/0.69 %---- property(reflexivity,op(subset,2,predicate))
% 0.21/0.69 fof(reflexivity_of_subset,axiom,
% 0.21/0.69 ! [B] : subset(B,B) ).
% 0.21/0.69
% 0.21/0.69 %---- line(hidden - axiom230,1832628)
% 0.21/0.69 fof(empty_defn,axiom,
% 0.21/0.69 ! [B] :
% 0.21/0.69 ( empty(B)
% 0.21/0.69 <=> ! [C] : ~ member(C,B) ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(hidden - axiom231,1832615)
% 0.21/0.69 fof(equal_member_defn,axiom,
% 0.21/0.69 ! [B,C] :
% 0.21/0.69 ( B = C
% 0.21/0.69 <=> ! [D] :
% 0.21/0.69 ( member(D,B)
% 0.21/0.69 <=> member(D,C) ) ) ).
% 0.21/0.69
% 0.21/0.69 %---- line(boole - th(120),1834506)
% 0.21/0.69 fof(prove_th120,conjecture,
% 0.21/0.69 ! [B,C,D] :
% 0.21/0.69 ( ( subset(B,union(C,D))
% 0.21/0.69 & intersection(B,D) = empty_set )
% 0.21/0.69 => subset(B,C) ) ).
% 0.21/0.69
% 0.21/0.69 %--------------------------------------------------------------------------
% 0.21/0.69 %-------------------------------------------
% 0.21/0.69 % Proof found
% 0.21/0.69 % SZS status Theorem for theBenchmark
% 0.21/0.69 % SZS output start Proof
% 0.21/0.69 %ClaNum:44(EqnAxiom:17)
% 0.21/0.69 %VarNum:110(SingletonVarNum:50)
% 0.21/0.69 %MaxLitNum:3
% 0.21/0.69 %MaxfuncDepth:2
% 0.21/0.69 %SharedTerms:9
% 0.21/0.69 %goalClause: 18 23 26
% 0.21/0.69 %singleGoalClaCount:3
% 0.21/0.69 [26]~P1(a1,a7)
% 0.21/0.69 [18]E(f8(a1,a6),a2)
% 0.21/0.69 [23]P1(a1,f9(a7,a6))
% 0.21/0.69 [20]P1(x201,x201)
% 0.21/0.69 [27]~P2(x271,a2)
% 0.21/0.69 [19]E(f9(x191,a2),x191)
% 0.21/0.69 [21]E(f8(x211,x212),f8(x212,x211))
% 0.21/0.69 [22]E(f9(x221,x222),f9(x222,x221))
% 0.21/0.69 [24]P1(f8(x241,x242),x241)
% 0.21/0.69 [25]E(f9(f8(x251,x252),f8(x251,x253)),f8(x251,f9(x252,x253)))
% 0.21/0.69 [30]P3(x301)+P2(f3(x301),x301)
% 0.21/0.69 [29]~E(x291,x292)+P1(x291,x292)
% 0.21/0.69 [31]~P3(x311)+~P2(x312,x311)
% 0.21/0.69 [32]~P1(x321,x322)+E(f8(x321,x322),x321)
% 0.21/0.69 [34]P1(x341,x342)+P2(f4(x341,x342),x341)
% 0.21/0.69 [40]P1(x401,x402)+~P2(f4(x401,x402),x402)
% 0.21/0.69 [36]~P2(x361,x363)+P2(x361,f9(x362,x363))
% 0.21/0.69 [37]~P2(x371,x372)+P2(x371,f9(x372,x373))
% 0.21/0.69 [38]P2(x381,x382)+~P2(x381,f8(x383,x382))
% 0.21/0.69 [39]P2(x391,x392)+~P2(x391,f8(x392,x393))
% 0.21/0.69 [33]~P1(x332,x331)+~P1(x331,x332)+E(x331,x332)
% 0.21/0.69 [41]E(x411,x412)+P2(f5(x411,x412),x412)+P2(f5(x411,x412),x411)
% 0.21/0.69 [44]E(x441,x442)+~P2(f5(x441,x442),x442)+~P2(f5(x441,x442),x441)
% 0.21/0.69 [35]~P2(x351,x353)+P2(x351,x352)+~P1(x353,x352)
% 0.21/0.69 [42]~P2(x421,x423)+~P2(x421,x422)+P2(x421,f8(x422,x423))
% 0.21/0.69 [43]P2(x431,x432)+P2(x431,x433)+~P2(x431,f9(x433,x432))
% 0.21/0.69 %EqnAxiom
% 0.21/0.69 [1]E(x11,x11)
% 0.21/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.69 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43))
% 0.21/0.69 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52))
% 0.21/0.69 [6]~E(x61,x62)+E(f9(x61,x63),f9(x62,x63))
% 0.21/0.69 [7]~E(x71,x72)+E(f9(x73,x71),f9(x73,x72))
% 0.21/0.70 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.21/0.70 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.21/0.70 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.21/0.70 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.21/0.70 [12]~E(x121,x122)+E(f3(x121),f3(x122))
% 0.21/0.70 [13]P1(x132,x133)+~E(x131,x132)+~P1(x131,x133)
% 0.21/0.70 [14]P1(x143,x142)+~E(x141,x142)+~P1(x143,x141)
% 0.21/0.70 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.21/0.70 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.21/0.70 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.21/0.70
% 0.21/0.70 %-------------------------------------------
% 0.21/0.70 cnf(49,plain,
% 0.21/0.70 (~P2(x491,a2)),
% 0.21/0.70 inference(rename_variables,[],[27])).
% 0.21/0.70 cnf(52,plain,
% 0.21/0.70 (~P2(x521,a2)),
% 0.21/0.70 inference(rename_variables,[],[27])).
% 0.21/0.70 cnf(55,plain,
% 0.21/0.70 (~E(f9(a7,a6),a7)),
% 0.21/0.70 inference(scs_inference,[],[18,27,49,26,23,2,29,30,34,17,14])).
% 0.21/0.70 cnf(57,plain,
% 0.21/0.70 (P1(x571,x571)),
% 0.21/0.70 inference(rename_variables,[],[20])).
% 0.21/0.70 cnf(65,plain,
% 0.21/0.70 (~P2(x651,a2)),
% 0.21/0.70 inference(rename_variables,[],[27])).
% 0.21/0.70 cnf(80,plain,
% 0.21/0.70 (~P2(f4(a1,a7),a7)),
% 0.21/0.70 inference(scs_inference,[],[18,20,27,49,52,65,26,23,24,19,2,29,30,34,17,14,13,3,35,33,41,39,38,12,11,10,9,8,7,6,5,4,40])).
% 0.21/0.70 cnf(84,plain,
% 0.21/0.70 (~P2(x841,f8(a1,a6))),
% 0.21/0.70 inference(scs_inference,[],[18,20,57,27,49,52,65,26,23,24,19,2,29,30,34,17,14,13,3,35,33,41,39,38,12,11,10,9,8,7,6,5,4,40,32,16])).
% 0.21/0.70 cnf(95,plain,
% 0.21/0.70 (P2(f4(a1,a7),a1)),
% 0.21/0.70 inference(scs_inference,[],[18,26,55,2,29,34])).
% 0.21/0.70 cnf(134,plain,
% 0.21/0.70 ($false),
% 0.21/0.70 inference(scs_inference,[],[23,95,84,80,35,42,43]),
% 0.21/0.70 ['proof']).
% 0.21/0.70 % SZS output end Proof
% 0.21/0.70 % Total time :0.030000s
%------------------------------------------------------------------------------