TSTP Solution File: SET585+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET585+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 : n008.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 14:30:14 EDT 2023
% Result : Theorem 0.17s 0.64s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET585+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 12:34:32 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.57 start to proof:theBenchmark
% 0.17/0.63 %-------------------------------------------
% 0.17/0.63 % File :CSE---1.6
% 0.17/0.63 % Problem :theBenchmark
% 0.17/0.63 % Transform :cnf
% 0.17/0.63 % Format :tptp:raw
% 0.17/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.17/0.63
% 0.17/0.63 % Result :Theorem 0.010000s
% 0.17/0.63 % Output :CNFRefutation 0.010000s
% 0.17/0.63 %-------------------------------------------
% 0.17/0.64 %--------------------------------------------------------------------------
% 0.17/0.64 % File : SET585+3 : TPTP v8.1.2. Released v2.2.0.
% 0.17/0.64 % Domain : Set Theory
% 0.17/0.64 % Problem : The intersection of X and Y is a subset of the union of X and Z
% 0.17/0.64 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.17/0.64 % English :
% 0.17/0.64
% 0.17/0.64 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.17/0.64 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.17/0.64 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.17/0.64 % Source : [ILF]
% 0.17/0.64 % Names : BOOLE (38) [TS89]
% 0.17/0.64
% 0.17/0.64 % Status : Theorem
% 0.17/0.64 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.07 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, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 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 v2.2.1
% 0.17/0.64 % Syntax : Number of formulae : 11 ( 6 unt; 0 def)
% 0.17/0.64 % Number of atoms : 21 ( 3 equ)
% 0.17/0.64 % Maximal formula atoms : 3 ( 1 avg)
% 0.17/0.64 % Number of connectives : 10 ( 0 ~; 1 |; 2 &)
% 0.17/0.64 % ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.64 % Maximal formula depth : 6 ( 4 avg)
% 0.17/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.17/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.17/0.64 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.17/0.64 % Number of variables : 27 ( 27 !; 0 ?)
% 0.17/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.17/0.64
% 0.17/0.64 % Comments :
% 0.17/0.64 %--------------------------------------------------------------------------
% 0.17/0.64 %---- line(boole - th(29),1833172)
% 0.17/0.64 fof(transitivity_of_subset,axiom,
% 0.17/0.64 ! [B,C,D] :
% 0.17/0.64 ( ( subset(B,C)
% 0.17/0.64 & subset(C,D) )
% 0.17/0.64 => subset(B,D) ) ).
% 0.17/0.64
% 0.17/0.64 %---- line(boole - th(31),1833190)
% 0.17/0.64 fof(subset_of_union,axiom,
% 0.17/0.64 ! [B,C] : subset(B,union(B,C)) ).
% 0.17/0.64
% 0.17/0.64 %---- line(boole - th(37),1833277)
% 0.17/0.64 fof(intersection_is_subset,axiom,
% 0.17/0.64 ! [B,C] : subset(intersection(B,C),B) ).
% 0.17/0.64
% 0.17/0.64 %---- line(boole - df(2),1833042)
% 0.17/0.64 fof(union_defn,axiom,
% 0.17/0.64 ! [B,C,D] :
% 0.17/0.64 ( member(D,union(B,C))
% 0.17/0.64 <=> ( member(D,B)
% 0.17/0.64 | member(D,C) ) ) ).
% 0.17/0.64
% 0.17/0.64 %---- line(boole - df(3),1833060)
% 0.17/0.64 fof(intersection_defn,axiom,
% 0.17/0.64 ! [B,C,D] :
% 0.17/0.64 ( member(D,intersection(B,C))
% 0.17/0.64 <=> ( member(D,B)
% 0.17/0.64 & member(D,C) ) ) ).
% 0.17/0.64
% 0.17/0.64 %---- line(tarski - df(3),1832749)
% 0.17/0.64 fof(subset_defn,axiom,
% 0.17/0.64 ! [B,C] :
% 0.17/0.64 ( subset(B,C)
% 0.17/0.64 <=> ! [D] :
% 0.17/0.64 ( member(D,B)
% 0.17/0.64 => member(D,C) ) ) ).
% 0.17/0.64
% 0.17/0.64 %---- property(commutativity,op(union,2,function))
% 0.17/0.64 fof(commutativity_of_union,axiom,
% 0.17/0.64 ! [B,C] : union(B,C) = union(C,B) ).
% 0.17/0.64
% 0.17/0.64 %---- property(commutativity,op(intersection,2,function))
% 0.17/0.64 fof(commutativity_of_intersection,axiom,
% 0.17/0.64 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.17/0.64
% 0.17/0.64 %---- property(reflexivity,op(subset,2,predicate))
% 0.17/0.64 fof(reflexivity_of_subset,axiom,
% 0.17/0.64 ! [B] : subset(B,B) ).
% 0.17/0.64
% 0.17/0.64 %---- line(hidden - axiom47,1832615)
% 0.17/0.64 fof(equal_member_defn,axiom,
% 0.17/0.64 ! [B,C] :
% 0.17/0.64 ( B = C
% 0.17/0.64 <=> ! [D] :
% 0.17/0.64 ( member(D,B)
% 0.17/0.64 <=> member(D,C) ) ) ).
% 0.17/0.64
% 0.17/0.64 %---- line(boole - th(38),1833287)
% 0.17/0.64 fof(prove_intersection_subset_of_union,conjecture,
% 0.17/0.64 ! [B,C,D] : subset(intersection(B,C),union(B,D)) ).
% 0.17/0.64
% 0.17/0.64 %--------------------------------------------------------------------------
% 0.17/0.64 %-------------------------------------------
% 0.17/0.64 % Proof found
% 0.17/0.64 % SZS status Theorem for theBenchmark
% 0.17/0.64 % SZS output start Proof
% 0.17/0.64 %ClaNum:33(EqnAxiom:15)
% 0.17/0.64 %VarNum:88(SingletonVarNum:41)
% 0.17/0.64 %MaxLitNum:3
% 0.17/0.64 %MaxfuncDepth:1
% 0.17/0.64 %SharedTerms:6
% 0.17/0.64 %goalClause: 21
% 0.17/0.64 %singleGoalClaCount:1
% 0.17/0.64 [21]~P1(f2(a3,a6),f1(a3,a7))
% 0.17/0.64 [16]P1(x161,x161)
% 0.17/0.64 [17]E(f1(x171,x172),f1(x172,x171))
% 0.17/0.64 [18]E(f2(x181,x182),f2(x182,x181))
% 0.17/0.64 [19]P1(x191,f1(x191,x192))
% 0.17/0.64 [20]P1(f2(x201,x202),x201)
% 0.17/0.64 [22]P1(x221,x222)+P2(f4(x221,x222),x221)
% 0.17/0.64 [29]P1(x291,x292)+~P2(f4(x291,x292),x292)
% 0.17/0.64 [25]~P2(x251,x253)+P2(x251,f1(x252,x253))
% 0.17/0.64 [26]~P2(x261,x262)+P2(x261,f1(x262,x263))
% 0.17/0.64 [27]P2(x271,x272)+~P2(x271,f2(x273,x272))
% 0.17/0.64 [28]P2(x281,x282)+~P2(x281,f2(x282,x283))
% 0.17/0.64 [30]E(x301,x302)+P2(f5(x301,x302),x302)+P2(f5(x301,x302),x301)
% 0.17/0.64 [33]E(x331,x332)+~P2(f5(x331,x332),x332)+~P2(f5(x331,x332),x331)
% 0.17/0.64 [23]~P1(x231,x233)+P1(x231,x232)+~P1(x233,x232)
% 0.17/0.64 [24]~P2(x241,x243)+P2(x241,x242)+~P1(x243,x242)
% 0.17/0.64 [31]~P2(x311,x313)+~P2(x311,x312)+P2(x311,f2(x312,x313))
% 0.17/0.64 [32]P2(x321,x322)+P2(x321,x323)+~P2(x321,f1(x323,x322))
% 0.17/0.64 %EqnAxiom
% 0.17/0.64 [1]E(x11,x11)
% 0.17/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.17/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.17/0.64 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.17/0.64 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.17/0.64 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.17/0.64 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.17/0.64 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.17/0.64 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.17/0.64 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.17/0.64 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.17/0.64 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123)
% 0.17/0.64 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131)
% 0.17/0.64 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.17/0.64 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.17/0.64
% 0.17/0.64 %-------------------------------------------
% 0.17/0.64 cnf(35,plain,
% 0.17/0.64 (P1(x351,x351)),
% 0.17/0.64 inference(rename_variables,[],[16])).
% 0.17/0.64 cnf(39,plain,
% 0.17/0.64 (E(f1(x391,x392),f1(x392,x391))),
% 0.17/0.64 inference(rename_variables,[],[17])).
% 0.17/0.64 cnf(41,plain,
% 0.17/0.64 (~P2(f4(f2(a3,a6),f1(a3,a7)),f1(a3,a7))),
% 0.17/0.64 inference(scs_inference,[],[21,16,35,17,13,12,3,2,29])).
% 0.17/0.64 cnf(51,plain,
% 0.17/0.64 (P2(f4(f2(a3,a6),f1(a3,a7)),a3)),
% 0.17/0.64 inference(scs_inference,[],[21,16,35,19,17,39,13,12,3,2,29,22,15,14,23,28])).
% 0.17/0.64 cnf(89,plain,
% 0.17/0.64 ($false),
% 0.17/0.64 inference(scs_inference,[],[51,41,26]),
% 0.17/0.64 ['proof']).
% 0.17/0.64 % SZS output end Proof
% 0.17/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------