TSTP Solution File: SET630+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n024.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 14:30:29 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 13:31:39 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.010000s
% 0.19/0.61 % Output :CNFRefutation 0.010000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 % File : SET630+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.61 % Domain : Set Theory
% 0.19/0.61 % Problem : X ^ Y is disjoint from X sym\ Y
% 0.19/0.61 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.61 % English : The intersection of X and Y is disjoint from the symmetric
% 0.19/0.61 % difference of X and Y.
% 0.19/0.61
% 0.19/0.61 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.61 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.61 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.61 % Source : [ILF]
% 0.19/0.61 % Names : BOOLE (112) [TS89]
% 0.19/0.61
% 0.19/0.61 % Status : Theorem
% 0.19/0.61 % Rating : 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.26 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.32 v3.3.0, 0.29 v3.2.0, 0.36 v3.1.0, 0.44 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.38 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1
% 0.19/0.61 % Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% 0.19/0.61 % Number of atoms : 22 ( 5 equ)
% 0.19/0.61 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.61 % Number of connectives : 11 ( 1 ~; 1 |; 2 &)
% 0.19/0.61 % ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.61 % Maximal formula depth : 6 ( 4 avg)
% 0.19/0.61 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.61 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 0.19/0.61 % Number of functors : 4 ( 4 usr; 0 con; 2-2 aty)
% 0.19/0.61 % Number of variables : 28 ( 27 !; 1 ?)
% 0.19/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.61
% 0.19/0.61 % Comments :
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 %---- line(boole - df(7),1833089)
% 0.19/0.61 fof(symmetric_difference_defn,axiom,
% 0.19/0.61 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - th(100),1834297)
% 0.19/0.61 fof(intersect_with_union,axiom,
% 0.19/0.61 ! [B,C,D] :
% 0.19/0.61 ( intersect(B,union(C,D))
% 0.19/0.61 <=> ( intersect(B,C)
% 0.19/0.61 | intersect(B,D) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - th(111),1834358)
% 0.19/0.61 fof(intersection_and_union_disjoint,axiom,
% 0.19/0.61 ! [B,C] : disjoint(intersection(B,C),difference(B,C)) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - df(3),1833060)
% 0.19/0.61 fof(intersection_defn,axiom,
% 0.19/0.61 ! [B,C,D] :
% 0.19/0.61 ( member(D,intersection(B,C))
% 0.19/0.61 <=> ( member(D,B)
% 0.19/0.61 & member(D,C) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - df(5),1833080)
% 0.19/0.61 fof(intersect_defn,axiom,
% 0.19/0.61 ! [B,C] :
% 0.19/0.61 ( intersect(B,C)
% 0.19/0.61 <=> ? [D] :
% 0.19/0.61 ( member(D,B)
% 0.19/0.61 & member(D,C) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - axiom202,1833083)
% 0.19/0.61 fof(disjoint_defn,axiom,
% 0.19/0.61 ! [B,C] :
% 0.19/0.61 ( disjoint(B,C)
% 0.19/0.61 <=> ~ intersect(B,C) ) ).
% 0.19/0.61
% 0.19/0.61 %---- property(commutativity,op(union,2,function))
% 0.19/0.61 fof(commutativity_of_union,axiom,
% 0.19/0.61 ! [B,C] : union(B,C) = union(C,B) ).
% 0.19/0.61
% 0.19/0.61 %---- property(commutativity,op(intersection,2,function))
% 0.19/0.61 fof(commutativity_of_intersection,axiom,
% 0.19/0.61 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.19/0.61
% 0.19/0.61 %---- property(commutativity,op(symmetric_difference,2,function))
% 0.19/0.61 fof(commutativity_of_symmetric_difference,axiom,
% 0.19/0.61 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).
% 0.19/0.61
% 0.19/0.61 %---- property(symmetry,op(intersect,2,predicate))
% 0.19/0.61 fof(symmetry_of_intersect,axiom,
% 0.19/0.61 ! [B,C] :
% 0.19/0.61 ( intersect(B,C)
% 0.19/0.61 => intersect(C,B) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(hidden - axiom203,1832615)
% 0.19/0.61 fof(equal_member_defn,axiom,
% 0.19/0.61 ! [B,C] :
% 0.19/0.61 ( B = C
% 0.19/0.61 <=> ! [D] :
% 0.19/0.61 ( member(D,B)
% 0.19/0.61 <=> member(D,C) ) ) ).
% 0.19/0.61
% 0.19/0.61 %---- line(boole - th(112),1834367)
% 0.19/0.61 fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
% 0.19/0.61 ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)) ).
% 0.19/0.61
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark
% 0.19/0.61 % SZS output start Proof
% 0.19/0.61 %ClaNum:38(EqnAxiom:19)
% 0.19/0.62 %VarNum:90(SingletonVarNum:41)
% 0.19/0.62 %MaxLitNum:3
% 0.19/0.62 %MaxfuncDepth:2
% 0.19/0.62 %SharedTerms:7
% 0.19/0.62 %goalClause: 24
% 0.19/0.62 %singleGoalClaCount:1
% 0.19/0.62 [24]~P1(f2(a4,a7),f1(f3(a4,a7),f3(a7,a4)))
% 0.19/0.62 [20]E(f1(x201,x202),f1(x202,x201))
% 0.19/0.62 [21]E(f2(x211,x212),f2(x212,x211))
% 0.19/0.62 [22]P1(f2(x221,x222),f3(x221,x222))
% 0.19/0.62 [25]P1(x251,x252)+P2(x251,x252)
% 0.19/0.62 [26]~P2(x262,x261)+P2(x261,x262)
% 0.19/0.62 [27]~P1(x271,x272)+~P2(x271,x272)
% 0.19/0.62 [31]~P2(x311,x312)+P3(f5(x311,x312),x312)
% 0.19/0.62 [32]~P2(x321,x322)+P3(f5(x321,x322),x321)
% 0.19/0.62 [29]~P2(x291,x293)+P2(x291,f1(x292,x293))
% 0.19/0.62 [30]~P2(x301,x302)+P2(x301,f1(x302,x303))
% 0.19/0.62 [33]P3(x331,x332)+~P3(x331,f2(x333,x332))
% 0.19/0.62 [34]P3(x341,x342)+~P3(x341,f2(x342,x343))
% 0.19/0.62 [35]E(x351,x352)+P3(f6(x351,x352),x352)+P3(f6(x351,x352),x351)
% 0.19/0.62 [38]E(x381,x382)+~P3(f6(x381,x382),x382)+~P3(f6(x381,x382),x381)
% 0.19/0.62 [28]~P3(x283,x281)+P2(x281,x282)+~P3(x283,x282)
% 0.19/0.62 [36]~P3(x361,x363)+~P3(x361,x362)+P3(x361,f2(x362,x363))
% 0.19/0.62 [37]P2(x371,x372)+P2(x371,x373)+~P2(x371,f1(x373,x372))
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.62 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.19/0.62 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.19/0.62 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.19/0.62 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.19/0.62 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.19/0.62 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.19/0.62 [12]~E(x121,x122)+E(f3(x121,x123),f3(x122,x123))
% 0.19/0.62 [13]~E(x131,x132)+E(f3(x133,x131),f3(x133,x132))
% 0.19/0.62 [14]P1(x142,x143)+~E(x141,x142)+~P1(x141,x143)
% 0.19/0.62 [15]P1(x153,x152)+~E(x151,x152)+~P1(x153,x151)
% 0.19/0.62 [16]P3(x162,x163)+~E(x161,x162)+~P3(x161,x163)
% 0.19/0.62 [17]P3(x173,x172)+~E(x171,x172)+~P3(x173,x171)
% 0.19/0.62 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183)
% 0.19/0.62 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(40,plain,
% 0.19/0.62 (P1(f2(x401,x402),f3(x401,x402))),
% 0.19/0.62 inference(rename_variables,[],[22])).
% 0.19/0.62 cnf(41,plain,
% 0.19/0.62 (P1(f2(x411,x412),f3(x412,x411))),
% 0.19/0.62 inference(scs_inference,[],[24,21,22,40,15,14])).
% 0.19/0.62 cnf(42,plain,
% 0.19/0.62 (P1(f2(x421,x422),f3(x421,x422))),
% 0.19/0.62 inference(rename_variables,[],[22])).
% 0.19/0.62 cnf(46,plain,
% 0.19/0.62 (~P2(f2(x461,x462),f3(x461,x462))),
% 0.19/0.62 inference(scs_inference,[],[24,20,21,22,40,42,15,14,3,2,27])).
% 0.19/0.62 cnf(48,plain,
% 0.19/0.62 (P2(f2(a4,a7),f1(f3(a4,a7),f3(a7,a4)))),
% 0.19/0.62 inference(scs_inference,[],[24,20,21,22,40,42,15,14,3,2,27,25])).
% 0.19/0.62 cnf(72,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[41,46,48,37,27]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.010000s
%------------------------------------------------------------------------------