TSTP Solution File: SET621+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET621+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 : 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 14:30:26 EDT 2023
% Result : Theorem 0.21s 0.72s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET621+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 08:52:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.59 start to proof:theBenchmark
% 0.21/0.71 %-------------------------------------------
% 0.21/0.71 % File :CSE---1.6
% 0.21/0.71 % Problem :theBenchmark
% 0.21/0.71 % Transform :cnf
% 0.21/0.71 % Format :tptp:raw
% 0.21/0.71 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.71
% 0.21/0.71 % Result :Theorem 0.070000s
% 0.21/0.71 % Output :CNFRefutation 0.070000s
% 0.21/0.71 %-------------------------------------------
% 0.21/0.72 %--------------------------------------------------------------------------
% 0.21/0.72 % File : SET621+3 : TPTP v8.1.2. Released v2.2.0.
% 0.21/0.72 % Domain : Set Theory
% 0.21/0.72 % Problem : (X sym\ Y) \ Z = (X \ (Y U Z)) U (Y \ (X U Z))
% 0.21/0.72 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.21/0.72 % English : The difference of (the symmetric difference of X and Y) and Z
% 0.21/0.72 % is the union of (the difference of X and (the union of Y and Z))
% 0.21/0.72 % and (the difference of Y and (the union of X and Z)).
% 0.21/0.72
% 0.21/0.72 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.21/0.72 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.21/0.72 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.21/0.72 % Source : [ILF]
% 0.21/0.72 % Names : BOOLE (97) [TS89]
% 0.21/0.72
% 0.21/0.72 % Status : Theorem
% 0.21/0.72 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.3.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.17 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.0, 0.33 v3.7.0, 0.30 v3.5.0, 0.32 v3.4.0, 0.26 v3.3.0, 0.21 v3.2.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.00 v2.2.1
% 0.21/0.72 % Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% 0.21/0.72 % Number of atoms : 22 ( 8 equ)
% 0.21/0.72 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.72 % Number of connectives : 11 ( 1 ~; 1 |; 2 &)
% 0.21/0.72 % ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.72 % Maximal formula depth : 7 ( 4 avg)
% 0.21/0.72 % Maximal term depth : 4 ( 1 avg)
% 0.21/0.72 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.21/0.72 % Number of functors : 3 ( 3 usr; 0 con; 2-2 aty)
% 0.21/0.72 % Number of variables : 30 ( 30 !; 0 ?)
% 0.21/0.72 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.72
% 0.21/0.72 % Comments :
% 0.21/0.72 %--------------------------------------------------------------------------
% 0.21/0.72 %---- line(boole - df(7),1833089)
% 0.21/0.72 fof(symmetric_difference_defn,axiom,
% 0.21/0.72 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - th(88),1834157)
% 0.21/0.72 fof(difference_difference_union,axiom,
% 0.21/0.72 ! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - th(89),1834187)
% 0.21/0.72 fof(difference_distributes_over_union,axiom,
% 0.21/0.72 ! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - df(2),1833042)
% 0.21/0.72 fof(union_defn,axiom,
% 0.21/0.72 ! [B,C,D] :
% 0.21/0.72 ( member(D,union(B,C))
% 0.21/0.72 <=> ( member(D,B)
% 0.21/0.72 | member(D,C) ) ) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - df(4),1833078)
% 0.21/0.72 fof(difference_defn,axiom,
% 0.21/0.72 ! [B,C,D] :
% 0.21/0.72 ( member(D,difference(B,C))
% 0.21/0.72 <=> ( member(D,B)
% 0.21/0.72 & ~ member(D,C) ) ) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - df(8),1833103)
% 0.21/0.72 fof(equal_defn,axiom,
% 0.21/0.72 ! [B,C] :
% 0.21/0.72 ( B = C
% 0.21/0.72 <=> ( subset(B,C)
% 0.21/0.72 & subset(C,B) ) ) ).
% 0.21/0.72
% 0.21/0.72 %---- property(commutativity,op(union,2,function))
% 0.21/0.72 fof(commutativity_of_union,axiom,
% 0.21/0.72 ! [B,C] : union(B,C) = union(C,B) ).
% 0.21/0.72
% 0.21/0.72 %---- property(commutativity,op(symmetric_difference,2,function))
% 0.21/0.72 fof(commutativity_of_symmetric_difference,axiom,
% 0.21/0.72 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).
% 0.21/0.72
% 0.21/0.72 %---- line(hidden - axiom179,1832615)
% 0.21/0.72 fof(equal_member_defn,axiom,
% 0.21/0.72 ! [B,C] :
% 0.21/0.72 ( B = C
% 0.21/0.72 <=> ! [D] :
% 0.21/0.72 ( member(D,B)
% 0.21/0.72 <=> member(D,C) ) ) ).
% 0.21/0.72
% 0.21/0.72 %---- line(tarski - df(3),1832749)
% 0.21/0.72 fof(subset_defn,axiom,
% 0.21/0.72 ! [B,C] :
% 0.21/0.72 ( subset(B,C)
% 0.21/0.72 <=> ! [D] :
% 0.21/0.72 ( member(D,B)
% 0.21/0.72 => member(D,C) ) ) ).
% 0.21/0.72
% 0.21/0.72 %---- property(reflexivity,op(subset,2,predicate))
% 0.21/0.72 fof(reflexivity_of_subset,axiom,
% 0.21/0.72 ! [B] : subset(B,B) ).
% 0.21/0.72
% 0.21/0.72 %---- line(boole - th(97),1834236)
% 0.21/0.72 fof(prove_th97,conjecture,
% 0.21/0.72 ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))) ).
% 0.21/0.72
% 0.21/0.72 %--------------------------------------------------------------------------
% 0.21/0.72 %-------------------------------------------
% 0.21/0.72 % Proof found
% 0.21/0.72 % SZS status Theorem for theBenchmark
% 0.21/0.72 % SZS output start Proof
% 0.21/0.72 %ClaNum:35(EqnAxiom:15)
% 0.21/0.72 %VarNum:95(SingletonVarNum:42)
% 0.21/0.72 %MaxLitNum:3
% 0.21/0.72 %MaxfuncDepth:3
% 0.21/0.72 %SharedTerms:12
% 0.21/0.72 %goalClause: 21
% 0.21/0.72 %singleGoalClaCount:1
% 0.21/0.72 [21]~E(f1(f2(a3,f1(a6,a7)),f2(a6,f1(a3,a7))),f2(f1(f2(a3,a6),f2(a6,a3)),a7))
% 0.21/0.72 [16]P1(x161,x161)
% 0.21/0.72 [17]E(f1(x171,x172),f1(x172,x171))
% 0.21/0.72 [18]E(f2(f2(x181,x182),x183),f2(x181,f1(x182,x183)))
% 0.21/0.72 [19]E(f1(f2(x191,x192),f2(x193,x192)),f2(f1(x191,x193),x192))
% 0.21/0.72 [23]~E(x231,x232)+P1(x231,x232)
% 0.21/0.72 [25]P1(x251,x252)+P2(f4(x251,x252),x251)
% 0.21/0.72 [31]P1(x311,x312)+~P2(f4(x311,x312),x312)
% 0.21/0.72 [27]~P2(x271,x273)+P2(x271,f1(x272,x273))
% 0.21/0.72 [28]~P2(x281,x282)+P2(x281,f1(x282,x283))
% 0.21/0.72 [30]P2(x301,x302)+~P2(x301,f2(x302,x303))
% 0.21/0.72 [33]~P2(x331,x332)+~P2(x331,f2(x333,x332))
% 0.21/0.72 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242)
% 0.21/0.72 [32]E(x321,x322)+P2(f5(x321,x322),x322)+P2(f5(x321,x322),x321)
% 0.21/0.72 [35]E(x351,x352)+~P2(f5(x351,x352),x352)+~P2(f5(x351,x352),x351)
% 0.21/0.72 [26]~P1(x263,x262)+P2(x261,x262)+~P2(x261,x263)
% 0.21/0.72 [29]~P2(x291,x293)+P2(x291,x292)+P2(x291,f2(x293,x292))
% 0.21/0.72 [34]P2(x341,x342)+P2(x341,x343)+~P2(x341,f1(x343,x342))
% 0.21/0.72 %EqnAxiom
% 0.21/0.72 [1]E(x11,x11)
% 0.21/0.72 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.72 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.21/0.72 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.21/0.72 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.21/0.72 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.21/0.72 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.21/0.72 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.21/0.72 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.21/0.72 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.21/0.72 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123)
% 0.21/0.72 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131)
% 0.21/0.72 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.21/0.72 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.21/0.72
% 0.21/0.72 %-------------------------------------------
% 0.21/0.72 cnf(36,plain,
% 0.21/0.72 (E(f2(x361,f1(x362,x363)),f2(f2(x361,x362),x363))),
% 0.21/0.72 inference(scs_inference,[],[18,2])).
% 0.21/0.72 cnf(37,plain,
% 0.21/0.72 (P1(f1(x371,x372),f1(x372,x371))),
% 0.21/0.72 inference(scs_inference,[],[16,17,18,2,13])).
% 0.21/0.72 cnf(39,plain,
% 0.21/0.72 (~E(f1(f2(a3,f1(a6,a7)),f2(a6,f1(a3,a7))),f1(f2(f2(a3,a6),a7),f2(f2(a6,a3),a7)))),
% 0.21/0.72 inference(scs_inference,[],[21,16,17,18,19,2,13,3])).
% 0.21/0.72 cnf(57,plain,
% 0.21/0.72 (~E(f1(f2(a6,f1(a3,a7)),f2(a3,f1(a6,a7))),f2(f1(f2(a3,a6),f2(a6,a3)),a7))),
% 0.21/0.72 inference(scs_inference,[],[21,17,3])).
% 0.21/0.72 cnf(79,plain,
% 0.21/0.72 (E(f1(f2(x791,f1(x792,x793)),f2(x794,f1(x792,x793))),f2(f2(f1(x791,x794),x792),x793))),
% 0.21/0.72 inference(scs_inference,[],[36,19,23,3])).
% 0.21/0.72 cnf(80,plain,
% 0.21/0.72 (E(f1(f2(x801,x802),f2(x803,x802)),f2(f1(x801,x803),x802))),
% 0.21/0.72 inference(rename_variables,[],[19])).
% 0.21/0.73 cnf(82,plain,
% 0.21/0.73 (E(f2(f1(x821,x822),x823),f1(f2(x821,x823),f2(x822,x823)))),
% 0.21/0.73 inference(scs_inference,[],[36,19,80,23,3,2])).
% 0.21/0.73 cnf(90,plain,
% 0.21/0.73 (E(f1(f2(x901,x902),f2(x903,x902)),f2(f1(x901,x903),x902))),
% 0.21/0.73 inference(rename_variables,[],[19])).
% 0.21/0.73 cnf(91,plain,
% 0.21/0.73 (~E(f2(f1(f2(a3,a6),f2(a6,a3)),a7),f1(f2(a6,f1(a3,a7)),f2(a3,f1(a6,a7))))),
% 0.21/0.73 inference(scs_inference,[],[19,57,3,2])).
% 0.21/0.73 cnf(94,plain,
% 0.21/0.73 (P1(f1(f2(x941,x942),f2(x943,x942)),f2(f1(x943,x941),x942))),
% 0.21/0.73 inference(scs_inference,[],[16,19,90,79,37,57,3,2,12,13])).
% 0.21/0.73 cnf(102,plain,
% 0.21/0.73 (E(f2(x1021,f1(x1022,x1023)),f2(f2(x1021,x1022),x1023))),
% 0.21/0.73 inference(rename_variables,[],[36])).
% 0.21/0.73 cnf(107,plain,
% 0.21/0.73 (E(f1(x1071,f2(x1072,f1(x1073,x1074))),f1(x1071,f2(f2(x1072,x1073),x1074)))),
% 0.21/0.73 inference(scs_inference,[],[17,36,102,82,94,91,79,3,2,12,13,9,8,6,5])).
% 0.21/0.73 cnf(108,plain,
% 0.21/0.73 (E(f1(f2(x1081,f1(x1082,x1083)),x1084),f1(f2(f2(x1081,x1082),x1083),x1084))),
% 0.21/0.73 inference(scs_inference,[],[17,36,102,82,94,91,79,3,2,12,13,9,8,6,5,4])).
% 0.21/0.73 cnf(125,plain,
% 0.21/0.73 ($false),
% 0.21/0.73 inference(scs_inference,[],[39,107,108,3]),
% 0.21/0.73 ['proof']).
% 0.21/0.73 % SZS output end Proof
% 0.21/0.73 % Total time :0.070000s
%------------------------------------------------------------------------------