TSTP Solution File: SET622+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET622+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 : n017.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 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:22:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 % File :CSE---1.6
% 0.19/0.66 % Problem :theBenchmark
% 0.19/0.66 % Transform :cnf
% 0.19/0.66 % Format :tptp:raw
% 0.19/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.66
% 0.19/0.66 % Result :Theorem 0.050000s
% 0.19/0.66 % Output :CNFRefutation 0.050000s
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 % File : SET622+3 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.66 % Domain : Set Theory
% 0.19/0.66 % Problem : X \ (Y sym\ Z) = (X \ (Y U Z)) U X ^ Y ^ Z
% 0.19/0.66 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.19/0.66 % English : The difference of X and (the symmetric difference of Y and Z)
% 0.19/0.66 % is the union of (the difference of X and (the union of Y and Z))
% 0.19/0.66 % and the intersection of X and the intersection of Y and Z.
% 0.19/0.66
% 0.19/0.66 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.19/0.66 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.19/0.66 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.19/0.66 % Source : [ILF]
% 0.19/0.66 % Names : BOOLE (98) [TS89]
% 0.19/0.66
% 0.19/0.66 % Status : Theorem
% 0.19/0.66 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.00 v6.2.0, 0.08 v6.1.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.33 v5.2.0, 0.05 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.19/0.66 % Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% 0.19/0.66 % Number of atoms : 27 ( 10 equ)
% 0.19/0.66 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.66 % Number of connectives : 13 ( 1 ~; 1 |; 3 &)
% 0.19/0.66 % ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.66 % Maximal formula depth : 7 ( 4 avg)
% 0.19/0.66 % Maximal term depth : 4 ( 1 avg)
% 0.19/0.66 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.66 % Number of functors : 4 ( 4 usr; 0 con; 2-2 aty)
% 0.19/0.66 % Number of variables : 37 ( 37 !; 0 ?)
% 0.19/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.66
% 0.19/0.66 % Comments :
% 0.19/0.66 %--------------------------------------------------------------------------
% 0.19/0.66 %---- line(boole - th(67),1833740)
% 0.19/0.66 fof(associativity_of_intersection,axiom,
% 0.19/0.66 ! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)) ).
% 0.19/0.66
% 0.19/0.66 %---- line(boole - th(81),1833972)
% 0.19/0.66 fof(difference_difference_union2,axiom,
% 0.19/0.66 ! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)) ).
% 0.19/0.66
% 0.19/0.66 %---- line(boole - th(96),1834227)
% 0.19/0.66 fof(symmetric_difference_and_difference,axiom,
% 0.19/0.66 ! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)) ).
% 0.19/0.66
% 0.19/0.66 %---- line(boole - df(2),1833042)
% 0.19/0.66 fof(union_defn,axiom,
% 0.19/0.66 ! [B,C,D] :
% 0.19/0.66 ( member(D,union(B,C))
% 0.19/0.67 <=> ( member(D,B)
% 0.19/0.67 | member(D,C) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- line(boole - df(3),1833060)
% 0.19/0.67 fof(intersection_defn,axiom,
% 0.19/0.67 ! [B,C,D] :
% 0.19/0.67 ( member(D,intersection(B,C))
% 0.19/0.67 <=> ( member(D,B)
% 0.19/0.67 & member(D,C) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- line(boole - df(4),1833078)
% 0.19/0.67 fof(difference_defn,axiom,
% 0.19/0.67 ! [B,C,D] :
% 0.19/0.67 ( member(D,difference(B,C))
% 0.19/0.67 <=> ( member(D,B)
% 0.19/0.67 & ~ member(D,C) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- line(boole - df(7),1833089)
% 0.19/0.67 fof(symmetric_difference_defn,axiom,
% 0.19/0.67 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ).
% 0.19/0.67
% 0.19/0.67 %---- line(boole - df(8),1833103)
% 0.19/0.67 fof(equal_defn,axiom,
% 0.19/0.67 ! [B,C] :
% 0.19/0.67 ( B = C
% 0.19/0.67 <=> ( subset(B,C)
% 0.19/0.67 & subset(C,B) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- property(commutativity,op(union,2,function))
% 0.19/0.67 fof(commutativity_of_union,axiom,
% 0.19/0.67 ! [B,C] : union(B,C) = union(C,B) ).
% 0.19/0.67
% 0.19/0.67 %---- property(commutativity,op(intersection,2,function))
% 0.19/0.67 fof(commutativity_of_intersection,axiom,
% 0.19/0.67 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.19/0.67
% 0.19/0.67 %---- property(commutativity,op(symmetric_difference,2,function))
% 0.19/0.67 fof(commutativity_of_symmetric_difference,axiom,
% 0.19/0.67 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ).
% 0.19/0.67
% 0.19/0.67 %---- line(hidden - axiom181,1832615)
% 0.19/0.67 fof(equal_member_defn,axiom,
% 0.19/0.67 ! [B,C] :
% 0.19/0.67 ( B = C
% 0.19/0.67 <=> ! [D] :
% 0.19/0.67 ( member(D,B)
% 0.19/0.67 <=> member(D,C) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- line(tarski - df(3),1832749)
% 0.19/0.67 fof(subset_defn,axiom,
% 0.19/0.67 ! [B,C] :
% 0.19/0.67 ( subset(B,C)
% 0.19/0.67 <=> ! [D] :
% 0.19/0.67 ( member(D,B)
% 0.19/0.67 => member(D,C) ) ) ).
% 0.19/0.67
% 0.19/0.67 %---- property(reflexivity,op(subset,2,predicate))
% 0.19/0.67 fof(reflexivity_of_subset,axiom,
% 0.19/0.67 ! [B] : subset(B,B) ).
% 0.19/0.67
% 0.19/0.67 %---- line(boole - th(98),1834245)
% 0.19/0.67 fof(prove_th98,conjecture,
% 0.19/0.67 ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)) ).
% 0.19/0.67
% 0.19/0.67 %--------------------------------------------------------------------------
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 %ClaNum:42(EqnAxiom:17)
% 0.19/0.67 %VarNum:132(SingletonVarNum:57)
% 0.19/0.67 %MaxLitNum:3
% 0.19/0.67 %MaxfuncDepth:3
% 0.19/0.67 %SharedTerms:12
% 0.19/0.67 %goalClause: 25
% 0.19/0.67 %singleGoalClaCount:1
% 0.19/0.67 [25]~E(f8(f2(a3,f8(a6,a7)),f1(f1(a3,a6),a7)),f2(a3,f2(f8(a6,a7),f1(a6,a7))))
% 0.19/0.67 [18]P1(x181,x181)
% 0.19/0.67 [19]E(f1(x191,x192),f1(x192,x191))
% 0.19/0.67 [20]E(f8(x201,x202),f8(x202,x201))
% 0.19/0.67 [23]E(f2(f8(x231,x232),f1(x231,x232)),f2(f8(x232,x231),f1(x232,x231)))
% 0.19/0.67 [24]E(f2(f8(x241,x242),f1(x241,x242)),f8(f2(x241,x242),f2(x242,x241)))
% 0.19/0.67 [21]E(f1(f1(x211,x212),x213),f1(x211,f1(x212,x213)))
% 0.19/0.67 [22]E(f8(f2(x221,x222),f1(x221,x223)),f2(x221,f2(x222,x223)))
% 0.19/0.67 [27]~E(x271,x272)+P1(x271,x272)
% 0.19/0.67 [29]P1(x291,x292)+P2(f4(x291,x292),x291)
% 0.19/0.67 [37]P1(x371,x372)+~P2(f4(x371,x372),x372)
% 0.19/0.67 [31]~P2(x311,x313)+P2(x311,f8(x312,x313))
% 0.19/0.67 [32]~P2(x321,x322)+P2(x321,f8(x322,x323))
% 0.19/0.67 [34]P2(x341,x342)+~P2(x341,f1(x343,x342))
% 0.19/0.67 [35]P2(x351,x352)+~P2(x351,f1(x352,x353))
% 0.19/0.67 [36]P2(x361,x362)+~P2(x361,f2(x362,x363))
% 0.19/0.67 [40]~P2(x401,x402)+~P2(x401,f2(x403,x402))
% 0.19/0.67 [28]~P1(x282,x281)+~P1(x281,x282)+E(x281,x282)
% 0.19/0.67 [38]E(x381,x382)+P2(f5(x381,x382),x382)+P2(f5(x381,x382),x381)
% 0.19/0.67 [42]E(x421,x422)+~P2(f5(x421,x422),x422)+~P2(f5(x421,x422),x421)
% 0.19/0.67 [30]~P1(x303,x302)+P2(x301,x302)+~P2(x301,x303)
% 0.19/0.67 [33]~P2(x331,x333)+P2(x331,x332)+P2(x331,f2(x333,x332))
% 0.19/0.67 [39]~P2(x391,x393)+~P2(x391,x392)+P2(x391,f1(x392,x393))
% 0.19/0.67 [41]P2(x411,x412)+P2(x411,x413)+~P2(x411,f8(x413,x412))
% 0.19/0.67 %EqnAxiom
% 0.19/0.67 [1]E(x11,x11)
% 0.19/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.67 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.67 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.67 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.19/0.67 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.19/0.67 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 0.19/0.67 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 0.19/0.67 [10]~E(x101,x102)+E(f2(x101,x103),f2(x102,x103))
% 0.19/0.67 [11]~E(x111,x112)+E(f2(x113,x111),f2(x113,x112))
% 0.19/0.67 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.19/0.67 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.19/0.67 [14]P1(x142,x143)+~E(x141,x142)+~P1(x141,x143)
% 0.19/0.67 [15]P1(x153,x152)+~E(x151,x152)+~P1(x153,x151)
% 0.19/0.67 [16]P2(x162,x163)+~E(x161,x162)+~P2(x161,x163)
% 0.19/0.67 [17]P2(x173,x172)+~E(x171,x172)+~P2(x173,x171)
% 0.19/0.67
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 cnf(43,plain,
% 0.19/0.67 (E(f1(x431,f1(x432,x433)),f1(f1(x431,x432),x433))),
% 0.19/0.67 inference(scs_inference,[],[21,2])).
% 0.19/0.67 cnf(44,plain,
% 0.19/0.67 (P1(f1(x441,x442),f1(x442,x441))),
% 0.19/0.67 inference(scs_inference,[],[18,19,21,2,15])).
% 0.19/0.67 cnf(46,plain,
% 0.19/0.67 (E(f1(x461,f1(x462,x463)),f1(x462,f1(x463,x461)))),
% 0.19/0.67 inference(scs_inference,[],[18,19,21,2,15,3])).
% 0.19/0.67 cnf(48,plain,
% 0.19/0.67 (E(f1(x481,x482),f1(x482,x481))),
% 0.19/0.67 inference(rename_variables,[],[19])).
% 0.19/0.67 cnf(54,plain,
% 0.19/0.67 (E(f2(f1(x541,x542),x543),f2(f1(x542,x541),x543))),
% 0.19/0.67 inference(scs_inference,[],[18,19,48,20,21,2,15,3,27,13,12,11,10])).
% 0.19/0.67 cnf(77,plain,
% 0.19/0.67 (~E(f8(f1(f1(a3,a6),a7),f2(a3,f8(a6,a7))),f2(a3,f2(f8(a6,a7),f1(a6,a7))))),
% 0.19/0.67 inference(scs_inference,[],[25,20,3])).
% 0.19/0.67 cnf(79,plain,
% 0.19/0.67 (P1(f2(x791,f2(x792,x793)),f8(f2(x791,x792),f1(x791,x793)))),
% 0.19/0.67 inference(scs_inference,[],[25,22,18,20,3,14])).
% 0.19/0.67 cnf(81,plain,
% 0.19/0.67 (~E(f2(a3,f2(f8(a6,a7),f1(a6,a7))),f8(f2(a3,f8(a6,a7)),f1(f1(a3,a6),a7)))),
% 0.19/0.67 inference(scs_inference,[],[25,22,18,20,3,14,2])).
% 0.19/0.67 cnf(99,plain,
% 0.19/0.67 (P1(f1(x991,f1(x992,x993)),f1(f1(x991,x992),x993))),
% 0.19/0.67 inference(scs_inference,[],[43,27])).
% 0.19/0.67 cnf(111,plain,
% 0.19/0.67 (P1(f2(f8(x1111,x1112),f1(x1111,x1112)),f2(f8(x1112,x1111),f1(x1112,x1111)))),
% 0.19/0.67 inference(scs_inference,[],[18,23,14])).
% 0.19/0.67 cnf(114,plain,
% 0.19/0.67 (E(f2(f8(x1141,x1142),f1(x1141,x1142)),f8(f2(x1142,x1141),f2(x1141,x1142)))),
% 0.19/0.67 inference(scs_inference,[],[18,23,24,77,14,2,3])).
% 0.19/0.67 cnf(116,plain,
% 0.19/0.67 (P1(f2(x1161,f2(x1162,x1163)),f8(f1(x1161,x1163),f2(x1161,x1162)))),
% 0.19/0.67 inference(scs_inference,[],[18,23,24,20,79,77,14,2,3,15])).
% 0.19/0.67 cnf(129,plain,
% 0.19/0.67 (E(f1(x1291,f1(x1292,x1293)),f1(f1(x1291,x1292),x1293))),
% 0.19/0.67 inference(rename_variables,[],[43])).
% 0.19/0.67 cnf(134,plain,
% 0.19/0.67 (E(f8(f1(x1341,f1(x1342,x1343)),x1344),f8(f1(f1(x1341,x1342),x1343),x1344))),
% 0.19/0.67 inference(scs_inference,[],[44,43,129,21,22,116,54,27,14,2,15,13,11,9,8])).
% 0.19/0.67 cnf(150,plain,
% 0.19/0.67 (~E(f8(f2(a3,f8(a6,a7)),f1(a3,f1(a6,a7))),f8(f1(f1(a3,a6),a7),f2(a3,f8(a6,a7))))),
% 0.19/0.67 inference(scs_inference,[],[22,81,77,3,28,2])).
% 0.19/0.67 cnf(164,plain,
% 0.19/0.67 (P1(f8(f2(x1641,x1642),f2(x1642,x1641)),f2(f8(x1642,x1641),f1(x1642,x1641)))),
% 0.19/0.67 inference(scs_inference,[],[46,24,21,111,114,2,3,14])).
% 0.19/0.67 cnf(180,plain,
% 0.19/0.67 ($false),
% 0.19/0.67 inference(scs_inference,[],[20,46,23,164,99,134,150,27,15,14,3]),
% 0.19/0.67 ['proof']).
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67 % Total time :0.050000s
%------------------------------------------------------------------------------