TSTP Solution File: SET629+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET629+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 : n021.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 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET629+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 11:46:56 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.010000s
% 0.20/0.63 % Output :CNFRefutation 0.010000s
% 0.20/0.63 %-------------------------------------------
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 % File : SET629+3 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.64 % Domain : Set Theory
% 0.20/0.64 % Problem : X ^ Y is disjoint from X \ Y
% 0.20/0.64 % Version : [Try90] axioms : Reduced > Incomplete.
% 0.20/0.64 % English : The intersection of X and Y is disjoint from the difference of
% 0.20/0.64 % X and Y.
% 0.20/0.64
% 0.20/0.64 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int
% 0.20/0.64 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory
% 0.20/0.64 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.20/0.64 % Source : [ILF]
% 0.20/0.64 % Names : BOOLE (111) [TS89]
% 0.20/0.64
% 0.20/0.64 % Status : Theorem
% 0.20/0.64 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 0.20/0.64 % Syntax : Number of formulae : 8 ( 2 unt; 0 def)
% 0.20/0.64 % Number of atoms : 18 ( 2 equ)
% 0.20/0.64 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.64 % Number of connectives : 12 ( 2 ~; 0 |; 3 &)
% 0.20/0.64 % ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.64 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.64 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 0.20/0.64 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.20/0.64 % Number of variables : 20 ( 19 !; 1 ?)
% 0.20/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.64
% 0.20/0.64 % Comments :
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %---- line(boole - df(3),1833060)
% 0.20/0.64 fof(intersection_defn,axiom,
% 0.20/0.64 ! [B,C,D] :
% 0.20/0.64 ( member(D,intersection(B,C))
% 0.20/0.64 <=> ( member(D,B)
% 0.20/0.64 & member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(boole - df(4),1833078)
% 0.20/0.64 fof(difference_defn,axiom,
% 0.20/0.64 ! [B,C,D] :
% 0.20/0.64 ( member(D,difference(B,C))
% 0.20/0.64 <=> ( member(D,B)
% 0.20/0.64 & ~ member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(boole - df(5),1833080)
% 0.20/0.64 fof(intersect_defn,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( intersect(B,C)
% 0.20/0.64 <=> ? [D] :
% 0.20/0.64 ( member(D,B)
% 0.20/0.64 & member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(boole - axiom199,1833083)
% 0.20/0.64 fof(disjoint_defn,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( disjoint(B,C)
% 0.20/0.64 <=> ~ intersect(B,C) ) ).
% 0.20/0.64
% 0.20/0.64 %---- property(commutativity,op(intersection,2,function))
% 0.20/0.64 fof(commutativity_of_intersection,axiom,
% 0.20/0.64 ! [B,C] : intersection(B,C) = intersection(C,B) ).
% 0.20/0.64
% 0.20/0.64 %---- property(symmetry,op(intersect,2,predicate))
% 0.20/0.64 fof(symmetry_of_intersect,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( intersect(B,C)
% 0.20/0.64 => intersect(C,B) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(hidden - axiom201,1832615)
% 0.20/0.64 fof(equal_member_defn,axiom,
% 0.20/0.64 ! [B,C] :
% 0.20/0.64 ( B = C
% 0.20/0.64 <=> ! [D] :
% 0.20/0.64 ( member(D,B)
% 0.20/0.64 <=> member(D,C) ) ) ).
% 0.20/0.64
% 0.20/0.64 %---- line(boole - th(111),1834358)
% 0.20/0.64 fof(prove_intersection_and_difference_disjoint,conjecture,
% 0.20/0.64 ! [B,C] : disjoint(intersection(B,C),difference(B,C)) ).
% 0.20/0.64
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:33(EqnAxiom:17)
% 0.20/0.64 %VarNum:82(SingletonVarNum:37)
% 0.20/0.64 %MaxLitNum:3
% 0.20/0.64 %MaxfuncDepth:1
% 0.20/0.64 %SharedTerms:5
% 0.20/0.64 %goalClause: 19
% 0.20/0.64 %singleGoalClaCount:1
% 0.20/0.64 [19]~P1(f1(a2,a6),f3(a2,a6))
% 0.20/0.64 [18]E(f1(x181,x182),f1(x182,x181))
% 0.20/0.64 [20]P1(x201,x202)+P2(x201,x202)
% 0.20/0.64 [21]~P2(x212,x211)+P2(x211,x212)
% 0.20/0.64 [22]~P1(x221,x222)+~P2(x221,x222)
% 0.20/0.64 [24]~P2(x241,x242)+P3(f4(x241,x242),x242)
% 0.20/0.64 [25]~P2(x251,x252)+P3(f4(x251,x252),x251)
% 0.20/0.64 [27]P3(x271,x272)+~P3(x271,f1(x273,x272))
% 0.20/0.64 [28]P3(x281,x282)+~P3(x281,f1(x282,x283))
% 0.20/0.64 [29]P3(x291,x292)+~P3(x291,f3(x292,x293))
% 0.20/0.64 [32]~P3(x321,x322)+~P3(x321,f3(x323,x322))
% 0.20/0.64 [30]E(x301,x302)+P3(f5(x301,x302),x302)+P3(f5(x301,x302),x301)
% 0.20/0.64 [33]E(x331,x332)+~P3(f5(x331,x332),x332)+~P3(f5(x331,x332),x331)
% 0.20/0.64 [23]~P3(x233,x231)+P2(x231,x232)+~P3(x233,x232)
% 0.20/0.64 [26]~P3(x261,x263)+P3(x261,x262)+P3(x261,f3(x263,x262))
% 0.20/0.64 [31]~P3(x311,x313)+~P3(x311,x312)+P3(x311,f1(x312,x313))
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.20/0.64 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.20/0.64 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.20/0.64 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.20/0.64 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.20/0.64 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.20/0.64 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.20/0.64 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.20/0.64 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123)
% 0.20/0.64 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131)
% 0.20/0.64 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.20/0.64 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.20/0.64 [16]P3(x162,x163)+~E(x161,x162)+~P3(x161,x163)
% 0.20/0.64 [17]P3(x173,x172)+~E(x171,x172)+~P3(x173,x171)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(34,plain,
% 0.20/0.64 (P2(f1(a2,a6),f3(a2,a6))),
% 0.20/0.64 inference(scs_inference,[],[19,20])).
% 0.20/0.64 cnf(35,plain,
% 0.20/0.64 (P3(f4(f1(a2,a6),f3(a2,a6)),f1(a2,a6))),
% 0.20/0.64 inference(scs_inference,[],[19,20,25])).
% 0.20/0.64 cnf(44,plain,
% 0.20/0.64 (~P3(f4(f1(a2,a6),f3(a2,a6)),a6)),
% 0.20/0.64 inference(scs_inference,[],[19,18,20,25,24,13,12,23,22,32])).
% 0.20/0.64 cnf(46,plain,
% 0.20/0.64 (P3(f4(f1(a2,a6),f3(a2,a6)),a2)),
% 0.20/0.64 inference(scs_inference,[],[19,18,20,25,24,13,12,23,22,32,29])).
% 0.20/0.64 cnf(66,plain,
% 0.20/0.64 ($false),
% 0.20/0.65 inference(scs_inference,[],[46,35,34,44,21,28,32,29,27]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------