%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET618+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n026.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 : Mon Jun 24 14:22:00 EDT 2024 % Result : Theorem 0.55s 0.61s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET618+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n026.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 : Sun Jun 23 13:34:09 EDT 2024 % 0.13/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 0.55/0.60 %------------------------------------------- % 0.55/0.60 % File :CSE---1.7 % 0.55/0.60 % Problem :theBenchmark % 0.55/0.60 % Transform :cnf % 0.55/0.60 % Format :tptp:raw % 0.55/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.60 % 0.55/0.60 % Result :Theorem 0.000000s % 0.55/0.60 % Output :CNFRefutation 0.000000s % 0.55/0.60 %------------------------------------------- % 0.55/0.60 %-------------------------------------------------------------------------- % 0.55/0.60 % File : SET618+3 : TPTP v8.2.0. Released v2.2.0. % 0.55/0.60 % Domain : Set Theory % 0.55/0.60 % Problem : The symmetric difference of X and X is the empty set % 0.55/0.60 % Version : [Try90] axioms : Reduced > Incomplete. % 0.55/0.60 % English : % 0.55/0.60 % 0.55/0.60 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.55/0.60 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.55/0.60 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.55/0.60 % Source : [ILF] % 0.55/0.60 % Names : BOOLE (93) [TS89] % 0.55/0.60 % 0.55/0.60 % Status : Theorem % 0.55/0.60 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.1.0, 0.10 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, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.33 v2.2.1 % 0.55/0.60 % Syntax : Number of formulae : 12 ( 8 unt; 0 def) % 0.55/0.60 % Number of atoms : 19 ( 8 equ) % 0.55/0.60 % Maximal formula atoms : 3 ( 1 avg) % 0.55/0.60 % Number of connectives : 9 ( 2 ~; 0 |; 1 &) % 0.55/0.60 % ( 5 <=>; 1 =>; 0 <=; 0 <~>) % 0.55/0.60 % Maximal formula depth : 6 ( 4 avg) % 0.55/0.60 % Maximal term depth : 3 ( 1 avg) % 0.55/0.60 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.55/0.60 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 0.55/0.60 % Number of variables : 21 ( 21 !; 0 ?) % 0.55/0.60 % SPC : FOF_THM_RFO_SEQ % 0.55/0.60 % 0.55/0.60 % Comments : % 0.55/0.60 %-------------------------------------------------------------------------- % 0.55/0.60 %---- line(boole - df(7),1833089) % 0.55/0.60 fof(symmetric_difference_defn,axiom, % 0.55/0.60 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ). % 0.55/0.60 % 0.55/0.60 %---- line(boole - th(62),1833685) % 0.55/0.60 fof(idempotency_of_union,axiom, % 0.55/0.60 ! [B] : union(B,B) = B ). % 0.55/0.60 % 0.55/0.60 %---- line(boole - th(73),1833852) % 0.55/0.60 fof(self_difference_is_empty_set,axiom, % 0.55/0.60 ! [B] : difference(B,B) = empty_set ). % 0.55/0.60 % 0.55/0.60 %---- line(hidden - axiom171,1832636) % 0.55/0.60 fof(empty_set_defn,axiom, % 0.55/0.60 ! [B] : ~ member(B,empty_set) ). % 0.55/0.60 % 0.55/0.60 %---- line(boole - df(8),1833103) % 0.55/0.60 fof(equal_defn,axiom, % 0.55/0.60 ! [B,C] : % 0.55/0.60 ( B = C % 0.55/0.60 <=> ( subset(B,C) % 0.55/0.60 & subset(C,B) ) ) ). % 0.55/0.60 % 0.55/0.61 %---- property(commutativity,op(union,2,function)) % 0.55/0.61 fof(commutativity_of_union,axiom, % 0.55/0.61 ! [B,C] : union(B,C) = union(C,B) ). % 0.55/0.61 % 0.55/0.61 %---- property(commutativity,op(symmetric_difference,2,function)) % 0.55/0.61 fof(commutativity_of_symmetric_difference,axiom, % 0.55/0.61 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ). % 0.55/0.61 % 0.55/0.61 %---- line(hidden - axiom172,1832615) % 0.55/0.61 fof(equal_member_defn,axiom, % 0.55/0.61 ! [B,C] : % 0.55/0.61 ( B = C % 0.55/0.61 <=> ! [D] : % 0.55/0.61 ( member(D,B) % 0.55/0.61 <=> member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(tarski - df(3),1832749) % 0.55/0.61 fof(subset_defn,axiom, % 0.55/0.61 ! [B,C] : % 0.55/0.61 ( subset(B,C) % 0.55/0.61 <=> ! [D] : % 0.55/0.61 ( member(D,B) % 0.55/0.61 => member(D,C) ) ) ). % 0.55/0.61 % 0.55/0.61 %---- property(reflexivity,op(subset,2,predicate)) % 0.55/0.61 fof(reflexivity_of_subset,axiom, % 0.55/0.61 ! [B] : subset(B,B) ). % 0.55/0.61 % 0.55/0.61 %---- line(hidden - axiom174,1832628) % 0.55/0.61 fof(empty_defn,axiom, % 0.55/0.61 ! [B] : % 0.55/0.61 ( empty(B) % 0.55/0.61 <=> ! [C] : ~ member(C,B) ) ). % 0.55/0.61 % 0.55/0.61 %---- line(boole - th(93),1834213) % 0.55/0.61 fof(prove_th93,conjecture, % 0.55/0.61 ! [B] : symmetric_difference(B,B) = empty_set ). % 0.55/0.61 % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 %------------------------------------------- % 0.55/0.61 % Proof found % 0.55/0.61 % SZS status Theorem for theBenchmark % 0.55/0.61 % SZS output start Proof % 0.55/0.61 %ClaNum:34(EqnAxiom:17) % 0.55/0.61 %VarNum:60(SingletonVarNum:24) % 0.55/0.61 %MaxLitNum:3 % 0.55/0.61 %MaxfuncDepth:2 % 0.55/0.61 %SharedTerms:5 % 0.55/0.61 %goalClause: 24 % 0.55/0.61 %singleGoalClaCount:1 % 0.55/0.61 [24]~E(f3(f1(a4,a4),f1(a4,a4)),a2) % 0.55/0.61 [19]P1(x191,x191) % 0.55/0.61 [23]~P2(x231,a2) % 0.55/0.61 [18]E(f1(x181,x181),a2) % 0.55/0.61 [20]E(f3(x201,x201),x201) % 0.55/0.61 [21]E(f3(x211,x212),f3(x212,x211)) % 0.55/0.61 [27]P3(x271)+P2(f5(x271),x271) % 0.55/0.61 [26]~E(x261,x262)+P1(x261,x262) % 0.55/0.61 [28]~P3(x281)+~P2(x282,x281) % 0.55/0.61 [30]P1(x301,x302)+P2(f6(x301,x302),x301) % 0.55/0.61 [32]P1(x321,x322)+~P2(f6(x321,x322),x322) % 0.55/0.61 [29]~P1(x292,x291)+~P1(x291,x292)+E(x291,x292) % 0.55/0.61 [33]E(x331,x332)+P2(f7(x331,x332),x332)+P2(f7(x331,x332),x331) % 0.55/0.61 [34]E(x341,x342)+~P2(f7(x341,x342),x342)+~P2(f7(x341,x342),x341) % 0.55/0.61 [31]~P1(x313,x312)+P2(x311,x312)+~P2(x311,x313) % 0.55/0.61 %EqnAxiom % 0.55/0.61 [1]E(x11,x11) % 0.55/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.61 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.55/0.61 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.55/0.61 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.55/0.61 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.55/0.61 [8]~E(x81,x82)+E(f5(x81),f5(x82)) % 0.55/0.61 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93)) % 0.55/0.61 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102)) % 0.55/0.61 [11]~E(x111,x112)+E(f7(x111,x113),f7(x112,x113)) % 0.55/0.61 [12]~E(x121,x122)+E(f7(x123,x121),f7(x123,x122)) % 0.55/0.61 [13]P1(x132,x133)+~E(x131,x132)+~P1(x131,x133) % 0.55/0.61 [14]P1(x143,x142)+~E(x141,x142)+~P1(x143,x141) % 0.55/0.61 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153) % 0.55/0.61 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161) % 0.55/0.61 [17]~P3(x171)+P3(x172)+~E(x171,x172) % 0.55/0.61 % 0.55/0.61 %------------------------------------------- % 0.55/0.61 cnf(36,plain, % 0.55/0.61 (E(x361,f3(x361,x361))), % 0.55/0.61 inference(scs_inference,[],[20,2])). % 0.55/0.61 cnf(38,plain, % 0.55/0.61 (~P2(x381,a2)), % 0.55/0.61 inference(rename_variables,[],[23])). % 0.55/0.61 cnf(44,plain, % 0.55/0.61 (E(f3(x441,x441),x441)), % 0.55/0.61 inference(rename_variables,[],[20])). % 0.55/0.61 cnf(45,plain, % 0.55/0.61 (P1(x451,f3(x451,x451))), % 0.55/0.61 inference(scs_inference,[],[24,19,23,38,20,44,2,30,27,3,13])). % 0.55/0.61 cnf(46,plain, % 0.55/0.61 (P1(x461,x461)), % 0.55/0.61 inference(rename_variables,[],[19])). % 0.55/0.61 cnf(47,plain, % 0.55/0.61 (P1(f3(x471,x471),x471)), % 0.57/0.61 inference(scs_inference,[],[24,19,46,23,38,20,44,2,30,27,3,13,14])). % 0.57/0.61 cnf(50,plain, % 0.57/0.61 (~P2(x501,f3(a2,a2))), % 0.57/0.61 inference(scs_inference,[],[24,19,46,23,38,20,44,2,30,27,3,13,14,17,28])). % 0.57/0.61 cnf(57,plain, % 0.57/0.61 (E(x571,f3(x571,x571))), % 0.57/0.61 inference(rename_variables,[],[36])). % 0.57/0.61 cnf(60,plain, % 0.57/0.61 ($false), % 0.57/0.61 inference(scs_inference,[],[24,36,57,45,47,50,18,20,30,2,13,14,3]), % 0.57/0.61 ['proof']). % 0.57/0.61 % SZS output end Proof % 0.57/0.61 % Total time :0.000000s %------------------------------------------------------------------------------