%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET633+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 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 : Mon Jun 24 14:22:04 EDT 2024 % Result : Theorem 0.58s 0.63s % Output : CNFRefutation 0.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET633+3 : TPTP v8.2.0. Released v2.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 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 : Sun Jun 23 12:09:24 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.59 start to proof:theBenchmark % 0.57/0.62 %------------------------------------------- % 0.57/0.62 % File :CSE---1.7 % 0.57/0.62 % Problem :theBenchmark % 0.57/0.62 % Transform :cnf % 0.57/0.62 % Format :tptp:raw % 0.57/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.57/0.62 % 0.57/0.62 % Result :Theorem 0.000000s % 0.57/0.62 % Output :CNFRefutation 0.000000s % 0.57/0.62 %------------------------------------------- % 0.58/0.62 %-------------------------------------------------------------------------- % 0.58/0.62 % File : SET633+3 : TPTP v8.2.0. Released v2.2.0. % 0.58/0.62 % Domain : Set Theory % 0.58/0.62 % Problem : If X \ Y (= Z and Y \ X (= Z, then X sym\ Y (= Z % 0.58/0.62 % Version : [Try90] axioms : Reduced > Incomplete. % 0.58/0.62 % English : If the difference of X and Y is a subset of Z and the % 0.58/0.62 % difference of Y and X is a subset of Z, then the symmetric % 0.58/0.62 % difference of X and Y is a subset of Z. % 0.58/0.62 % 0.58/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.58/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.58/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.58/0.62 % Source : [ILF] % 0.58/0.62 % Names : BOOLE (115) [TS89] % 0.58/0.62 % 0.58/0.62 % Status : Theorem % 0.58/0.62 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.00 v6.2.0, 0.08 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 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 % 0.58/0.62 % Syntax : Number of formulae : 9 ( 4 unt; 0 def) % 0.58/0.62 % Number of atoms : 19 ( 4 equ) % 0.58/0.62 % Maximal formula atoms : 3 ( 2 avg) % 0.58/0.62 % Number of connectives : 11 ( 1 ~; 0 |; 3 &) % 0.58/0.62 % ( 4 <=>; 3 =>; 0 <=; 0 <~>) % 0.58/0.62 % Maximal formula depth : 7 ( 5 avg) % 0.58/0.62 % Maximal term depth : 3 ( 1 avg) % 0.58/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.58/0.62 % Number of functors : 3 ( 3 usr; 0 con; 2-2 aty) % 0.58/0.62 % Number of variables : 22 ( 22 !; 0 ?) % 0.58/0.62 % SPC : FOF_THM_RFO_SEQ % 0.58/0.62 % 0.58/0.62 % Comments : % 0.58/0.62 %-------------------------------------------------------------------------- % 0.58/0.62 %---- line(boole - df(7),1833089) % 0.58/0.62 fof(symmetric_difference_defn,axiom, % 0.58/0.62 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ). % 0.58/0.62 % 0.58/0.62 %---- line(boole - th(32),1833206) % 0.58/0.62 fof(union_subset,axiom, % 0.58/0.62 ! [B,C,D] : % 0.58/0.62 ( ( subset(B,C) % 0.58/0.62 & subset(D,C) ) % 0.58/0.62 => subset(union(B,D),C) ) ). % 0.58/0.62 % 0.58/0.62 %---- line(boole - df(4),1833078) % 0.58/0.62 fof(difference_defn,axiom, % 0.58/0.62 ! [B,C,D] : % 0.58/0.62 ( member(D,difference(B,C)) % 0.58/0.62 <=> ( member(D,B) % 0.58/0.62 & ~ member(D,C) ) ) ). % 0.58/0.62 % 0.58/0.62 %---- line(tarski - df(3),1832749) % 0.58/0.62 fof(subset_defn,axiom, % 0.58/0.62 ! [B,C] : % 0.58/0.62 ( subset(B,C) % 0.58/0.62 <=> ! [D] : % 0.58/0.62 ( member(D,B) % 0.58/0.62 => member(D,C) ) ) ). % 0.58/0.62 % 0.58/0.62 %---- property(commutativity,op(union,2,function)) % 0.58/0.62 fof(commutativity_of_union,axiom, % 0.58/0.62 ! [B,C] : union(B,C) = union(C,B) ). % 0.58/0.62 % 0.58/0.62 %---- property(commutativity,op(symmetric_difference,2,function)) % 0.58/0.62 fof(commutativity_of_symmetric_difference,axiom, % 0.58/0.62 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ). % 0.58/0.62 % 0.58/0.62 %---- line(hidden - axiom210,1832615) % 0.58/0.62 fof(equal_member_defn,axiom, % 0.58/0.63 ! [B,C] : % 0.58/0.63 ( B = C % 0.58/0.63 <=> ! [D] : % 0.58/0.63 ( member(D,B) % 0.58/0.63 <=> member(D,C) ) ) ). % 0.58/0.63 % 0.58/0.63 %---- property(reflexivity,op(subset,2,predicate)) % 0.58/0.63 fof(reflexivity_of_subset,axiom, % 0.58/0.63 ! [B] : subset(B,B) ). % 0.58/0.63 % 0.58/0.63 %---- line(boole - th(115),1834412) % 0.58/0.63 fof(prove_th115,conjecture, % 0.58/0.63 ! [B,C,D] : % 0.58/0.63 ( ( subset(difference(B,C),D) % 0.58/0.63 & subset(difference(C,B),D) ) % 0.58/0.63 => subset(symmetric_difference(B,C),D) ) ). % 0.58/0.63 % 0.58/0.63 %-------------------------------------------------------------------------- % 0.58/0.63 %------------------------------------------- % 0.58/0.63 % Proof found % 0.58/0.63 % SZS status Theorem for theBenchmark % 0.58/0.63 % SZS output start Proof % 0.58/0.63 %ClaNum:30(EqnAxiom:15) % 0.58/0.63 %VarNum:62(SingletonVarNum:26) % 0.58/0.63 %MaxLitNum:3 % 0.58/0.63 %MaxfuncDepth:2 % 0.58/0.63 %SharedTerms:9 % 0.58/0.63 %goalClause: 18 19 21 % 0.58/0.63 %singleGoalClaCount:3 % 0.58/0.63 [18]P1(f3(a2,a6),a7) % 0.58/0.63 [19]P1(f3(a6,a2),a7) % 0.58/0.63 [21]~P1(f1(f3(a2,a6),f3(a6,a2)),a7) % 0.58/0.63 [16]P1(x161,x161) % 0.58/0.63 [17]E(f1(x171,x172),f1(x172,x171)) % 0.58/0.63 [22]P1(x221,x222)+P2(f4(x221,x222),x221) % 0.58/0.63 [26]P1(x261,x262)+~P2(f4(x261,x262),x262) % 0.58/0.63 [25]P2(x251,x252)+~P2(x251,f3(x252,x253)) % 0.58/0.63 [29]~P2(x291,x292)+~P2(x291,f3(x293,x292)) % 0.58/0.63 [27]E(x271,x272)+P2(f5(x271,x272),x272)+P2(f5(x271,x272),x271) % 0.58/0.63 [30]E(x301,x302)+~P2(f5(x301,x302),x302)+~P2(f5(x301,x302),x301) % 0.58/0.63 [23]~P2(x231,x233)+P2(x231,x232)+~P1(x233,x232) % 0.58/0.63 [24]~P2(x241,x243)+P2(x241,x242)+P2(x241,f3(x243,x242)) % 0.58/0.63 [28]~P1(x282,x283)+~P1(x281,x283)+P1(f1(x281,x282),x283) % 0.58/0.63 %EqnAxiom % 0.58/0.63 [1]E(x11,x11) % 0.58/0.63 [2]E(x22,x21)+~E(x21,x22) % 0.58/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.58/0.63 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.58/0.63 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.58/0.63 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.58/0.63 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.58/0.63 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83)) % 0.58/0.63 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92)) % 0.58/0.63 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.58/0.63 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.58/0.63 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 0.58/0.63 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 0.58/0.63 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.58/0.63 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.58/0.63 % 0.58/0.63 %------------------------------------------- % 0.58/0.63 cnf(31,plain, % 0.58/0.63 ($false), % 0.58/0.63 inference(scs_inference,[],[18,19,21,28]), % 0.58/0.63 ['proof']). % 0.58/0.63 % SZS output end Proof % 0.58/0.63 % Total time :0.000000s %------------------------------------------------------------------------------