%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET584+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 : n029.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 14:21:50 EDT 2024 % Result : Theorem 0.61s 1.03s % Output : CNFRefutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET584+3 : TPTP v8.2.0. Released v2.2.0. % 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.35 % Computer : n029.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Jun 23 12:58:54 EDT 2024 % 0.13/0.35 % CPUTime : % 0.58/0.63 start to proof:theBenchmark % 0.61/1.02 %------------------------------------------- % 0.61/1.02 % File :CSE---1.7 % 0.61/1.02 % Problem :theBenchmark % 0.61/1.02 % Transform :cnf % 0.61/1.02 % Format :tptp:raw % 0.61/1.02 % Command :java -jar mcs_scs.jar %d %s % 0.61/1.02 % 0.61/1.02 % Result :Theorem 0.360000s % 0.61/1.02 % Output :CNFRefutation 0.360000s % 0.61/1.02 %------------------------------------------- % 0.61/1.03 %-------------------------------------------------------------------------- % 0.61/1.03 % File : SET584+3 : TPTP v8.2.0. Released v2.2.0. % 0.61/1.03 % Domain : Set Theory % 0.61/1.03 % Problem : If X (= Y, then X U Z (= Y U Z % 0.61/1.03 % Version : [Try90] axioms : Reduced > Incomplete. % 0.61/1.03 % English : If X is a subset of Y, then the union of X and Z is a subset of % 0.61/1.03 % the union of Y and Z. % 0.61/1.03 % 0.61/1.03 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.61/1.03 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.61/1.03 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.61/1.03 % Source : [ILF] % 0.61/1.03 % Names : BOOLE (33) [TS89] % 0.61/1.03 % 0.61/1.03 % Status : Theorem % 0.61/1.03 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.04 v6.1.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.17 v3.7.0, 0.15 v3.5.0, 0.21 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, 0.14 v2.5.0, 0.12 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1 % 0.61/1.03 % Syntax : Number of formulae : 6 ( 2 unt; 0 def) % 0.61/1.03 % Number of atoms : 13 ( 2 equ) % 0.61/1.03 % Maximal formula atoms : 3 ( 2 avg) % 0.61/1.03 % Number of connectives : 7 ( 0 ~; 1 |; 0 &) % 0.61/1.03 % ( 4 <=>; 2 =>; 0 <=; 0 <~>) % 0.61/1.03 % Maximal formula depth : 6 ( 5 avg) % 0.61/1.03 % Maximal term depth : 2 ( 1 avg) % 0.61/1.03 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.61/1.03 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.61/1.03 % Number of variables : 15 ( 15 !; 0 ?) % 0.61/1.03 % SPC : FOF_THM_RFO_SEQ % 0.61/1.03 % 0.61/1.03 % Comments : % 0.61/1.03 %-------------------------------------------------------------------------- % 0.61/1.03 %---- line(boole - df(2),1833042) % 0.61/1.03 fof(union_defn,axiom, % 0.61/1.03 ! [B,C,D] : % 0.61/1.03 ( member(D,union(B,C)) % 0.61/1.03 <=> ( member(D,B) % 0.61/1.03 | member(D,C) ) ) ). % 0.61/1.03 % 0.61/1.03 %---- line(tarski - df(3),1832749) % 0.61/1.03 fof(subset_defn,axiom, % 0.61/1.03 ! [B,C] : % 0.61/1.03 ( subset(B,C) % 0.61/1.03 <=> ! [D] : % 0.61/1.03 ( member(D,B) % 0.61/1.03 => member(D,C) ) ) ). % 0.61/1.03 % 0.61/1.03 %---- property(commutativity,op(union,2,function)) % 0.61/1.03 fof(commutativity_of_union,axiom, % 0.61/1.03 ! [B,C] : union(B,C) = union(C,B) ). % 0.61/1.03 % 0.61/1.03 %---- property(reflexivity,op(subset,2,predicate)) % 0.61/1.03 fof(reflexivity_of_subset,axiom, % 0.61/1.03 ! [B] : subset(B,B) ). % 0.61/1.03 % 0.61/1.03 %---- line(hidden - axiom39,1832615) % 0.61/1.03 fof(equal_member_defn,axiom, % 0.61/1.03 ! [B,C] : % 0.61/1.03 ( B = C % 0.61/1.03 <=> ! [D] : % 0.61/1.03 ( member(D,B) % 0.61/1.03 <=> member(D,C) ) ) ). % 0.61/1.03 % 0.61/1.03 %---- line(boole - th(33),1833222) (Looks like Quaife's LA3.1, but not mine) % 0.61/1.03 fof(prove_th33,conjecture, % 0.61/1.03 ! [B,C,D] : % 0.61/1.03 ( subset(B,C) % 0.61/1.03 => subset(union(B,D),union(C,D)) ) ). % 0.61/1.03 % 0.61/1.03 %-------------------------------------------------------------------------- % 0.61/1.03 %------------------------------------------- % 0.61/1.03 % Proof found % 0.61/1.03 % SZS status Theorem for theBenchmark % 0.61/1.03 % SZS output start Proof % 0.61/1.03 %ClaNum:25(EqnAxiom:13) % 0.61/1.03 %VarNum:55(SingletonVarNum:23) % 0.61/1.03 %MaxLitNum:3 % 0.61/1.03 %MaxfuncDepth:1 % 0.61/1.03 %SharedTerms:7 % 0.61/1.03 %goalClause: 14 17 % 0.61/1.03 %singleGoalClaCount:2 % 0.61/1.03 [14]P1(a1,a4) % 0.61/1.03 [17]~P1(f5(a1,a6),f5(a4,a6)) % 0.61/1.03 [15]P1(x151,x151) % 0.61/1.03 [16]E(f5(x161,x162),f5(x162,x161)) % 0.61/1.03 [18]P1(x181,x182)+P2(f2(x181,x182),x181) % 0.61/1.03 [22]P1(x221,x222)+~P2(f2(x221,x222),x222) % 0.61/1.03 [20]~P2(x201,x203)+P2(x201,f5(x202,x203)) % 0.61/1.03 [21]~P2(x211,x212)+P2(x211,f5(x212,x213)) % 0.61/1.03 [23]E(x231,x232)+P2(f3(x231,x232),x232)+P2(f3(x231,x232),x231) % 0.61/1.03 [25]E(x251,x252)+~P2(f3(x251,x252),x252)+~P2(f3(x251,x252),x251) % 0.61/1.03 [19]~P1(x193,x192)+P2(x191,x192)+~P2(x191,x193) % 0.61/1.03 [24]P2(x241,x242)+P2(x241,x243)+~P2(x241,f5(x243,x242)) % 0.61/1.03 %EqnAxiom % 0.61/1.03 [1]E(x11,x11) % 0.61/1.03 [2]E(x22,x21)+~E(x21,x22) % 0.61/1.03 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.61/1.03 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 0.61/1.03 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 0.61/1.03 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) % 0.61/1.03 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) % 0.61/1.03 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.61/1.03 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.61/1.03 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103) % 0.61/1.03 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111) % 0.61/1.03 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123) % 0.61/1.03 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131) % 0.61/1.03 % 0.61/1.03 %------------------------------------------- % 0.61/1.03 cnf(54,plain, % 0.61/1.03 (~P2(f2(f5(a1,a6),f5(a6,a4)),f5(a6,a4))), % 0.61/1.03 inference(scs_inference,[],[17,16,22,11])). % 0.61/1.03 cnf(55,plain, % 0.61/1.03 (~P2(f2(f5(a1,a6),f5(a6,a4)),a4)), % 0.61/1.03 inference(scs_inference,[],[54,20])). % 0.61/1.03 cnf(57,plain, % 0.61/1.03 (~P2(f2(f5(a1,a6),f5(a6,a4)),a6)), % 0.61/1.03 inference(scs_inference,[],[54,20,21])). % 0.61/1.03 cnf(80,plain, % 0.61/1.03 (~P2(f2(f5(a1,a6),f5(a6,a4)),f5(a1,a1))), % 0.61/1.03 inference(scs_inference,[],[14,55,19,24])). % 0.61/1.03 cnf(81,plain, % 0.61/1.03 (~P2(f2(f5(a1,a6),f5(a6,a4)),a1)), % 0.61/1.04 inference(scs_inference,[],[80,21])). % 0.61/1.04 cnf(99,plain, % 0.61/1.04 (P1(f5(x991,x992),f5(x992,x991))), % 0.61/1.04 inference(scs_inference,[],[16,15,2,10])). % 0.61/1.04 cnf(176,plain, % 0.61/1.04 (P2(f2(f5(a1,a6),f5(a6,a4)),f5(a1,a6))), % 0.61/1.04 inference(scs_inference,[],[17,16,18,11])). % 0.61/1.04 cnf(180,plain, % 0.61/1.04 ($false), % 0.61/1.04 inference(scs_inference,[],[99,57,81,176,19,24]), % 0.61/1.04 ['proof']). % 0.61/1.04 % SZS output end Proof % 0.61/1.04 % Total time :0.360000s %------------------------------------------------------------------------------