%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET588+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 : 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 14:21:51 EDT 2024 % Result : Theorem 0.55s 0.62s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : SET588+3 : TPTP v8.2.0. Released v2.2.0. % 0.09/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n026.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 11:58:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.55/0.61 %------------------------------------------- % 0.55/0.61 % File :CSE---1.7 % 0.55/0.61 % Problem :theBenchmark % 0.55/0.61 % Transform :cnf % 0.55/0.61 % Format :tptp:raw % 0.55/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.61 % 0.55/0.61 % Result :Theorem 0.020000s % 0.55/0.61 % Output :CNFRefutation 0.020000s % 0.55/0.61 %------------------------------------------- % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 % File : SET588+3 : TPTP v8.2.0. Released v2.2.0. % 0.55/0.61 % Domain : Set Theory % 0.55/0.61 % Problem : If X (= Y, then X \ Z (= Y \ Z % 0.55/0.61 % Version : [Try90] axioms : Reduced > Incomplete. % 0.55/0.61 % English : If X is a subset of Y, then the difference of X and Z is a % 0.55/0.62 % subset of the difference of Y and Z. % 0.55/0.62 % 0.55/0.62 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.55/0.62 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.55/0.62 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.55/0.62 % Source : [ILF] % 0.55/0.62 % Names : BOOLE (46) [TS89] % 0.55/0.62 % 0.55/0.62 % Status : Theorem % 0.55/0.62 % Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.08 v6.0.0, 0.00 v5.5.0, 0.12 v5.4.0, 0.17 v5.3.0, 0.22 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.00 v4.0.1, 0.05 v3.7.0, 0.14 v3.5.0, 0.25 v3.4.0, 0.00 v3.1.0, 0.25 v2.7.0, 0.00 v2.2.1 % 0.55/0.62 % Syntax : Number of formulae : 4 ( 1 unt; 0 def) % 0.55/0.62 % Number of atoms : 9 ( 0 equ) % 0.55/0.62 % Maximal formula atoms : 3 ( 2 avg) % 0.55/0.62 % Number of connectives : 6 ( 1 ~; 0 |; 1 &) % 0.55/0.62 % ( 2 <=>; 2 =>; 0 <=; 0 <~>) % 0.55/0.62 % Maximal formula depth : 7 ( 5 avg) % 0.55/0.62 % Maximal term depth : 2 ( 1 avg) % 0.55/0.62 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty) % 0.55/0.62 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.55/0.62 % Number of variables : 10 ( 10 !; 0 ?) % 0.55/0.62 % SPC : FOF_THM_RFO_NEQ % 0.55/0.62 % 0.55/0.62 % Comments : % 0.55/0.62 %-------------------------------------------------------------------------- % 0.55/0.62 %---- line(boole - df(4),1833078) % 0.55/0.62 fof(difference_defn,axiom, % 0.55/0.62 ! [B,C,D] : % 0.55/0.62 ( member(D,difference(B,C)) % 0.55/0.62 <=> ( member(D,B) % 0.55/0.62 & ~ member(D,C) ) ) ). % 0.55/0.62 % 0.55/0.62 %---- line(tarski - df(3),1832749) % 0.55/0.62 fof(subset_defn,axiom, % 0.55/0.62 ! [B,C] : % 0.55/0.62 ( subset(B,C) % 0.55/0.62 <=> ! [D] : % 0.55/0.62 ( member(D,B) % 0.55/0.62 => member(D,C) ) ) ). % 0.55/0.62 % 0.55/0.62 %---- property(reflexivity,op(subset,2,predicate)) % 0.55/0.62 fof(reflexivity_of_subset,axiom, % 0.55/0.62 ! [B] : subset(B,B) ). % 0.55/0.62 % 0.55/0.62 %---- line(boole - th(46),1833421) % 0.55/0.62 fof(prove_difference_subset1,conjecture, % 0.55/0.62 ! [B,C,D] : % 0.55/0.62 ( subset(B,C) % 0.55/0.62 => subset(difference(B,D),difference(C,D)) ) ). % 0.55/0.62 % 0.55/0.62 %-------------------------------------------------------------------------- % 0.55/0.62 %------------------------------------------- % 0.55/0.62 % Proof found % 0.55/0.62 % SZS status Theorem for theBenchmark % 0.55/0.62 % SZS output start Proof % 0.55/0.62 %ClaNum:9(EqnAxiom:0) % 0.55/0.62 %VarNum:35(SingletonVarNum:17) % 0.55/0.62 %MaxLitNum:3 % 0.55/0.62 %MaxfuncDepth:1 % 0.55/0.62 %SharedTerms:7 % 0.55/0.62 %goalClause: 1 3 % 0.55/0.62 %singleGoalClaCount:2 % 0.55/0.62 [1]P1(a1,a4) % 0.55/0.62 [3]~P1(f2(a1,a5),f2(a4,a5)) % 0.55/0.62 [2]P1(x21,x21) % 0.55/0.62 [4]P1(x41,x42)+P2(f3(x41,x42),x41) % 0.55/0.62 [8]P1(x81,x82)+~P2(f3(x81,x82),x82) % 0.55/0.62 [7]P2(x71,x72)+~P2(x71,f2(x72,x73)) % 0.55/0.62 [9]~P2(x91,x92)+~P2(x91,f2(x93,x92)) % 0.55/0.62 [5]~P1(x53,x52)+P2(x51,x52)+~P2(x51,x53) % 0.55/0.62 [6]~P2(x61,x63)+P2(x61,x62)+P2(x61,f2(x63,x62)) % 0.55/0.62 %EqnAxiom % 0.55/0.62 % 0.55/0.62 %------------------------------------------- % 0.55/0.62 cnf(10,plain, % 0.55/0.62 (~P2(x101,x102)+P2(x101,x103)+P2(f3(x102,x103),x102)), % 0.55/0.62 inference(scs_inference,[],[4,5])). % 0.55/0.62 cnf(13,plain, % 0.55/0.62 (~P2(x131,a1)+P2(x131,x132)+P2(x131,f2(a4,x132))), % 0.55/0.62 inference(scs_inference,[],[1,6,5])). % 0.55/0.62 cnf(14,plain, % 0.55/0.62 (~P2(x141,f2(x142,x143))+P2(f3(f2(x142,x143),x144),x142)+P2(x141,x144)), % 0.55/0.62 inference(scs_inference,[],[10,7])). % 0.55/0.62 cnf(17,plain, % 0.55/0.62 (~P2(f3(f2(a1,a5),f2(a4,a5)),f2(x171,x172))+P2(f3(f2(x171,x172),f2(a4,a5)),x171)), % 0.55/0.62 inference(scs_inference,[],[3,14,8])). % 0.55/0.62 cnf(18,plain, % 0.55/0.62 (P2(f3(f2(a1,a5),f2(a4,a5)),a1)), % 0.55/0.62 inference(scs_inference,[],[3,17,4])). % 0.55/0.62 cnf(30,plain, % 0.55/0.62 (~P2(f3(f2(a1,a5),f2(a4,a5)),a5)), % 0.55/0.62 inference(scs_inference,[],[3,4,9])). % 0.55/0.62 cnf(33,plain, % 0.55/0.62 ($false), % 0.55/0.62 inference(scs_inference,[],[3,18,30,13,8]), % 0.55/0.62 ['proof']). % 0.55/0.62 % SZS output end Proof % 0.55/0.62 % Total time :0.020000s %------------------------------------------------------------------------------