%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET589+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 : n023.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 0.68s 0.78s % Output : CNFRefutation 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET589+3 : TPTP v8.2.0. Released v2.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n023.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % 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 14:34:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.18/0.56 start to proof:theBenchmark % 0.68/0.77 %------------------------------------------- % 0.68/0.77 % File :CSE---1.7 % 0.68/0.77 % Problem :theBenchmark % 0.68/0.77 % Transform :cnf % 0.68/0.77 % Format :tptp:raw % 0.68/0.77 % Command :java -jar mcs_scs.jar %d %s % 0.68/0.77 % 0.68/0.77 % Result :Theorem 0.180000s % 0.68/0.77 % Output :CNFRefutation 0.180000s % 0.68/0.77 %------------------------------------------- % 0.68/0.78 %-------------------------------------------------------------------------- % 0.68/0.78 % File : SET589+3 : TPTP v8.2.0. Released v2.2.0. % 0.68/0.78 % Domain : Set Theory % 0.68/0.78 % Problem : If X (= Y and Z (= V, then X \ V (= Y \ Z % 0.68/0.78 % Version : [Try90] axioms : Reduced > Incomplete. % 0.68/0.78 % English : If X is a subset of Y and Z is a subset of V, then the % 0.68/0.78 % difference of X and V is a subset of the difference of Y and Z. % 0.68/0.78 % 0.68/0.78 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.68/0.78 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.68/0.78 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.68/0.78 % Source : [ILF] % 0.68/0.78 % Names : BOOLE (48) [TS89] % 0.68/0.78 % 0.68/0.78 % Status : Theorem % 0.68/0.78 % Rating : 0.00 v5.3.0, 0.13 v5.2.0, 0.00 v2.2.1 % 0.68/0.78 % Syntax : Number of formulae : 7 ( 1 unt; 0 def) % 0.68/0.78 % Number of atoms : 17 ( 0 equ) % 0.68/0.78 % Maximal formula atoms : 3 ( 2 avg) % 0.68/0.78 % Number of connectives : 11 ( 1 ~; 0 |; 3 &) % 0.68/0.78 % ( 2 <=>; 5 =>; 0 <=; 0 <~>) % 0.68/0.78 % Maximal formula depth : 7 ( 5 avg) % 0.68/0.78 % Maximal term depth : 2 ( 1 avg) % 0.68/0.78 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty) % 0.68/0.78 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty) % 0.68/0.78 % Number of variables : 20 ( 20 !; 0 ?) % 0.68/0.78 % SPC : FOF_THM_RFO_NEQ % 0.68/0.78 % 0.68/0.78 % Comments : % 0.68/0.78 %-------------------------------------------------------------------------- % 0.68/0.78 %---- line(boole - th(29),1833172) % 0.68/0.78 fof(transitivity_of_subset,axiom, % 0.68/0.78 ! [B,C,D] : % 0.68/0.78 ( ( subset(B,C) % 0.68/0.78 & subset(C,D) ) % 0.68/0.78 => subset(B,D) ) ). % 0.68/0.78 % 0.68/0.78 %---- line(boole - th(46),1833421) % 0.68/0.78 fof(difference_subset1,axiom, % 0.68/0.78 ! [B,C,D] : % 0.68/0.78 ( subset(B,C) % 0.68/0.78 => subset(difference(B,D),difference(C,D)) ) ). % 0.68/0.78 % 0.68/0.78 %---- line(boole - th(47),1833437) % 0.68/0.78 fof(difference_subset2,axiom, % 0.68/0.78 ! [B,C,D] : % 0.68/0.78 ( subset(B,C) % 0.68/0.78 => subset(difference(D,C),difference(D,B)) ) ). % 0.68/0.78 % 0.68/0.78 %---- line(boole - df(4),1833078) % 0.68/0.78 fof(difference_defn,axiom, % 0.68/0.78 ! [B,C,D] : % 0.68/0.78 ( member(D,difference(B,C)) % 0.68/0.78 <=> ( member(D,B) % 0.68/0.78 & ~ member(D,C) ) ) ). % 0.68/0.78 % 0.68/0.78 %---- line(tarski - df(3),1832749) % 0.68/0.78 fof(subset_defn,axiom, % 0.68/0.78 ! [B,C] : % 0.68/0.78 ( subset(B,C) % 0.68/0.78 <=> ! [D] : % 0.68/0.78 ( member(D,B) % 0.68/0.78 => member(D,C) ) ) ). % 0.68/0.78 % 0.68/0.78 %---- property(reflexivity,op(subset,2,predicate)) % 0.68/0.78 fof(reflexivity_of_subset,axiom, % 0.68/0.78 ! [B] : subset(B,B) ). % 0.68/0.78 % 0.68/0.78 %---- line(boole - th(48),1833454) % 0.68/0.78 fof(prove_th48,conjecture, % 0.68/0.78 ! [B,C,D,E] : % 0.68/0.78 ( ( subset(B,C) % 0.68/0.78 & subset(D,E) ) % 0.68/0.78 => subset(difference(B,E),difference(C,D)) ) ). % 0.68/0.78 % 0.68/0.78 %-------------------------------------------------------------------------- % 0.68/0.78 %------------------------------------------- % 0.68/0.78 % Proof found % 0.68/0.78 % SZS status Theorem for theBenchmark % 0.68/0.78 % SZS output start Proof % 0.68/0.78 %ClaNum:13(EqnAxiom:0) % 0.68/0.78 %VarNum:53(SingletonVarNum:26) % 0.68/0.78 %MaxLitNum:3 % 0.68/0.78 %MaxfuncDepth:1 % 0.68/0.78 %SharedTerms:9 % 0.68/0.78 %goalClause: 1 2 4 % 0.68/0.78 %singleGoalClaCount:3 % 0.68/0.78 [1]P1(a1,a4) % 0.68/0.78 [2]P1(a5,a6) % 0.68/0.78 [4]~P1(f2(a1,a6),f2(a4,a5)) % 0.68/0.78 [3]P1(x31,x31) % 0.68/0.78 [5]P1(x51,x52)+P2(f3(x51,x52),x51) % 0.68/0.78 [10]P1(x101,x102)+~P2(f3(x101,x102),x102) % 0.68/0.78 [9]P2(x91,x92)+~P2(x91,f2(x92,x93)) % 0.68/0.78 [11]~P2(x111,x112)+~P2(x111,f2(x113,x112)) % 0.68/0.78 [12]~P1(x123,x122)+P1(f2(x121,x122),f2(x121,x123)) % 0.68/0.78 [13]~P1(x131,x133)+P1(f2(x131,x132),f2(x133,x132)) % 0.68/0.78 [6]~P1(x61,x63)+P1(x61,x62)+~P1(x63,x62) % 0.68/0.78 [7]~P2(x71,x73)+P2(x71,x72)+~P1(x73,x72) % 0.68/0.78 [8]~P2(x81,x83)+P2(x81,x82)+P2(x81,f2(x83,x82)) % 0.68/0.78 %EqnAxiom % 0.68/0.78 % 0.68/0.78 %------------------------------------------- % 0.68/0.78 cnf(14,plain, % 0.68/0.78 (~P2(x141,a1)+P2(x141,a4)), % 0.68/0.78 inference(scs_inference,[],[1,7])). % 0.68/0.78 cnf(19,plain, % 0.68/0.78 (~P2(x191,a5)+P2(x191,a6)), % 0.68/0.78 inference(scs_inference,[],[2,7])). % 0.68/0.78 cnf(28,plain, % 0.68/0.78 (~P2(x281,a5)+~P2(x281,f2(x282,a6))), % 0.68/0.78 inference(scs_inference,[],[19,11])). % 0.68/0.78 cnf(33,plain, % 0.68/0.78 (~P2(f3(f2(a1,a6),f2(a4,a5)),a5)), % 0.68/0.78 inference(scs_inference,[],[4,28,5])). % 0.68/0.78 cnf(40,plain, % 0.68/0.78 (P2(x401,a4)+~P2(x401,f2(a1,x402))), % 0.68/0.78 inference(scs_inference,[],[14,9])). % 0.68/0.78 cnf(41,plain, % 0.68/0.79 (P2(f3(f2(a1,a6),f2(a4,a5)),a4)), % 0.68/0.79 inference(scs_inference,[],[4,40,5])). % 0.68/0.79 cnf(109,plain, % 0.68/0.79 ($false), % 0.68/0.79 inference(scs_inference,[],[4,33,41,10,8]), % 0.68/0.79 ['proof']). % 0.68/0.79 % SZS output end Proof % 0.68/0.79 % Total time :0.180000s %------------------------------------------------------------------------------