%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET912+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n025.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 14:22:57 EDT 2024 % Result : Theorem 0.54s 0.62s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET912+1 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n025.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 13:16:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.54/0.58 start to proof:theBenchmark % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % File :CSE---1.7 % 0.54/0.61 % Problem :theBenchmark % 0.54/0.61 % Transform :cnf % 0.54/0.61 % Format :tptp:raw % 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.61 % 0.54/0.61 % Result :Theorem 0.000000s % 0.54/0.61 % Output :CNFRefutation 0.000000s % 0.54/0.61 %------------------------------------------- % 0.54/0.62 %------------------------------------------------------------------------------ % 0.54/0.62 % File : SET912+1 : TPTP v8.2.0. Released v3.2.0. % 0.54/0.62 % Domain : Set theory % 0.54/0.62 % Problem : ( in(A,B) & in(C,B) ) => intsctn(uno_pair(A,C),B) = uno_pair(A,C) % 0.54/0.62 % Version : [Urb06] axioms : Especial. % 0.54/0.62 % English : % 0.54/0.62 % 0.54/0.62 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 0.54/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.54/0.62 % Source : [Urb06] % 0.54/0.62 % Names : zfmisc_1__t53_zfmisc_1 [Urb06] % 0.54/0.62 % 0.54/0.62 % Status : Theorem % 0.54/0.62 % Rating : 0.03 v8.1.0, 0.06 v7.4.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.04 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0 % 0.54/0.62 % Syntax : Number of formulae : 10 ( 6 unt; 0 def) % 0.54/0.62 % Number of atoms : 16 ( 5 equ) % 0.54/0.62 % Maximal formula atoms : 3 ( 1 avg) % 0.54/0.62 % Number of connectives : 8 ( 2 ~; 0 |; 2 &) % 0.54/0.62 % ( 1 <=>; 3 =>; 0 <=; 0 <~>) % 0.54/0.62 % Maximal formula depth : 6 ( 4 avg) % 0.54/0.62 % Maximal term depth : 3 ( 1 avg) % 0.54/0.62 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 0.54/0.62 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 0.54/0.62 % Number of variables : 20 ( 18 !; 2 ?) % 0.54/0.62 % SPC : FOF_THM_RFO_SEQ % 0.54/0.62 % 0.54/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.54/0.62 % library, www.mizar.org % 0.54/0.62 %------------------------------------------------------------------------------ % 0.54/0.62 fof(antisymmetry_r2_hidden,axiom, % 0.54/0.62 ! [A,B] : % 0.54/0.62 ( in(A,B) % 0.54/0.62 => ~ in(B,A) ) ). % 0.54/0.62 % 0.54/0.62 fof(commutativity_k2_tarski,axiom, % 0.54/0.62 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.54/0.62 % 0.54/0.62 fof(commutativity_k3_xboole_0,axiom, % 0.54/0.62 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.54/0.62 % 0.54/0.62 fof(idempotence_k3_xboole_0,axiom, % 0.54/0.62 ! [A,B] : set_intersection2(A,A) = A ). % 0.54/0.62 % 0.54/0.62 fof(rc1_xboole_0,axiom, % 0.54/0.62 ? [A] : empty(A) ). % 0.54/0.62 % 0.54/0.62 fof(rc2_xboole_0,axiom, % 0.54/0.62 ? [A] : ~ empty(A) ). % 0.54/0.62 % 0.54/0.62 fof(reflexivity_r1_tarski,axiom, % 0.54/0.62 ! [A,B] : subset(A,A) ). % 0.54/0.62 % 0.54/0.62 fof(t28_xboole_1,axiom, % 0.54/0.62 ! [A,B] : % 0.54/0.62 ( subset(A,B) % 0.54/0.62 => set_intersection2(A,B) = A ) ). % 0.54/0.62 % 0.54/0.62 fof(t38_zfmisc_1,axiom, % 0.54/0.62 ! [A,B,C] : % 0.54/0.62 ( subset(unordered_pair(A,B),C) % 0.54/0.62 <=> ( in(A,C) % 0.54/0.62 & in(B,C) ) ) ). % 0.54/0.62 % 0.54/0.62 fof(t53_zfmisc_1,conjecture, % 0.54/0.62 ! [A,B,C] : % 0.54/0.62 ( ( in(A,B) % 0.54/0.62 & in(C,B) ) % 0.54/0.62 => set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ) ). % 0.54/0.62 % 0.54/0.62 %------------------------------------------------------------------------------ % 0.54/0.62 %------------------------------------------- % 0.54/0.62 % Proof found % 0.54/0.62 % SZS status Theorem for theBenchmark % 0.54/0.62 % SZS output start Proof % 0.54/0.62 %ClaNum:26(EqnAxiom:12) % 0.54/0.62 %VarNum:39(SingletonVarNum:19) % 0.54/0.62 %MaxLitNum:3 % 0.54/0.62 %MaxfuncDepth:2 % 0.54/0.62 %SharedTerms:12 % 0.54/0.62 %goalClause: 14 15 21 % 0.54/0.62 %singleGoalClaCount:3 % 0.54/0.62 [13]P1(a1) % 0.54/0.62 [14]P2(a2,a4) % 0.54/0.62 [15]P2(a5,a4) % 0.54/0.62 [20]~P1(a3) % 0.54/0.62 [21]~E(f6(f7(a2,a5),a4),f7(a2,a5)) % 0.54/0.62 [16]P3(x161,x161) % 0.54/0.62 [17]E(f6(x171,x171),x171) % 0.54/0.62 [18]E(f7(x181,x182),f7(x182,x181)) % 0.54/0.62 [19]E(f6(x191,x192),f6(x192,x191)) % 0.54/0.62 [23]~P2(x232,x231)+~P2(x231,x232) % 0.54/0.62 [22]~P3(x221,x222)+E(f6(x221,x222),x221) % 0.54/0.62 [24]P2(x241,x242)+~P3(f7(x243,x241),x242) % 0.54/0.62 [25]P2(x251,x252)+~P3(f7(x251,x253),x252) % 0.54/0.62 [26]~P2(x262,x263)+~P2(x261,x263)+P3(f7(x261,x262),x263) % 0.54/0.62 %EqnAxiom % 0.54/0.62 [1]E(x11,x11) % 0.54/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.62 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43)) % 0.54/0.62 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52)) % 0.54/0.62 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 0.54/0.62 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 0.54/0.62 [8]~P1(x81)+P1(x82)+~E(x81,x82) % 0.54/0.62 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93) % 0.54/0.62 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101) % 0.54/0.62 [11]P3(x112,x113)+~E(x111,x112)+~P3(x111,x113) % 0.54/0.62 [12]P3(x123,x122)+~E(x121,x122)+~P3(x123,x121) % 0.54/0.62 % 0.54/0.62 %------------------------------------------- % 0.54/0.62 cnf(32,plain, % 0.54/0.62 (P3(x321,x321)), % 0.54/0.62 inference(rename_variables,[],[16])). % 0.54/0.62 cnf(38,plain, % 0.54/0.62 ($false), % 0.54/0.62 inference(scs_inference,[],[14,15,21,16,32,17,23,22,24,2,25,26]), % 0.54/0.62 ['proof']). % 0.54/0.62 % SZS output end Proof % 0.54/0.62 % Total time :0.000000s %------------------------------------------------------------------------------