%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET928+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 : n022.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 14:23:01 EDT 2024 % Result : Theorem 2.59s 2.82s % Output : CNFRefutation 2.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET928+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n022.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 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sun Jun 23 15:32:23 EDT 2024 % 0.12/0.33 % CPUTime : % 0.47/0.55 start to proof:theBenchmark % 2.59/2.81 %------------------------------------------- % 2.59/2.81 % File :CSE---1.7 % 2.59/2.81 % Problem :theBenchmark % 2.59/2.81 % Transform :cnf % 2.59/2.81 % Format :tptp:raw % 2.59/2.81 % Command :java -jar mcs_scs.jar %d %s % 2.59/2.81 % 2.59/2.81 % Result :Theorem 2.110000s % 2.59/2.81 % Output :CNFRefutation 2.110000s % 2.59/2.81 %------------------------------------------- % 2.59/2.82 %------------------------------------------------------------------------------ % 2.59/2.82 % File : SET928+1 : TPTP v8.2.0. Released v3.2.0. % 2.59/2.82 % Domain : Set theory % 2.59/2.82 % Problem : diff(uno_pair(A,B),C) = uno_pair(A,B) <=> (~in(A,C) & ~in(B,C)) % 2.59/2.82 % Version : [Urb06] axioms : Especial. % 2.59/2.82 % English : % 2.59/2.82 % 2.59/2.82 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets % 2.59/2.82 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 2.59/2.82 % Source : [Urb06] % 2.59/2.82 % Names : zfmisc_1__t72_zfmisc_1 [Urb06] % 2.59/2.82 % 2.59/2.82 % Status : Theorem % 2.59/2.82 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.05 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0 % 2.59/2.82 % Syntax : Number of formulae : 9 ( 3 unt; 0 def) % 2.59/2.82 % Number of atoms : 17 ( 3 equ) % 2.59/2.82 % Maximal formula atoms : 3 ( 1 avg) % 2.59/2.82 % Number of connectives : 17 ( 9 ~; 0 |; 4 &) % 2.59/2.82 % ( 2 <=>; 2 =>; 0 <=; 0 <~>) % 2.59/2.82 % Maximal formula depth : 8 ( 5 avg) % 2.59/2.82 % Maximal term depth : 3 ( 1 avg) % 2.59/2.82 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty) % 2.59/2.82 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty) % 2.59/2.82 % Number of variables : 19 ( 17 !; 2 ?) % 2.59/2.82 % SPC : FOF_THM_RFO_SEQ % 2.59/2.82 % 2.59/2.82 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 2.59/2.82 % library, www.mizar.org % 2.59/2.82 %------------------------------------------------------------------------------ % 2.59/2.82 fof(antisymmetry_r2_hidden,axiom, % 2.59/2.82 ! [A,B] : % 2.59/2.82 ( in(A,B) % 2.59/2.82 => ~ in(B,A) ) ). % 2.59/2.82 % 2.59/2.82 fof(commutativity_k2_tarski,axiom, % 2.59/2.82 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 2.59/2.82 % 2.59/2.82 fof(rc1_xboole_0,axiom, % 2.59/2.82 ? [A] : empty(A) ). % 2.59/2.82 % 2.59/2.82 fof(rc2_xboole_0,axiom, % 2.59/2.82 ? [A] : ~ empty(A) ). % 2.59/2.82 % 2.59/2.82 fof(symmetry_r1_xboole_0,axiom, % 2.59/2.82 ! [A,B] : % 2.59/2.82 ( disjoint(A,B) % 2.59/2.82 => disjoint(B,A) ) ). % 2.59/2.82 % 2.59/2.82 fof(t55_zfmisc_1,axiom, % 2.59/2.82 ! [A,B,C] : % 2.59/2.82 ~ ( disjoint(unordered_pair(A,B),C) % 2.59/2.82 & in(A,C) ) ). % 2.59/2.82 % 2.59/2.82 fof(t57_zfmisc_1,axiom, % 2.59/2.82 ! [A,B,C] : % 2.59/2.82 ~ ( ~ in(A,B) % 2.59/2.82 & ~ in(C,B) % 2.59/2.82 & ~ disjoint(unordered_pair(A,C),B) ) ). % 2.59/2.82 % 2.59/2.82 fof(t72_zfmisc_1,conjecture, % 2.59/2.82 ! [A,B,C] : % 2.59/2.82 ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) % 2.59/2.82 <=> ( ~ in(A,C) % 2.59/2.82 & ~ in(B,C) ) ) ). % 2.59/2.82 % 2.59/2.82 fof(t83_xboole_1,axiom, % 2.59/2.82 ! [A,B] : % 2.59/2.82 ( disjoint(A,B) % 2.59/2.82 <=> set_difference(A,B) = A ) ). % 2.59/2.82 % 2.59/2.82 %------------------------------------------------------------------------------ % 2.59/2.82 %------------------------------------------- % 2.59/2.82 % Proof found % 2.59/2.82 % SZS status Theorem for theBenchmark % 2.59/2.82 % SZS output start Proof % 2.59/2.82 %ClaNum:24(EqnAxiom:12) % 2.59/2.82 %VarNum:34(SingletonVarNum:16) % 2.59/2.82 %MaxLitNum:3 % 2.59/2.82 %MaxfuncDepth:2 % 2.59/2.82 %SharedTerms:15 % 2.59/2.82 %goalClause: 20 21 24 % 2.59/2.82 [13]P1(a1) % 2.59/2.82 [15]~P1(a3) % 2.59/2.82 [14]E(f2(x141,x142),f2(x142,x141)) % 2.59/2.82 [20]~P3(a5,a7)+E(f4(f2(a5,a6),a7),f2(a5,a6)) % 2.59/2.82 [21]~P3(a6,a7)+E(f4(f2(a5,a6),a7),f2(a5,a6)) % 2.59/2.82 [16]~P2(x162,x161)+P2(x161,x162) % 2.59/2.82 [19]~P3(x192,x191)+~P3(x191,x192) % 2.59/2.82 [17]~P2(x171,x172)+E(f4(x171,x172),x171) % 2.59/2.82 [18]P2(x181,x182)+~E(f4(x181,x182),x181) % 2.59/2.82 [23]~P3(x231,x232)+~P2(f2(x231,x233),x232) % 2.59/2.82 [24]P3(a5,a7)+P3(a6,a7)+~E(f4(f2(a5,a6),a7),f2(a5,a6)) % 2.59/2.82 [22]P3(x221,x222)+P3(x223,x222)+P2(f2(x223,x221),x222) % 2.59/2.82 %EqnAxiom % 2.59/2.82 [1]E(x11,x11) % 2.59/2.82 [2]E(x22,x21)+~E(x21,x22) % 2.59/2.82 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 2.59/2.82 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 2.59/2.82 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 2.59/2.82 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 2.59/2.82 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 2.59/2.82 [8]~P1(x81)+P1(x82)+~E(x81,x82) % 2.59/2.82 [9]P3(x92,x93)+~E(x91,x92)+~P3(x91,x93) % 2.59/2.82 [10]P3(x103,x102)+~E(x101,x102)+~P3(x103,x101) % 2.59/2.82 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113) % 2.59/2.82 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121) % 2.59/2.82 % 2.59/2.82 %------------------------------------------- % 2.59/2.82 cnf(29,plain, % 2.59/2.82 (~P2(x291,x292)+E(f4(x292,x291),x292)), % 2.59/2.82 inference(scs_inference,[],[16,17])). % 2.59/2.82 cnf(31,plain, % 2.59/2.82 (~P3(x311,x312)+~E(f4(f2(x311,x313),x312),f2(x311,x313))), % 2.59/2.82 inference(scs_inference,[],[18,23])). % 2.59/2.82 cnf(34,plain, % 2.59/2.82 (P2(f2(a5,a5),a7)+E(f4(f2(a5,a6),a7),f2(a5,a6))), % 2.59/2.82 inference(scs_inference,[],[20,22])). % 2.59/2.82 cnf(35,plain, % 2.59/2.82 (P2(f2(a6,a6),a7)+E(f4(f2(a5,a6),a7),f2(a5,a6))), % 2.59/2.82 inference(scs_inference,[],[21,22])). % 2.59/2.83 cnf(38,plain, % 2.59/2.83 (~P3(a5,a7)+P2(f2(a5,a5),a7)), % 2.59/2.83 inference(scs_inference,[],[31,34])). % 2.59/2.83 cnf(39,plain, % 2.59/2.83 (P2(f2(a5,a5),a7)), % 2.59/2.83 inference(scs_inference,[],[38,22])). % 2.59/2.83 cnf(40,plain, % 2.59/2.83 (~P3(a5,a7)), % 2.59/2.83 inference(scs_inference,[],[39,23])). % 2.59/2.83 cnf(42,plain, % 2.59/2.83 (P2(f2(a5,a5),x421)+~E(a7,x421)), % 2.59/2.83 inference(scs_inference,[],[39,23,12])). % 2.59/2.83 cnf(44,plain, % 2.59/2.83 (P3(a6,a7)+~E(f4(f2(a5,a6),a7),f2(a5,a6))), % 2.59/2.83 inference(scs_inference,[],[40,24])). % 2.59/2.83 cnf(60,plain, % 2.59/2.83 (E(x601,f2(a5,a5))+~E(x601,f4(f2(a5,a5),a7))), % 2.59/2.83 inference(scs_inference,[],[39,3,17])). % 2.59/2.83 cnf(61,plain, % 2.59/2.83 (E(f4(f2(a5,a5),a7),f2(a5,a5))), % 2.59/2.83 inference(equality_inference,[],[60])). % 2.59/2.83 cnf(62,plain, % 2.59/2.83 (E(f2(a5,a5),f4(f2(a5,a5),a7))), % 2.59/2.83 inference(scs_inference,[],[61,2])). % 2.59/2.83 cnf(65,plain, % 2.59/2.83 (P2(f4(f2(a5,a5),a7),x651)+~E(a7,x651)), % 2.59/2.83 inference(scs_inference,[],[39,62,11,12])). % 2.59/2.83 cnf(84,plain, % 2.59/2.83 (E(a7,f4(a7,f2(a5,a5)))), % 2.59/2.83 inference(scs_inference,[],[39,2,29])). % 2.59/2.83 cnf(89,plain, % 2.59/2.83 (E(f4(a7,f2(a5,a5)),a7)), % 2.59/2.83 inference(scs_inference,[],[84,42,65,23,2])). % 2.59/2.83 cnf(124,plain, % 2.59/2.83 (~P3(a7,x1241)+P2(f2(a5,x1241),a7)), % 2.59/2.83 inference(scs_inference,[],[40,19,22])). % 2.59/2.83 cnf(130,plain, % 2.59/2.83 (P2(f2(a5,a6),a7)+P2(f2(a6,a6),a7)), % 2.59/2.83 inference(scs_inference,[],[18,35])). % 2.59/2.83 cnf(198,plain, % 2.59/2.83 (P2(a7,f2(a5,x1981))+~P3(a7,x1981)), % 2.59/2.83 inference(scs_inference,[],[124,16])). % 2.59/2.83 cnf(215,plain, % 2.59/2.83 (~P3(f4(a7,f2(a5,a5)),x2151)+P2(a7,f2(a5,x2151))), % 2.59/2.83 inference(scs_inference,[],[89,198,9])). % 2.59/2.83 cnf(342,plain, % 2.59/2.83 (P2(f2(a6,a5),a7)+P2(f2(a6,a6),a7)), % 2.59/2.83 inference(scs_inference,[],[14,130,11])). % 2.59/2.83 cnf(439,plain, % 2.59/2.83 (~P3(a6,a7)+P2(f2(a6,a6),a7)), % 2.59/2.83 inference(scs_inference,[],[342,23])). % 2.59/2.83 cnf(451,plain, % 2.59/2.83 (P2(f2(a6,a6),a7)), % 2.59/2.83 inference(scs_inference,[],[439,22])). % 2.59/2.83 cnf(452,plain, % 2.59/2.83 (~P3(a6,a7)), % 2.59/2.83 inference(scs_inference,[],[451,23])). % 2.59/2.83 cnf(454,plain, % 2.59/2.83 (P2(f2(a6,a6),f4(a7,f2(a5,a5)))), % 2.59/2.83 inference(scs_inference,[],[84,451,23,12])). % 2.59/2.83 cnf(455,plain, % 2.59/2.83 (~E(f4(f2(a5,a6),a7),f2(a5,a6))), % 2.59/2.83 inference(scs_inference,[],[452,44])). % 2.59/2.83 cnf(471,plain, % 2.59/2.83 ($false), % 2.59/2.83 inference(scs_inference,[],[455,40,454,452,29,215,16,198,23,22]), % 2.59/2.83 ['proof']). % 2.59/2.83 % SZS output end Proof % 2.59/2.83 % Total time :2.110000s %------------------------------------------------------------------------------