%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG227+1 : TPTP v8.2.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n006.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 03:41:07 EDT 2024 % Result : Theorem 0.54s 0.65s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG227+1 : TPTP v8.2.0. Released v3.4.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n006.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 : Wed Jun 19 15:45:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.51/0.57 start to proof:theBenchmark % 0.54/0.64 %------------------------------------------- % 0.54/0.64 % File :CSE---1.7 % 0.54/0.64 % Problem :theBenchmark % 0.54/0.64 % Transform :cnf % 0.54/0.64 % Format :tptp:raw % 0.54/0.64 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.64 % 0.54/0.64 % Result :Theorem 0.010000s % 0.54/0.64 % Output :CNFRefutation 0.010000s % 0.54/0.64 %------------------------------------------- % 0.54/0.65 %------------------------------------------------------------------------------ % 0.54/0.65 % File : ALG227+1 : TPTP v8.2.0. Released v3.4.0. % 0.54/0.65 % Domain : General Algebra % 0.54/0.65 % Problem : Algebraic Operation on Subsets of Many Sorted Sets T08 % 0.54/0.65 % Version : [Urb08] axioms : Especial. % 0.54/0.65 % English : % 0.54/0.65 % 0.54/0.65 % Refs : [Mar97] Marasik (1997), Algebraic Operation on Subsets of Many % 0.54/0.65 % : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In % 0.54/0.65 % : [Urb08] Urban (2006), Email to G. Sutcliffe % 0.54/0.65 % Source : [Urb08] % 0.54/0.65 % Names : t8_closure3 [Urb08] % 0.54/0.65 % 0.54/0.65 % Status : Theorem % 0.54/0.65 % Rating : 0.19 v7.5.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.24 v6.1.0, 0.23 v6.0.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0 % 0.54/0.65 % Syntax : Number of formulae : 29 ( 9 unt; 0 def) % 0.54/0.65 % Number of atoms : 72 ( 8 equ) % 0.54/0.65 % Maximal formula atoms : 6 ( 2 avg) % 0.54/0.65 % Number of connectives : 54 ( 11 ~; 1 |; 22 &) % 0.54/0.65 % ( 3 <=>; 17 =>; 0 <=; 0 <~>) % 0.54/0.65 % Maximal formula depth : 10 ( 4 avg) % 0.54/0.65 % Maximal term depth : 2 ( 1 avg) % 0.54/0.65 % Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty) % 0.54/0.65 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 0.54/0.65 % Number of variables : 41 ( 31 !; 10 ?) % 0.54/0.65 % SPC : FOF_THM_RFO_SEQ % 0.54/0.65 % 0.54/0.65 % Comments : Normal version: includes the axioms (which may be theorems from % 0.54/0.65 % other articles) and background that are possibly necessary. % 0.54/0.65 % : Translated by MPTP from the Mizar Mathematical Library 4.48.930. % 0.54/0.65 % : The problem encoding is based on set theory. % 0.54/0.65 %------------------------------------------------------------------------------ % 0.54/0.65 fof(t8_closure3,conjecture, % 0.54/0.65 ! [A] : % 0.54/0.65 ( ~ v1_xboole_0(A) % 0.54/0.65 => ! [B] : % 0.54/0.65 ( m1_pboole(B,A) % 0.54/0.65 => ! [C] : % 0.54/0.65 ( m1_subset_1(C,A) % 0.54/0.65 => ( ~ r2_hidden(C,k1_closure3(A,B)) % 0.54/0.65 => k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(antisymmetry_r2_hidden,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ( r2_hidden(A,B) % 0.54/0.65 => ~ r2_hidden(B,A) ) ). % 0.54/0.65 % 0.54/0.65 fof(cc1_closure2,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( v1_xboole_0(A) % 0.54/0.65 => v1_fraenkel(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(cc1_finset_1,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( v1_xboole_0(A) % 0.54/0.65 => v1_finset_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(cc1_funct_1,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( v1_xboole_0(A) % 0.54/0.65 => v1_funct_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(cc2_funct_1,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( ( v1_relat_1(A) % 0.54/0.65 & v1_xboole_0(A) % 0.54/0.65 & v1_funct_1(A) ) % 0.54/0.65 => ( v1_relat_1(A) % 0.54/0.65 & v1_funct_1(A) % 0.54/0.65 & v2_funct_1(A) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(d3_closure3,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( ~ v1_xboole_0(A) % 0.54/0.65 => ! [B] : % 0.54/0.65 ( m1_pboole(B,A) % 0.54/0.65 => ! [C] : % 0.54/0.65 ( C = k1_closure3(A,B) % 0.54/0.65 <=> C = a_2_0_closure3(A,B) ) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(dt_k1_closure3,axiom, % 0.54/0.65 $true ). % 0.54/0.65 % 0.54/0.65 fof(dt_k1_funct_1,axiom, % 0.54/0.65 $true ). % 0.54/0.65 % 0.54/0.65 fof(dt_k1_xboole_0,axiom, % 0.54/0.65 $true ). % 0.54/0.65 % 0.54/0.65 fof(dt_m1_pboole,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ( m1_pboole(B,A) % 0.54/0.65 => ( v1_relat_1(B) % 0.54/0.65 & v1_funct_1(B) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(dt_m1_subset_1,axiom, % 0.54/0.65 $true ). % 0.54/0.65 % 0.54/0.65 fof(existence_m1_pboole,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ? [B] : m1_pboole(B,A) ). % 0.54/0.65 % 0.54/0.65 fof(existence_m1_subset_1,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ? [B] : m1_subset_1(B,A) ). % 0.54/0.65 % 0.54/0.65 fof(fc1_xboole_0,axiom, % 0.54/0.65 v1_xboole_0(k1_xboole_0) ). % 0.54/0.65 % 0.54/0.65 fof(fraenkel_a_2_0_closure3,axiom, % 0.54/0.65 ! [A,B,C] : % 0.54/0.65 ( ( ~ v1_xboole_0(B) % 0.54/0.65 & m1_pboole(C,B) ) % 0.54/0.65 => ( r2_hidden(A,a_2_0_closure3(B,C)) % 0.54/0.65 <=> ? [D] : % 0.54/0.65 ( m1_subset_1(D,B) % 0.54/0.65 & A = D % 0.54/0.65 & k1_funct_1(C,D) != k1_xboole_0 ) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(rc1_closure2,axiom, % 0.54/0.65 ? [A] : % 0.54/0.65 ( v1_xboole_0(A) % 0.54/0.65 & v1_relat_1(A) % 0.54/0.65 & v1_funct_1(A) % 0.54/0.65 & v2_funct_1(A) % 0.54/0.65 & v1_finset_1(A) % 0.54/0.65 & v1_fraenkel(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(rc1_finset_1,axiom, % 0.54/0.65 ? [A] : % 0.54/0.65 ( ~ v1_xboole_0(A) % 0.54/0.65 & v1_finset_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(rc1_funct_1,axiom, % 0.54/0.65 ? [A] : % 0.54/0.65 ( v1_relat_1(A) % 0.54/0.65 & v1_funct_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(rc1_xboole_0,axiom, % 0.54/0.65 ? [A] : v1_xboole_0(A) ). % 0.54/0.65 % 0.54/0.65 fof(rc2_funct_1,axiom, % 0.54/0.65 ? [A] : % 0.54/0.65 ( v1_relat_1(A) % 0.54/0.65 & v1_xboole_0(A) % 0.54/0.65 & v1_funct_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(rc2_xboole_0,axiom, % 0.54/0.65 ? [A] : ~ v1_xboole_0(A) ). % 0.54/0.65 % 0.54/0.65 fof(rc3_funct_1,axiom, % 0.54/0.65 ? [A] : % 0.54/0.65 ( v1_relat_1(A) % 0.54/0.65 & v1_funct_1(A) % 0.54/0.65 & v2_funct_1(A) ) ). % 0.54/0.65 % 0.54/0.65 fof(t1_subset,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ( r2_hidden(A,B) % 0.54/0.65 => m1_subset_1(A,B) ) ). % 0.54/0.65 % 0.54/0.65 fof(t2_subset,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ( m1_subset_1(A,B) % 0.54/0.65 => ( v1_xboole_0(B) % 0.54/0.65 | r2_hidden(A,B) ) ) ). % 0.54/0.65 % 0.54/0.65 fof(t2_tarski,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ( ! [C] : % 0.54/0.65 ( r2_hidden(C,A) % 0.54/0.65 <=> r2_hidden(C,B) ) % 0.54/0.65 => A = B ) ). % 0.54/0.65 % 0.54/0.65 fof(t6_boole,axiom, % 0.54/0.65 ! [A] : % 0.54/0.65 ( v1_xboole_0(A) % 0.54/0.65 => A = k1_xboole_0 ) ). % 0.54/0.65 % 0.54/0.65 fof(t7_boole,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ~ ( r2_hidden(A,B) % 0.54/0.65 & v1_xboole_0(B) ) ). % 0.54/0.65 % 0.54/0.65 fof(t8_boole,axiom, % 0.54/0.65 ! [A,B] : % 0.54/0.65 ~ ( v1_xboole_0(A) % 0.54/0.65 & A != B % 0.54/0.65 & v1_xboole_0(B) ) ). % 0.54/0.65 % 0.54/0.65 %------------------------------------------------------------------------------ % 0.54/0.65 %------------------------------------------- % 0.54/0.65 % Proof found % 0.54/0.65 % SZS status Theorem for theBenchmark % 0.54/0.65 % SZS output start Proof % 0.54/0.65 %ClaNum:74(EqnAxiom:28) % 0.54/0.65 %VarNum:118(SingletonVarNum:44) % 0.54/0.65 %MaxLitNum:6 % 0.54/0.66 %MaxfuncDepth:2 % 0.54/0.66 %SharedTerms:37 % 0.54/0.66 %goalClause: 46 47 50 53 54 % 0.54/0.66 %singleGoalClaCount:5 % 0.54/0.66 [29]P1(a1) % 0.54/0.66 [30]P1(a2) % 0.54/0.66 [31]P1(a3) % 0.54/0.66 [32]P1(a5) % 0.54/0.66 [33]P2(a2) % 0.54/0.66 [34]P3(a2) % 0.54/0.66 [35]P3(a15) % 0.54/0.66 [36]P7(a2) % 0.54/0.66 [37]P7(a16) % 0.54/0.66 [38]P7(a5) % 0.54/0.66 [39]P7(a6) % 0.54/0.66 [40]P8(a2) % 0.54/0.66 [41]P8(a16) % 0.54/0.66 [42]P8(a5) % 0.54/0.66 [43]P8(a6) % 0.54/0.66 [44]P9(a2) % 0.54/0.66 [45]P9(a6) % 0.54/0.66 [46]P4(a8,a9) % 0.54/0.66 [47]P5(a11,a9) % 0.54/0.66 [50]~P1(a9) % 0.54/0.66 [51]~P1(a15) % 0.54/0.66 [52]~P1(a7) % 0.54/0.66 [53]~E(f17(a8,a11),a1) % 0.54/0.66 [54]~P6(a11,f18(a9,a8)) % 0.54/0.66 [48]P4(f12(x481),x481) % 0.54/0.66 [49]P5(f13(x491),x491) % 0.54/0.66 [55]~P1(x551)+E(x551,a1) % 0.54/0.66 [56]~P1(x561)+P2(x561) % 0.54/0.66 [57]~P1(x571)+P3(x571) % 0.54/0.66 [58]~P1(x581)+P7(x581) % 0.54/0.66 [61]P7(x611)+~P4(x611,x612) % 0.54/0.66 [62]P8(x621)+~P4(x621,x622) % 0.54/0.66 [63]~P1(x631)+~P6(x632,x631) % 0.54/0.66 [64]~P6(x641,x642)+P5(x641,x642) % 0.54/0.66 [66]~P6(x662,x661)+~P6(x661,x662) % 0.54/0.66 [59]~P1(x592)+~P1(x591)+E(x591,x592) % 0.54/0.66 [65]~P5(x652,x651)+P1(x651)+P6(x652,x651) % 0.54/0.66 [69]E(x691,x692)+P6(f10(x691,x692),x692)+P6(f10(x691,x692),x691) % 0.54/0.66 [71]E(x711,x712)+~P6(f10(x711,x712),x712)+~P6(f10(x711,x712),x711) % 0.54/0.66 [60]~P1(x601)+~P7(x601)+~P8(x601)+P9(x601) % 0.54/0.66 [67]P1(x672)+~P4(x673,x672)+~E(x671,f4(x672,x673))+E(x671,f18(x672,x673)) % 0.54/0.66 [68]P1(x682)+~P4(x683,x682)+~E(x681,f18(x682,x683))+E(x681,f4(x682,x683)) % 0.54/0.66 [72]P1(x722)+~P4(x723,x722)+~P6(x721,f4(x722,x723))+E(f14(x721,x722,x723),x721) % 0.54/0.66 [73]~P4(x733,x731)+P1(x731)+~P6(x732,f4(x731,x733))+P5(f14(x732,x731,x733),x731) % 0.54/0.66 [74]~P4(x742,x741)+P1(x741)+~P6(x743,f4(x741,x742))+~E(f17(x742,f14(x743,x741,x742)),a1) % 0.54/0.66 [70]~E(x702,x704)+~P4(x701,x703)+~P5(x702,x703)+P1(x703)+P6(x704,f4(x703,x701))+E(f17(x701,x702),a1) % 0.54/0.66 %EqnAxiom % 0.54/0.66 [1]E(x11,x11) % 0.54/0.66 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.66 [4]~E(x41,x42)+E(f12(x41),f12(x42)) % 0.54/0.66 [5]~E(x51,x52)+E(f13(x51),f13(x52)) % 0.54/0.66 [6]~E(x61,x62)+E(f17(x61,x63),f17(x62,x63)) % 0.54/0.66 [7]~E(x71,x72)+E(f17(x73,x71),f17(x73,x72)) % 0.54/0.66 [8]~E(x81,x82)+E(f18(x81,x83),f18(x82,x83)) % 0.54/0.66 [9]~E(x91,x92)+E(f18(x93,x91),f18(x93,x92)) % 0.54/0.66 [10]~E(x101,x102)+E(f14(x101,x103,x104),f14(x102,x103,x104)) % 0.54/0.66 [11]~E(x111,x112)+E(f14(x113,x111,x114),f14(x113,x112,x114)) % 0.54/0.66 [12]~E(x121,x122)+E(f14(x123,x124,x121),f14(x123,x124,x122)) % 0.54/0.66 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133)) % 0.54/0.66 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142)) % 0.54/0.66 [15]~E(x151,x152)+E(f10(x151,x153),f10(x152,x153)) % 0.54/0.66 [16]~E(x161,x162)+E(f10(x163,x161),f10(x163,x162)) % 0.54/0.66 [17]~P1(x171)+P1(x172)+~E(x171,x172) % 0.54/0.66 [18]P6(x182,x183)+~E(x181,x182)+~P6(x181,x183) % 0.54/0.66 [19]P6(x193,x192)+~E(x191,x192)+~P6(x193,x191) % 0.54/0.66 [20]P4(x202,x203)+~E(x201,x202)+~P4(x201,x203) % 0.54/0.66 [21]P4(x213,x212)+~E(x211,x212)+~P4(x213,x211) % 0.54/0.66 [22]~P7(x221)+P7(x222)+~E(x221,x222) % 0.54/0.66 [23]~P2(x231)+P2(x232)+~E(x231,x232) % 0.54/0.66 [24]~P3(x241)+P3(x242)+~E(x241,x242) % 0.54/0.66 [25]P5(x252,x253)+~E(x251,x252)+~P5(x251,x253) % 0.54/0.66 [26]P5(x263,x262)+~E(x261,x262)+~P5(x263,x261) % 0.54/0.66 [27]~P9(x271)+P9(x272)+~E(x271,x272) % 0.54/0.66 [28]~P8(x281)+P8(x282)+~E(x281,x282) % 0.54/0.66 % 0.54/0.66 %------------------------------------------- % 0.54/0.66 cnf(75,plain, % 0.54/0.66 (P1(x751)+~P4(x752,x751)+E(f4(x751,x752),f18(x751,x752))), % 0.54/0.66 inference(equality_inference,[],[67])). % 0.54/0.66 cnf(77,plain, % 0.54/0.66 (~P5(x771,x772)+P1(x772)+~P4(x773,x772)+P6(x771,f4(x772,x773))+E(f17(x773,x771),a1)), % 0.54/0.66 inference(equality_inference,[],[70])). % 0.54/0.66 cnf(78,plain, % 0.54/0.66 (~P1(f17(a8,a11))), % 0.54/0.66 inference(scs_inference,[],[53,55])). % 0.54/0.66 cnf(80,plain, % 0.54/0.66 (~P6(x801,a1)), % 0.54/0.66 inference(scs_inference,[],[53,29,55,63])). % 0.54/0.66 cnf(89,plain, % 0.54/0.66 (P6(a11,f4(a9,a8))), % 0.54/0.66 inference(scs_inference,[],[46,47,50,53,54,29,32,38,42,55,63,65,19,60,67,77])). % 0.54/0.66 cnf(116,plain, % 0.54/0.66 (P5(f13(x1161),x1161)), % 0.54/0.66 inference(rename_variables,[],[49])). % 0.54/0.66 cnf(124,plain, % 0.54/0.66 ($false), % 0.54/0.66 inference(scs_inference,[],[46,54,50,89,78,80,48,49,116,30,66,63,69,21,65,19,26,67,2,75]), % 0.54/0.66 ['proof']). % 0.54/0.66 % SZS output end Proof % 0.54/0.66 % Total time :0.010000s %------------------------------------------------------------------------------