%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU361+1 : TPTP v8.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n021.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 15:02:38 EDT 2024 % Result : Theorem 1.13s 1.20s % Output : CNFRefutation 1.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU361+1 : TPTP v8.2.0. Released v3.3.0. % 0.08/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n021.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 : Fri Jun 21 15:32:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 1.13/1.19 %------------------------------------------- % 1.13/1.19 % File :CSE---1.7 % 1.13/1.19 % Problem :theBenchmark % 1.13/1.19 % Transform :cnf % 1.13/1.19 % Format :tptp:raw % 1.13/1.19 % Command :java -jar mcs_scs.jar %d %s % 1.13/1.19 % 1.13/1.19 % Result :Theorem 0.570000s % 1.13/1.19 % Output :CNFRefutation 0.570000s % 1.13/1.19 %------------------------------------------- % 1.13/1.19 %------------------------------------------------------------------------------ % 1.13/1.19 % File : SEU361+1 : TPTP v8.2.0. Released v3.3.0. % 1.13/1.19 % Domain : Set theory % 1.13/1.19 % Problem : MPTP bushy problem t44_yellow_0 % 1.13/1.19 % Version : [Urb07] axioms : Especial. % 1.13/1.19 % English : % 1.13/1.19 % 1.13/1.19 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 1.13/1.19 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 1.13/1.19 % Source : [Urb07] % 1.13/1.19 % Names : bushy-t44_yellow_0 [Urb07] % 1.13/1.19 % 1.13/1.19 % Status : Theorem % 1.13/1.19 % Rating : 0.11 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.04 v5.5.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0 % 1.13/1.19 % Syntax : Number of formulae : 28 ( 10 unt; 0 def) % 1.13/1.19 % Number of atoms : 72 ( 5 equ) % 1.13/1.19 % Maximal formula atoms : 15 ( 2 avg) % 1.13/1.19 % Number of connectives : 55 ( 11 ~; 1 |; 20 &) % 1.13/1.19 % ( 0 <=>; 23 =>; 0 <=; 0 <~>) % 1.13/1.19 % Maximal formula depth : 12 ( 4 avg) % 1.13/1.19 % Maximal term depth : 2 ( 1 avg) % 1.13/1.19 % Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty) % 1.13/1.19 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 1.13/1.19 % Number of variables : 36 ( 29 !; 7 ?) % 1.13/1.19 % SPC : FOF_THM_RFO_SEQ % 1.13/1.19 % 1.13/1.19 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 1.13/1.19 % library, www.mizar.org % 1.13/1.19 %------------------------------------------------------------------------------ % 1.13/1.19 fof(antisymmetry_r2_hidden,axiom, % 1.13/1.19 ! [A,B] : % 1.13/1.19 ( in(A,B) % 1.13/1.19 => ~ in(B,A) ) ). % 1.13/1.19 % 1.13/1.19 fof(cc1_finset_1,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( empty(A) % 1.13/1.19 => finite(A) ) ). % 1.13/1.19 % 1.13/1.19 fof(d11_yellow_0,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( rel_str(A) % 1.13/1.19 => bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ). % 1.13/1.19 % 1.13/1.19 fof(dt_k1_xboole_0,axiom, % 1.13/1.19 $true ). % 1.13/1.19 % 1.13/1.19 fof(dt_k1_yellow_0,axiom, % 1.13/1.19 ! [A,B] : % 1.13/1.19 ( rel_str(A) % 1.13/1.19 => element(join_on_relstr(A,B),the_carrier(A)) ) ). % 1.13/1.19 % 1.13/1.19 fof(dt_k3_yellow_0,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( rel_str(A) % 1.13/1.19 => element(bottom_of_relstr(A),the_carrier(A)) ) ). % 1.13/1.19 % 1.13/1.19 fof(dt_l1_orders_2,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( rel_str(A) % 1.13/1.19 => one_sorted_str(A) ) ). % 1.13/1.19 % 1.13/1.19 fof(dt_l1_struct_0,axiom, % 1.13/1.19 $true ). % 1.13/1.19 % 1.13/1.19 fof(dt_m1_subset_1,axiom, % 1.13/1.19 $true ). % 1.13/1.19 % 1.13/1.19 fof(dt_u1_struct_0,axiom, % 1.13/1.19 $true ). % 1.13/1.19 % 1.13/1.19 fof(existence_l1_orders_2,axiom, % 1.13/1.19 ? [A] : rel_str(A) ). % 1.13/1.19 % 1.13/1.19 fof(existence_l1_struct_0,axiom, % 1.13/1.19 ? [A] : one_sorted_str(A) ). % 1.13/1.19 % 1.13/1.19 fof(existence_m1_subset_1,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ? [B] : element(B,A) ). % 1.13/1.19 % 1.13/1.19 fof(fc1_struct_0,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( ( ~ empty_carrier(A) % 1.13/1.19 & one_sorted_str(A) ) % 1.13/1.19 => ~ empty(the_carrier(A)) ) ). % 1.13/1.19 % 1.13/1.19 fof(fc1_xboole_0,axiom, % 1.13/1.19 empty(empty_set) ). % 1.13/1.19 % 1.13/1.19 fof(rc1_finset_1,axiom, % 1.13/1.19 ? [A] : % 1.13/1.19 ( ~ empty(A) % 1.13/1.19 & finite(A) ) ). % 1.13/1.19 % 1.13/1.19 fof(rc1_xboole_0,axiom, % 1.13/1.19 ? [A] : empty(A) ). % 1.13/1.19 % 1.13/1.19 fof(rc2_xboole_0,axiom, % 1.13/1.19 ? [A] : ~ empty(A) ). % 1.13/1.19 % 1.13/1.19 fof(rc3_struct_0,axiom, % 1.13/1.19 ? [A] : % 1.13/1.19 ( one_sorted_str(A) % 1.13/1.19 & ~ empty_carrier(A) ) ). % 1.13/1.19 % 1.13/1.19 fof(t1_subset,axiom, % 1.13/1.19 ! [A,B] : % 1.13/1.19 ( in(A,B) % 1.13/1.19 => element(A,B) ) ). % 1.13/1.19 % 1.13/1.19 fof(t2_subset,axiom, % 1.13/1.19 ! [A,B] : % 1.13/1.19 ( element(A,B) % 1.13/1.19 => ( empty(B) % 1.13/1.19 | in(A,B) ) ) ). % 1.13/1.19 % 1.13/1.19 fof(t30_yellow_0,axiom, % 1.13/1.19 ! [A] : % 1.13/1.19 ( ( antisymmetric_relstr(A) % 1.13/1.19 & rel_str(A) ) % 1.13/1.19 => ! [B] : % 1.13/1.19 ( element(B,the_carrier(A)) % 1.13/1.19 => ! [C] : % 1.13/1.19 ( ( ( B = join_on_relstr(A,C) % 1.13/1.19 & ex_sup_of_relstr_set(A,C) ) % 1.13/1.19 => ( relstr_set_smaller(A,C,B) % 1.13/1.19 & ! [D] : % 1.13/1.19 ( element(D,the_carrier(A)) % 1.13/1.19 => ( relstr_set_smaller(A,C,D) % 1.13/1.19 => related(A,B,D) ) ) ) ) % 1.13/1.19 & ( ( relstr_set_smaller(A,C,B) % 1.13/1.19 & ! [D] : % 1.13/1.20 ( element(D,the_carrier(A)) % 1.13/1.20 => ( relstr_set_smaller(A,C,D) % 1.13/1.20 => related(A,B,D) ) ) ) % 1.13/1.20 => ( B = join_on_relstr(A,C) % 1.13/1.20 & ex_sup_of_relstr_set(A,C) ) ) ) ) ) ). % 1.13/1.20 % 1.13/1.20 fof(t42_yellow_0,axiom, % 1.13/1.20 ! [A] : % 1.13/1.20 ( ( ~ empty_carrier(A) % 1.13/1.20 & antisymmetric_relstr(A) % 1.13/1.20 & lower_bounded_relstr(A) % 1.13/1.20 & rel_str(A) ) % 1.13/1.20 => ( ex_sup_of_relstr_set(A,empty_set) % 1.13/1.20 & ex_inf_of_relstr_set(A,the_carrier(A)) ) ) ). % 1.13/1.20 % 1.13/1.20 fof(t44_yellow_0,conjecture, % 1.13/1.20 ! [A] : % 1.13/1.20 ( ( ~ empty_carrier(A) % 1.13/1.20 & antisymmetric_relstr(A) % 1.13/1.20 & lower_bounded_relstr(A) % 1.13/1.20 & rel_str(A) ) % 1.13/1.20 => ! [B] : % 1.13/1.20 ( element(B,the_carrier(A)) % 1.13/1.20 => related(A,bottom_of_relstr(A),B) ) ) ). % 1.13/1.20 % 1.13/1.20 fof(t6_boole,axiom, % 1.13/1.20 ! [A] : % 1.13/1.20 ( empty(A) % 1.13/1.20 => A = empty_set ) ). % 1.13/1.20 % 1.13/1.20 fof(t6_yellow_0,axiom, % 1.13/1.20 ! [A] : % 1.13/1.20 ( rel_str(A) % 1.13/1.20 => ! [B] : % 1.13/1.20 ( element(B,the_carrier(A)) % 1.13/1.20 => ( relstr_set_smaller(A,empty_set,B) % 1.13/1.20 & relstr_element_smaller(A,empty_set,B) ) ) ) ). % 1.13/1.20 % 1.13/1.20 fof(t7_boole,axiom, % 1.13/1.20 ! [A,B] : % 1.13/1.20 ~ ( in(A,B) % 1.13/1.20 & empty(B) ) ). % 1.13/1.20 % 1.13/1.20 fof(t8_boole,axiom, % 1.13/1.20 ! [A,B] : % 1.13/1.20 ~ ( empty(A) % 1.13/1.20 & A != B % 1.13/1.20 & empty(B) ) ). % 1.13/1.20 % 1.13/1.20 %------------------------------------------------------------------------------ % 1.13/1.20 %------------------------------------------- % 1.13/1.20 % Proof found % 1.13/1.20 % SZS status Theorem for theBenchmark % 1.13/1.20 % SZS output start Proof % 1.13/1.20 %ClaNum:75(EqnAxiom:35) % 1.13/1.20 %VarNum:176(SingletonVarNum:50) % 1.13/1.20 %MaxLitNum:8 % 1.13/1.20 %MaxfuncDepth:1 % 1.13/1.20 %SharedTerms:26 % 1.13/1.20 %goalClause: 40 43 44 45 50 51 % 1.13/1.20 %singleGoalClaCount:6 % 1.13/1.20 [36]P1(a1) % 1.13/1.20 [37]P1(a3) % 1.13/1.20 [38]P4(a4) % 1.13/1.20 [39]P8(a5) % 1.13/1.20 [40]P8(a9) % 1.13/1.20 [41]P9(a7) % 1.13/1.20 [42]P9(a10) % 1.13/1.20 [43]P2(a9) % 1.13/1.20 [44]P10(a9) % 1.13/1.20 [47]~P1(a4) % 1.13/1.20 [48]~P1(a11) % 1.13/1.20 [49]~P5(a10) % 1.13/1.20 [50]~P5(a9) % 1.13/1.20 [45]P3(a6,f13(a9)) % 1.13/1.20 [51]~P12(a9,f2(a9),a6) % 1.13/1.20 [46]P3(f8(x461),x461) % 1.13/1.20 [52]~P1(x521)+E(x521,a1) % 1.13/1.20 [53]~P1(x531)+P4(x531) % 1.13/1.20 [54]~P8(x541)+P9(x541) % 1.13/1.20 [56]~P8(x561)+E(f14(x561,a1),f2(x561)) % 1.13/1.20 [59]~P8(x591)+P3(f2(x591),f13(x591)) % 1.13/1.20 [58]~P1(x581)+~P11(x582,x581) % 1.13/1.20 [60]~P11(x601,x602)+P3(x601,x602) % 1.13/1.20 [63]~P11(x632,x631)+~P11(x631,x632) % 1.13/1.20 [65]~P8(x651)+P3(f14(x651,x652),f13(x651)) % 1.13/1.20 [57]~P9(x571)+P5(x571)+~P1(f13(x571)) % 1.13/1.20 [55]~P1(x552)+~P1(x551)+E(x551,x552) % 1.13/1.20 [62]~P3(x622,x621)+P1(x621)+P11(x622,x621) % 1.13/1.20 [66]~P8(x661)+P13(x661,a1,x662)+~P3(x662,f13(x661)) % 1.13/1.20 [67]~P8(x671)+P14(x671,a1,x672)+~P3(x672,f13(x671)) % 1.13/1.20 [61]~P8(x611)+~P2(x611)+~P10(x611)+P5(x611)+P6(x611,a1) % 1.13/1.20 [64]~P8(x641)+~P2(x641)+~P10(x641)+P5(x641)+P7(x641,f13(x641)) % 1.13/1.20 [68]~P8(x681)+~P2(x681)+~P6(x681,x682)+P13(x681,x682,x683)+~E(x683,f14(x681,x682))+~P3(x683,f13(x681)) % 1.13/1.20 [70]~P8(x701)+~P2(x701)+~P13(x701,x702,x703)+P6(x701,x702)+~P3(x703,f13(x701))+P3(f12(x701,x703,x702),f13(x701)) % 1.13/1.20 [71]~P8(x712)+~P2(x712)+~P13(x712,x713,x711)+P3(f12(x712,x711,x713),f13(x712))+~P3(x711,f13(x712))+E(x711,f14(x712,x713)) % 1.13/1.20 [72]~P8(x721)+~P2(x721)+~P13(x721,x722,x723)+P6(x721,x722)+P13(x721,x722,f12(x721,x723,x722))+~P3(x723,f13(x721)) % 1.13/1.20 [73]~P8(x732)+~P2(x732)+~P13(x732,x733,x731)+P13(x732,x733,f12(x732,x731,x733))+~P3(x731,f13(x732))+E(x731,f14(x732,x733)) % 1.13/1.20 [74]~P8(x741)+~P2(x741)+P6(x741,x742)+~P13(x741,x742,x743)+~P12(x741,x743,f12(x741,x743,x742))+~P3(x743,f13(x741)) % 1.13/1.20 [75]~P8(x752)+~P2(x752)+~P13(x752,x753,x751)+~P12(x752,x751,f12(x752,x751,x753))+~P3(x751,f13(x752))+E(x751,f14(x752,x753)) % 1.13/1.20 [69]~P8(x691)+~P2(x691)+~P6(x691,x694)+~P13(x691,x694,x693)+P12(x691,x692,x693)+~P3(x692,f13(x691))+~P3(x693,f13(x691))+~E(x692,f14(x691,x694)) % 1.13/1.20 %EqnAxiom % 1.13/1.20 [1]E(x11,x11) % 1.13/1.20 [2]E(x22,x21)+~E(x21,x22) % 1.13/1.20 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.13/1.20 [4]~E(x41,x42)+E(f13(x41),f13(x42)) % 1.13/1.20 [5]~E(x51,x52)+E(f8(x51),f8(x52)) % 1.13/1.20 [6]~E(x61,x62)+E(f2(x61),f2(x62)) % 1.13/1.20 [7]~E(x71,x72)+E(f14(x71,x73),f14(x72,x73)) % 1.13/1.20 [8]~E(x81,x82)+E(f14(x83,x81),f14(x83,x82)) % 1.13/1.20 [9]~E(x91,x92)+E(f12(x91,x93,x94),f12(x92,x93,x94)) % 1.13/1.20 [10]~E(x101,x102)+E(f12(x103,x101,x104),f12(x103,x102,x104)) % 1.13/1.20 [11]~E(x111,x112)+E(f12(x113,x114,x111),f12(x113,x114,x112)) % 1.13/1.20 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 1.13/1.20 [13]P12(x132,x133,x134)+~E(x131,x132)+~P12(x131,x133,x134) % 1.13/1.20 [14]P12(x143,x142,x144)+~E(x141,x142)+~P12(x143,x141,x144) % 1.13/1.20 [15]P12(x153,x154,x152)+~E(x151,x152)+~P12(x153,x154,x151) % 1.13/1.20 [16]~P4(x161)+P4(x162)+~E(x161,x162) % 1.13/1.20 [17]~P8(x171)+P8(x172)+~E(x171,x172) % 1.13/1.20 [18]P13(x182,x183,x184)+~E(x181,x182)+~P13(x181,x183,x184) % 1.13/1.20 [19]P13(x193,x192,x194)+~E(x191,x192)+~P13(x193,x191,x194) % 1.13/1.20 [20]P13(x203,x204,x202)+~E(x201,x202)+~P13(x203,x204,x201) % 1.13/1.20 [21]~P9(x211)+P9(x212)+~E(x211,x212) % 1.13/1.20 [22]P6(x222,x223)+~E(x221,x222)+~P6(x221,x223) % 1.13/1.20 [23]P6(x233,x232)+~E(x231,x232)+~P6(x233,x231) % 1.13/1.20 [24]~P2(x241)+P2(x242)+~E(x241,x242) % 1.20/1.20 [25]~P10(x251)+P10(x252)+~E(x251,x252) % 1.20/1.20 [26]P3(x262,x263)+~E(x261,x262)+~P3(x261,x263) % 1.20/1.20 [27]P3(x273,x272)+~E(x271,x272)+~P3(x273,x271) % 1.20/1.20 [28]P11(x282,x283)+~E(x281,x282)+~P11(x281,x283) % 1.20/1.20 [29]P11(x293,x292)+~E(x291,x292)+~P11(x293,x291) % 1.20/1.20 [30]P7(x302,x303)+~E(x301,x302)+~P7(x301,x303) % 1.20/1.20 [31]P7(x313,x312)+~E(x311,x312)+~P7(x313,x311) % 1.20/1.20 [32]P14(x322,x323,x324)+~E(x321,x322)+~P14(x321,x323,x324) % 1.20/1.20 [33]P14(x333,x332,x334)+~E(x331,x332)+~P14(x333,x331,x334) % 1.20/1.20 [34]P14(x343,x344,x342)+~E(x341,x342)+~P14(x343,x344,x341) % 1.20/1.20 [35]~P5(x351)+P5(x352)+~E(x351,x352) % 1.20/1.20 % 1.20/1.20 %------------------------------------------- % 1.20/1.20 cnf(77,plain, % 1.20/1.20 (~P2(x771)+~P8(x771)+~P6(x771,x772)+~P13(x771,x772,x773)+P12(x771,f14(x771,x772),x773)+~P3(f14(x771,x772),f13(x771))+~P3(x773,f13(x771))), % 1.20/1.20 inference(equality_inference,[],[69])). % 1.20/1.20 cnf(83,plain, % 1.20/1.20 (P13(a9,a1,a6)), % 1.20/1.20 inference(scs_inference,[],[40,45,46,36,47,58,62,66])). % 1.20/1.20 cnf(160,plain, % 1.20/1.20 (P12(a9,f14(a9,a1),a6)+~P3(f14(a9,a1),f13(a9))+~P6(a9,a1)), % 1.20/1.20 inference(scs_inference,[],[40,45,43,83,77])). % 1.20/1.20 cnf(350,plain, % 1.20/1.20 (~E(a9,x3501)+P3(f14(x3501,x3502),f13(x3501))), % 1.20/1.20 inference(scs_inference,[],[40,65,17])). % 1.20/1.20 cnf(351,plain, % 1.20/1.20 (P3(f14(a9,x3511),f13(a9))), % 1.20/1.20 inference(equality_inference,[],[350])). % 1.20/1.20 cnf(352,plain, % 1.20/1.20 (~P6(a9,a1)+P12(a9,f14(a9,a1),a6)), % 1.20/1.20 inference(scs_inference,[],[351,160])). % 1.20/1.20 cnf(402,plain, % 1.20/1.20 (P12(a9,f14(a9,a1),a6)), % 1.20/1.20 inference(scs_inference,[],[43,44,50,40,352,61])). % 1.20/1.20 cnf(404,plain, % 1.20/1.20 ($false), % 1.20/1.20 inference(scs_inference,[],[40,51,402,14,56]), % 1.20/1.20 ['proof']). % 1.20/1.20 % SZS output end Proof % 1.20/1.20 % Total time :0.570000s %------------------------------------------------------------------------------