%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU187+1 : TPTP v8.2.0. Released v3.3.0. % 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 15:01:38 EDT 2024 % Result : Theorem 0.54s 0.64s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU187+1 : TPTP v8.2.0. Released v3.3.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n022.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 15:22:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.53/0.57 start to proof:theBenchmark % 0.54/0.63 %------------------------------------------- % 0.54/0.63 % File :CSE---1.7 % 0.54/0.63 % Problem :theBenchmark % 0.54/0.63 % Transform :cnf % 0.54/0.63 % Format :tptp:raw % 0.54/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.63 % 0.54/0.63 % Result :Theorem 0.020000s % 0.54/0.63 % Output :CNFRefutation 0.020000s % 0.54/0.63 %------------------------------------------- % 0.54/0.63 %------------------------------------------------------------------------------ % 0.54/0.63 % File : SEU187+1 : TPTP v8.2.0. Released v3.3.0. % 0.54/0.63 % Domain : Set theory % 0.54/0.63 % Problem : MPTP bushy problem t60_relat_1 % 0.54/0.63 % Version : [Urb07] axioms : Especial. % 0.54/0.63 % English : % 0.54/0.63 % 0.54/0.63 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.54/0.63 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.54/0.63 % Source : [Urb07] % 0.54/0.63 % Names : bushy-t60_relat_1 [Urb07] % 0.54/0.63 % 0.54/0.63 % Status : Theorem % 0.54/0.63 % Rating : 0.25 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.19 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 v4.1.0, 0.22 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.21 v3.3.0 % 0.54/0.63 % Syntax : Number of formulae : 32 ( 16 unt; 0 def) % 0.54/0.63 % Number of atoms : 57 ( 9 equ) % 0.54/0.63 % Maximal formula atoms : 4 ( 1 avg) % 0.54/0.63 % Number of connectives : 38 ( 13 ~; 1 |; 9 &) % 0.54/0.63 % ( 5 <=>; 10 =>; 0 <=; 0 <~>) % 0.54/0.63 % Maximal formula depth : 8 ( 3 avg) % 0.54/0.63 % Maximal term depth : 3 ( 1 avg) % 0.54/0.63 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty) % 0.54/0.63 % Number of functors : 6 ( 6 usr; 1 con; 0-2 aty) % 0.54/0.63 % Number of variables : 40 ( 33 !; 7 ?) % 0.54/0.63 % SPC : FOF_THM_RFO_SEQ % 0.54/0.63 % 0.54/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.54/0.63 % library, www.mizar.org % 0.54/0.63 %------------------------------------------------------------------------------ % 0.54/0.63 fof(antisymmetry_r2_hidden,axiom, % 0.54/0.63 ! [A,B] : % 0.54/0.63 ( in(A,B) % 0.54/0.63 => ~ in(B,A) ) ). % 0.54/0.63 % 0.54/0.63 fof(cc1_relat_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ( empty(A) % 0.54/0.63 => relation(A) ) ). % 0.54/0.63 % 0.54/0.63 fof(commutativity_k2_tarski,axiom, % 0.54/0.63 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.54/0.63 % 0.54/0.63 fof(d4_relat_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ( relation(A) % 0.54/0.63 => ! [B] : % 0.54/0.63 ( B = relation_dom(A) % 0.54/0.63 <=> ! [C] : % 0.54/0.63 ( in(C,B) % 0.54/0.63 <=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(d5_relat_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ( relation(A) % 0.54/0.63 => ! [B] : % 0.54/0.63 ( B = relation_rng(A) % 0.54/0.63 <=> ! [C] : % 0.54/0.63 ( in(C,B) % 0.54/0.63 <=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(d5_tarski,axiom, % 0.54/0.63 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ). % 0.54/0.63 % 0.54/0.63 fof(dt_k1_relat_1,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_k1_tarski,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_k1_xboole_0,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_k2_relat_1,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_k2_tarski,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_k4_tarski,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(dt_m1_subset_1,axiom, % 0.54/0.63 $true ). % 0.54/0.63 % 0.54/0.63 fof(existence_m1_subset_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ? [B] : element(B,A) ). % 0.54/0.63 % 0.54/0.63 fof(fc1_xboole_0,axiom, % 0.54/0.63 empty(empty_set) ). % 0.54/0.63 % 0.54/0.63 fof(fc1_zfmisc_1,axiom, % 0.54/0.63 ! [A,B] : ~ empty(ordered_pair(A,B)) ). % 0.54/0.63 % 0.54/0.63 fof(fc2_subset_1,axiom, % 0.54/0.63 ! [A] : ~ empty(singleton(A)) ). % 0.54/0.63 % 0.54/0.63 fof(fc3_subset_1,axiom, % 0.54/0.63 ! [A,B] : ~ empty(unordered_pair(A,B)) ). % 0.54/0.63 % 0.54/0.63 fof(fc4_relat_1,axiom, % 0.54/0.63 ( empty(empty_set) % 0.54/0.63 & relation(empty_set) ) ). % 0.54/0.63 % 0.54/0.63 fof(fc5_relat_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ( ( ~ empty(A) % 0.54/0.63 & relation(A) ) % 0.54/0.63 => ~ empty(relation_dom(A)) ) ). % 0.54/0.63 % 0.54/0.63 fof(fc6_relat_1,axiom, % 0.54/0.63 ! [A] : % 0.54/0.63 ( ( ~ empty(A) % 0.54/0.63 & relation(A) ) % 0.54/0.63 => ~ empty(relation_rng(A)) ) ). % 0.54/0.63 % 0.54/0.63 fof(rc1_relat_1,axiom, % 0.54/0.63 ? [A] : % 0.54/0.63 ( empty(A) % 0.54/0.63 & relation(A) ) ). % 0.54/0.63 % 0.54/0.63 fof(rc1_xboole_0,axiom, % 0.54/0.63 ? [A] : empty(A) ). % 0.54/0.63 % 0.54/0.63 fof(rc2_relat_1,axiom, % 0.54/0.63 ? [A] : % 0.54/0.63 ( ~ empty(A) % 0.54/0.63 & relation(A) ) ). % 0.54/0.63 % 0.54/0.63 fof(rc2_xboole_0,axiom, % 0.54/0.63 ? [A] : ~ empty(A) ). % 0.54/0.63 % 0.54/0.63 fof(t1_subset,axiom, % 0.54/0.63 ! [A,B] : % 0.54/0.63 ( in(A,B) % 0.54/0.63 => element(A,B) ) ). % 0.54/0.63 % 0.54/0.63 fof(t2_subset,axiom, % 0.54/0.63 ! [A,B] : % 0.54/0.63 ( element(A,B) % 0.54/0.63 => ( empty(B) % 0.54/0.63 | in(A,B) ) ) ). % 0.54/0.63 % 0.54/0.63 fof(t2_tarski,axiom, % 0.54/0.63 ! [A,B] : % 0.54/0.63 ( ! [C] : % 0.54/0.63 ( in(C,A) % 0.54/0.63 <=> in(C,B) ) % 0.54/0.63 => A = B ) ). % 0.54/0.63 % 0.54/0.63 fof(t60_relat_1,conjecture, % 0.54/0.63 ( relation_dom(empty_set) = empty_set % 0.54/0.64 & relation_rng(empty_set) = empty_set ) ). % 0.54/0.64 % 0.54/0.64 fof(t6_boole,axiom, % 0.54/0.64 ! [A] : % 0.54/0.64 ( empty(A) % 0.54/0.64 => A = empty_set ) ). % 0.54/0.64 % 0.54/0.64 fof(t7_boole,axiom, % 0.54/0.64 ! [A,B] : % 0.54/0.64 ~ ( in(A,B) % 0.54/0.64 & empty(B) ) ). % 0.54/0.64 % 0.54/0.64 fof(t8_boole,axiom, % 0.54/0.64 ! [A,B] : % 0.54/0.64 ~ ( empty(A) % 0.54/0.64 & A != B % 0.54/0.64 & empty(B) ) ). % 0.54/0.64 % 0.54/0.64 %------------------------------------------------------------------------------ % 0.54/0.64 %------------------------------------------- % 0.54/0.64 % Proof found % 0.54/0.64 % SZS status Theorem for theBenchmark % 0.54/0.64 % SZS output start Proof % 0.54/0.64 %ClaNum:65(EqnAxiom:31) % 0.54/0.64 %VarNum:146(SingletonVarNum:48) % 0.54/0.64 %MaxLitNum:4 % 0.54/0.64 %MaxfuncDepth:3 % 0.54/0.64 %SharedTerms:17 % 0.54/0.64 %goalClause: 47 % 0.54/0.64 [33]P1(a1) % 0.54/0.64 [34]P1(a2) % 0.54/0.64 [35]P1(a13) % 0.54/0.64 [36]P3(a1) % 0.54/0.64 [37]P3(a2) % 0.54/0.64 [38]P3(a3) % 0.54/0.64 [41]~P1(a3) % 0.54/0.64 [42]~P1(a5) % 0.54/0.64 [39]P2(f4(x391),x391) % 0.54/0.64 [43]~P1(f15(x431)) % 0.54/0.64 [40]E(f14(x401,x402),f14(x402,x401)) % 0.54/0.64 [44]~P1(f14(x441,x442)) % 0.54/0.64 [47]~E(f16(a1),a1)+~E(f17(a1),a1) % 0.54/0.64 [46]~P1(x461)+E(x461,a1) % 0.54/0.64 [48]~P1(x481)+P3(x481) % 0.54/0.64 [52]~P1(x521)+~P4(x522,x521) % 0.54/0.64 [53]~P4(x531,x532)+P2(x531,x532) % 0.54/0.64 [55]~P4(x552,x551)+~P4(x551,x552) % 0.54/0.64 [50]~P3(x501)+P1(x501)+~P1(f16(x501)) % 0.54/0.64 [51]~P3(x511)+P1(x511)+~P1(f17(x511)) % 0.54/0.64 [49]~P1(x492)+~P1(x491)+E(x491,x492) % 0.54/0.64 [54]~P2(x542,x541)+P1(x541)+P4(x542,x541) % 0.54/0.64 [56]E(x561,x562)+P4(f6(x561,x562),x562)+P4(f6(x561,x562),x561) % 0.54/0.64 [57]E(x571,x572)+~P4(f6(x571,x572),x572)+~P4(f6(x571,x572),x571) % 0.54/0.64 [61]~P3(x612)+P4(f8(x612,x611),x611)+E(x611,f16(x612))+P4(f14(f14(f8(x612,x611),f10(x612,x611)),f15(f8(x612,x611))),x612) % 0.54/0.64 [62]~P3(x622)+P4(f7(x622,x621),x621)+E(x621,f17(x622))+P4(f14(f14(f12(x622,x621),f7(x622,x621)),f15(f12(x622,x621))),x622) % 0.54/0.64 [60]~P3(x602)+~P4(f7(x602,x601),x601)+E(x601,f17(x602))+~P4(f14(f14(x603,f7(x602,x601)),f15(x603)),x602) % 0.54/0.64 [64]~P3(x642)+~P4(x641,x643)+~E(x643,f16(x642))+P4(f14(f14(x641,f9(x642,x643,x641)),f15(x641)),x642) % 0.54/0.64 [63]~P3(x632)+~P4(f8(x632,x631),x631)+E(x631,f16(x632))+~P4(f14(f14(f8(x632,x631),x633),f15(f8(x632,x631))),x632) % 0.54/0.64 [65]~P3(x651)+~P4(x653,x652)+~E(x652,f17(x651))+P4(f14(f14(f11(x651,x652,x653),x653),f15(f11(x651,x652,x653))),x651) % 0.54/0.64 [58]~P3(x583)+P4(x581,x582)+~E(x582,f17(x583))+~P4(f14(f14(x584,x581),f15(x584)),x583) % 0.54/0.64 [59]~P3(x593)+P4(x591,x592)+~E(x592,f16(x593))+~P4(f14(f14(x591,x594),f15(x591)),x593) % 0.54/0.64 %EqnAxiom % 0.54/0.64 [1]E(x11,x11) % 0.54/0.64 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.64 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 0.54/0.64 [5]~E(x51,x52)+E(f14(x51,x53),f14(x52,x53)) % 0.54/0.64 [6]~E(x61,x62)+E(f14(x63,x61),f14(x63,x62)) % 0.54/0.64 [7]~E(x71,x72)+E(f17(x71),f17(x72)) % 0.54/0.64 [8]~E(x81,x82)+E(f15(x81),f15(x82)) % 0.54/0.64 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93)) % 0.54/0.64 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102)) % 0.54/0.64 [11]~E(x111,x112)+E(f11(x111,x113,x114),f11(x112,x113,x114)) % 0.54/0.64 [12]~E(x121,x122)+E(f11(x123,x121,x124),f11(x123,x122,x124)) % 0.54/0.64 [13]~E(x131,x132)+E(f11(x133,x134,x131),f11(x133,x134,x132)) % 0.54/0.64 [14]~E(x141,x142)+E(f16(x141),f16(x142)) % 0.54/0.64 [15]~E(x151,x152)+E(f8(x151,x153),f8(x152,x153)) % 0.54/0.64 [16]~E(x161,x162)+E(f8(x163,x161),f8(x163,x162)) % 0.54/0.64 [17]~E(x171,x172)+E(f12(x171,x173),f12(x172,x173)) % 0.54/0.64 [18]~E(x181,x182)+E(f12(x183,x181),f12(x183,x182)) % 0.54/0.64 [19]~E(x191,x192)+E(f6(x191,x193),f6(x192,x193)) % 0.54/0.64 [20]~E(x201,x202)+E(f6(x203,x201),f6(x203,x202)) % 0.54/0.64 [21]~E(x211,x212)+E(f9(x211,x213,x214),f9(x212,x213,x214)) % 0.54/0.64 [22]~E(x221,x222)+E(f9(x223,x221,x224),f9(x223,x222,x224)) % 0.54/0.64 [23]~E(x231,x232)+E(f9(x233,x234,x231),f9(x233,x234,x232)) % 0.54/0.64 [24]~E(x241,x242)+E(f10(x241,x243),f10(x242,x243)) % 0.54/0.64 [25]~E(x251,x252)+E(f10(x253,x251),f10(x253,x252)) % 0.54/0.64 [26]~P1(x261)+P1(x262)+~E(x261,x262) % 0.54/0.64 [27]P4(x272,x273)+~E(x271,x272)+~P4(x271,x273) % 0.54/0.64 [28]P4(x283,x282)+~E(x281,x282)+~P4(x283,x281) % 0.54/0.64 [29]~P3(x291)+P3(x292)+~E(x291,x292) % 0.54/0.64 [30]P2(x302,x303)+~E(x301,x302)+~P2(x301,x303) % 0.54/0.64 [31]P2(x313,x312)+~E(x311,x312)+~P2(x313,x311) % 0.54/0.64 % 0.54/0.64 %------------------------------------------- % 0.54/0.64 cnf(68,plain, % 0.54/0.64 (~P3(x681)+~P4(x682,f16(x681))+P4(f14(f14(x682,f9(x681,f16(x681),x682)),f15(x682)),x681)), % 0.54/0.64 inference(equality_inference,[],[64])). % 0.54/0.64 cnf(70,plain, % 0.54/0.64 (~P4(x701,a1)), % 0.54/0.64 inference(scs_inference,[],[33,52])). % 0.54/0.64 cnf(75,plain, % 0.54/0.64 (~P4(x751,f16(a1))), % 0.54/0.64 inference(scs_inference,[],[33,39,36,41,52,54,68])). % 0.54/0.64 cnf(77,plain, % 0.54/0.64 (~E(a3,f16(a1))), % 0.54/0.64 inference(scs_inference,[],[33,39,36,41,52,54,68,28])). % 0.54/0.64 cnf(92,plain, % 0.54/0.64 (~P4(x921,a1)), % 0.54/0.64 inference(rename_variables,[],[70])). % 0.54/0.64 cnf(93,plain, % 0.54/0.64 (~P4(x931,f16(a1))), % 0.54/0.64 inference(rename_variables,[],[75])). % 0.54/0.64 cnf(101,plain, % 0.54/0.64 (~P4(x1011,f16(a1))), % 0.54/0.64 inference(rename_variables,[],[75])). % 0.54/0.64 cnf(103,plain, % 0.54/0.64 (~P4(x1031,a1)), % 0.54/0.64 inference(rename_variables,[],[70])). % 0.54/0.64 cnf(105,plain, % 0.54/0.64 (E(f16(a1),f17(a1))), % 0.54/0.64 inference(scs_inference,[],[34,75,93,101,70,92,103,77,37,42,39,36,52,56,54,68,28,61,62])). % 0.54/0.64 cnf(115,plain, % 0.54/0.64 (~E(f17(a1),f16(a1))), % 0.54/0.64 inference(scs_inference,[],[33,34,75,93,101,70,92,103,77,37,42,39,36,52,56,54,68,28,61,62,47,2,55,49,3])). % 0.54/0.64 cnf(126,plain, % 0.54/0.64 ($false), % 0.54/0.64 inference(scs_inference,[],[115,105,2]), % 0.54/0.64 ['proof']). % 0.54/0.64 % SZS output end Proof % 0.54/0.64 % Total time :0.020000s %------------------------------------------------------------------------------