%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU123+2 : 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 : n018.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 15:01:09 EDT 2024 % Result : Theorem 0.46s 0.62s % Output : CNFRefutation 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU123+2 : TPTP v8.2.0. Released v3.3.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n018.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 : Fri Jun 21 14:32:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.46/0.56 start to proof:theBenchmark % 0.46/0.61 %------------------------------------------- % 0.46/0.61 % File :CSE---1.7 % 0.46/0.61 % Problem :theBenchmark % 0.46/0.61 % Transform :cnf % 0.46/0.61 % Format :tptp:raw % 0.46/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.46/0.61 % 0.46/0.61 % Result :Theorem 0.010000s % 0.46/0.61 % Output :CNFRefutation 0.010000s % 0.46/0.61 %------------------------------------------- % 0.46/0.61 %------------------------------------------------------------------------------ % 0.46/0.61 % File : SEU123+2 : TPTP v8.2.0. Released v3.3.0. % 0.46/0.61 % Domain : Set theory % 0.46/0.62 % Problem : MPTP chainy problem t3_xboole_1 % 0.46/0.62 % Version : [Urb07] axioms : Especial. % 0.46/0.62 % English : % 0.46/0.62 % 0.46/0.62 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.46/0.62 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.46/0.62 % Source : [Urb07] % 0.46/0.62 % Names : chainy-t3_xboole_1 [Urb07] % 0.46/0.62 % 0.46/0.62 % Status : Theorem % 0.46/0.62 % Rating : 0.03 v8.1.0, 0.00 v6.3.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0 % 0.46/0.62 % Syntax : Number of formulae : 23 ( 9 unt; 0 def) % 0.46/0.62 % Number of atoms : 49 ( 9 equ) % 0.46/0.62 % Maximal formula atoms : 6 ( 2 avg) % 0.46/0.62 % Number of connectives : 40 ( 14 ~; 0 |; 14 &) % 0.46/0.62 % ( 6 <=>; 6 =>; 0 <=; 0 <~>) % 0.46/0.62 % Maximal formula depth : 9 ( 4 avg) % 0.46/0.62 % Maximal term depth : 2 ( 1 avg) % 0.46/0.62 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty) % 0.46/0.62 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty) % 0.46/0.62 % Number of variables : 43 ( 39 !; 4 ?) % 0.46/0.62 % SPC : FOF_THM_RFO_SEQ % 0.46/0.62 % 0.46/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.46/0.62 % library, www.mizar.org % 0.46/0.62 %------------------------------------------------------------------------------ % 0.46/0.62 fof(antisymmetry_r2_hidden,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( in(A,B) % 0.46/0.62 => ~ in(B,A) ) ). % 0.46/0.62 % 0.46/0.62 fof(commutativity_k3_xboole_0,axiom, % 0.46/0.62 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.46/0.62 % 0.46/0.62 fof(d10_xboole_0,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( A = B % 0.46/0.62 <=> ( subset(A,B) % 0.46/0.62 & subset(B,A) ) ) ). % 0.46/0.62 % 0.46/0.62 fof(d1_xboole_0,axiom, % 0.46/0.62 ! [A] : % 0.46/0.62 ( A = empty_set % 0.46/0.62 <=> ! [B] : ~ in(B,A) ) ). % 0.46/0.62 % 0.46/0.62 fof(d3_tarski,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( subset(A,B) % 0.46/0.62 <=> ! [C] : % 0.46/0.62 ( in(C,A) % 0.46/0.62 => in(C,B) ) ) ). % 0.46/0.62 % 0.46/0.62 fof(d3_xboole_0,axiom, % 0.46/0.62 ! [A,B,C] : % 0.46/0.62 ( C = set_intersection2(A,B) % 0.46/0.62 <=> ! [D] : % 0.46/0.62 ( in(D,C) % 0.46/0.62 <=> ( in(D,A) % 0.46/0.62 & in(D,B) ) ) ) ). % 0.46/0.62 % 0.46/0.62 fof(d7_xboole_0,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( disjoint(A,B) % 0.46/0.62 <=> set_intersection2(A,B) = empty_set ) ). % 0.46/0.62 % 0.46/0.62 fof(dt_k1_xboole_0,axiom, % 0.46/0.62 $true ). % 0.46/0.62 % 0.46/0.62 fof(dt_k3_xboole_0,axiom, % 0.46/0.62 $true ). % 0.46/0.62 % 0.46/0.62 fof(fc1_xboole_0,axiom, % 0.46/0.62 empty(empty_set) ). % 0.46/0.62 % 0.46/0.62 fof(idempotence_k3_xboole_0,axiom, % 0.46/0.62 ! [A,B] : set_intersection2(A,A) = A ). % 0.46/0.62 % 0.46/0.62 fof(rc1_xboole_0,axiom, % 0.46/0.62 ? [A] : empty(A) ). % 0.46/0.62 % 0.46/0.62 fof(rc2_xboole_0,axiom, % 0.46/0.62 ? [A] : ~ empty(A) ). % 0.46/0.62 % 0.46/0.62 fof(reflexivity_r1_tarski,axiom, % 0.46/0.62 ! [A,B] : subset(A,A) ). % 0.46/0.62 % 0.46/0.62 fof(symmetry_r1_xboole_0,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( disjoint(A,B) % 0.46/0.62 => disjoint(B,A) ) ). % 0.46/0.62 % 0.46/0.62 fof(t1_xboole_1,lemma, % 0.46/0.62 ! [A,B,C] : % 0.46/0.62 ( ( subset(A,B) % 0.46/0.62 & subset(B,C) ) % 0.46/0.62 => subset(A,C) ) ). % 0.46/0.62 % 0.46/0.62 fof(t2_xboole_1,lemma, % 0.46/0.62 ! [A] : subset(empty_set,A) ). % 0.46/0.62 % 0.46/0.62 fof(t3_xboole_0,lemma, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( ~ ( ~ disjoint(A,B) % 0.46/0.62 & ! [C] : % 0.46/0.62 ~ ( in(C,A) % 0.46/0.62 & in(C,B) ) ) % 0.46/0.62 & ~ ( ? [C] : % 0.46/0.62 ( in(C,A) % 0.46/0.62 & in(C,B) ) % 0.46/0.62 & disjoint(A,B) ) ) ). % 0.46/0.62 % 0.46/0.62 fof(t3_xboole_1,conjecture, % 0.46/0.62 ! [A] : % 0.46/0.62 ( subset(A,empty_set) % 0.46/0.62 => A = empty_set ) ). % 0.46/0.62 % 0.46/0.62 fof(t4_xboole_0,lemma, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ( ~ ( ~ disjoint(A,B) % 0.46/0.62 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.46/0.62 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.46/0.62 & disjoint(A,B) ) ) ). % 0.46/0.62 % 0.46/0.62 fof(t6_boole,axiom, % 0.46/0.62 ! [A] : % 0.46/0.62 ( empty(A) % 0.46/0.62 => A = empty_set ) ). % 0.46/0.62 % 0.46/0.62 fof(t7_boole,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ~ ( in(A,B) % 0.46/0.62 & empty(B) ) ). % 0.46/0.62 % 0.46/0.62 fof(t8_boole,axiom, % 0.46/0.62 ! [A,B] : % 0.46/0.62 ~ ( empty(A) % 0.46/0.62 & A != B % 0.46/0.62 & empty(B) ) ). % 0.46/0.62 % 0.46/0.62 %------------------------------------------------------------------------------ % 0.46/0.62 %------------------------------------------- % 0.46/0.62 % Proof found % 0.46/0.62 % SZS status Theorem for theBenchmark % 0.46/0.62 % SZS output start Proof % 0.46/0.62 %ClaNum:58(EqnAxiom:22) % 0.46/0.62 %VarNum:160(SingletonVarNum:68) % 0.46/0.62 %MaxLitNum:4 % 0.46/0.62 %MaxfuncDepth:1 % 0.46/0.62 %SharedTerms:9 % 0.46/0.62 %goalClause: 25 30 % 0.46/0.62 %singleGoalClaCount:2 % 0.46/0.62 [23]P1(a1) % 0.46/0.62 [24]P1(a2) % 0.46/0.62 [25]P3(a6,a1) % 0.46/0.62 [30]~E(a6,a1) % 0.46/0.62 [31]~P1(a7) % 0.46/0.62 [26]P3(a1,x261) % 0.46/0.62 [27]P3(x271,x271) % 0.46/0.62 [28]E(f9(x281,x281),x281) % 0.46/0.62 [29]E(f9(x291,x292),f9(x292,x291)) % 0.46/0.62 [32]~P1(x321)+E(x321,a1) % 0.46/0.62 [36]P4(f3(x361),x361)+E(x361,a1) % 0.46/0.62 [35]~E(x351,x352)+P3(x351,x352) % 0.46/0.62 [37]~P4(x372,x371)+~E(x371,a1) % 0.46/0.62 [38]~P1(x381)+~P4(x382,x381) % 0.46/0.62 [41]~P2(x412,x411)+P2(x411,x412) % 0.46/0.62 [42]~P4(x422,x421)+~P4(x421,x422) % 0.46/0.62 [39]~P2(x391,x392)+E(f9(x391,x392),a1) % 0.46/0.62 [40]P2(x401,x402)+~E(f9(x401,x402),a1) % 0.46/0.62 [44]P3(x441,x442)+P4(f4(x441,x442),x441) % 0.46/0.62 [45]P2(x451,x452)+P4(f8(x451,x452),x452) % 0.46/0.62 [46]P2(x461,x462)+P4(f8(x461,x462),x461) % 0.46/0.62 [52]P3(x521,x522)+~P4(f4(x521,x522),x522) % 0.46/0.62 [53]P2(x531,x532)+P4(f10(x531,x532),f9(x531,x532)) % 0.46/0.62 [55]~P2(x551,x552)+~P4(x553,f9(x551,x552)) % 0.46/0.62 [33]~P1(x332)+~P1(x331)+E(x331,x332) % 0.46/0.62 [43]~P3(x432,x431)+~P3(x431,x432)+E(x431,x432) % 0.46/0.62 [47]~P3(x473,x472)+P4(x471,x472)+~P4(x471,x473) % 0.46/0.62 [48]~P3(x481,x483)+P3(x481,x482)+~P3(x483,x482) % 0.46/0.62 [51]~P2(x513,x512)+~P4(x511,x512)+~P4(x511,x513) % 0.46/0.62 [56]P4(f5(x562,x563,x561),x561)+P4(f5(x562,x563,x561),x563)+E(x561,f9(x562,x563)) % 0.46/0.62 [57]P4(f5(x572,x573,x571),x571)+P4(f5(x572,x573,x571),x572)+E(x571,f9(x572,x573)) % 0.46/0.62 [49]~P4(x491,x493)+P4(x491,x492)+~E(x493,f9(x494,x492)) % 0.46/0.62 [50]~P4(x501,x503)+P4(x501,x502)+~E(x503,f9(x502,x504)) % 0.46/0.62 [58]~P4(f5(x582,x583,x581),x581)+~P4(f5(x582,x583,x581),x583)+~P4(f5(x582,x583,x581),x582)+E(x581,f9(x582,x583)) % 0.46/0.62 [54]~P4(x541,x544)+~P4(x541,x543)+P4(x541,x542)+~E(x542,f9(x543,x544)) % 0.46/0.62 %EqnAxiom % 0.46/0.62 [1]E(x11,x11) % 0.46/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.46/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.46/0.62 [4]~E(x41,x42)+E(f9(x41,x43),f9(x42,x43)) % 0.46/0.62 [5]~E(x51,x52)+E(f9(x53,x51),f9(x53,x52)) % 0.46/0.62 [6]~E(x61,x62)+E(f5(x61,x63,x64),f5(x62,x63,x64)) % 0.46/0.62 [7]~E(x71,x72)+E(f5(x73,x71,x74),f5(x73,x72,x74)) % 0.46/0.62 [8]~E(x81,x82)+E(f5(x83,x84,x81),f5(x83,x84,x82)) % 0.46/0.62 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93)) % 0.46/0.62 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102)) % 0.46/0.62 [11]~E(x111,x112)+E(f3(x111),f3(x112)) % 0.46/0.62 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123)) % 0.46/0.62 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132)) % 0.46/0.62 [14]~E(x141,x142)+E(f8(x141,x143),f8(x142,x143)) % 0.46/0.62 [15]~E(x151,x152)+E(f8(x153,x151),f8(x153,x152)) % 0.46/0.62 [16]~P1(x161)+P1(x162)+~E(x161,x162) % 0.46/0.62 [17]P4(x172,x173)+~E(x171,x172)+~P4(x171,x173) % 0.46/0.62 [18]P4(x183,x182)+~E(x181,x182)+~P4(x183,x181) % 0.46/0.62 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193) % 0.46/0.62 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201) % 0.46/0.62 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213) % 0.46/0.62 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221) % 0.46/0.62 % 0.46/0.62 %------------------------------------------- % 0.46/0.62 cnf(60,plain, % 0.46/0.62 (~P4(x601,a1)), % 0.46/0.62 inference(equality_inference,[],[37])). % 0.46/0.62 cnf(61,plain, % 0.46/0.62 (~P4(x611,f9(x612,x613))+P4(x611,x613)), % 0.46/0.62 inference(equality_inference,[],[49])). % 0.46/0.62 cnf(62,plain, % 0.46/0.62 (~P4(x621,f9(x622,x623))+P4(x621,x622)), % 0.46/0.62 inference(equality_inference,[],[50])). % 0.46/0.62 cnf(70,plain, % 0.46/0.62 (E(f9(x701,x701),x701)), % 0.46/0.62 inference(rename_variables,[],[28])). % 0.46/0.62 cnf(86,plain, % 0.46/0.62 (~P4(x861,a1)), % 0.46/0.62 inference(rename_variables,[],[60])). % 0.46/0.62 cnf(91,plain, % 0.46/0.62 ($false), % 0.46/0.62 inference(scs_inference,[],[25,30,26,60,86,28,70,24,32,36,2,37,40,44,61,62,38,42,45,46,43]), % 0.46/0.62 ['proof']). % 0.46/0.62 % SZS output end Proof % 0.46/0.62 % Total time :0.010000s %------------------------------------------------------------------------------