%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU130+2 : 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 : 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 15:01:12 EDT 2024 % Result : Theorem 0.48s 0.62s % Output : CNFRefutation 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU130+2 : TPTP v8.2.0. Released v3.3.0. % 0.08/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.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 12:11:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.48/0.56 start to proof:theBenchmark % 0.48/0.61 %------------------------------------------- % 0.48/0.61 % File :CSE---1.7 % 0.48/0.61 % Problem :theBenchmark % 0.48/0.61 % Transform :cnf % 0.48/0.61 % Format :tptp:raw % 0.48/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.48/0.61 % 0.48/0.61 % Result :Theorem 0.000000s % 0.48/0.61 % Output :CNFRefutation 0.000000s % 0.48/0.61 %------------------------------------------- % 0.48/0.62 %------------------------------------------------------------------------------ % 0.48/0.62 % File : SEU130+2 : TPTP v8.2.0. Released v3.3.0. % 0.48/0.62 % Domain : Set theory % 0.48/0.62 % Problem : MPTP chainy problem t28_xboole_1 % 0.48/0.62 % Version : [Urb07] axioms : Especial. % 0.48/0.62 % English : % 0.48/0.62 % 0.48/0.62 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.48/0.62 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.48/0.62 % Source : [Urb07] % 0.48/0.62 % Names : chainy-t28_xboole_1 [Urb07] % 0.48/0.62 % 0.48/0.62 % Status : Theorem % 0.48/0.62 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.20 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.16 v3.3.0 % 0.48/0.62 % Syntax : Number of formulae : 38 ( 16 unt; 0 def) % 0.48/0.62 % Number of atoms : 76 ( 16 equ) % 0.48/0.62 % Maximal formula atoms : 6 ( 2 avg) % 0.48/0.62 % Number of connectives : 56 ( 18 ~; 1 |; 16 &) % 0.48/0.62 % ( 8 <=>; 13 =>; 0 <=; 0 <~>) % 0.48/0.62 % Maximal formula depth : 9 ( 4 avg) % 0.48/0.62 % Maximal term depth : 2 ( 1 avg) % 0.48/0.62 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty) % 0.48/0.62 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.48/0.62 % Number of variables : 74 ( 70 !; 4 ?) % 0.48/0.62 % SPC : FOF_THM_RFO_SEQ % 0.48/0.62 % 0.48/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.48/0.62 % library, www.mizar.org % 0.48/0.62 %------------------------------------------------------------------------------ % 0.48/0.62 fof(antisymmetry_r2_hidden,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( in(A,B) % 0.48/0.62 => ~ in(B,A) ) ). % 0.48/0.62 % 0.48/0.62 fof(commutativity_k2_xboole_0,axiom, % 0.48/0.62 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.48/0.62 % 0.48/0.62 fof(commutativity_k3_xboole_0,axiom, % 0.48/0.62 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.48/0.62 % 0.48/0.62 fof(d10_xboole_0,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( A = B % 0.48/0.62 <=> ( subset(A,B) % 0.48/0.62 & subset(B,A) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(d1_xboole_0,axiom, % 0.48/0.62 ! [A] : % 0.48/0.62 ( A = empty_set % 0.48/0.62 <=> ! [B] : ~ in(B,A) ) ). % 0.48/0.62 % 0.48/0.62 fof(d2_xboole_0,axiom, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( C = set_union2(A,B) % 0.48/0.62 <=> ! [D] : % 0.48/0.62 ( in(D,C) % 0.48/0.62 <=> ( in(D,A) % 0.48/0.62 | in(D,B) ) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(d3_tarski,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( subset(A,B) % 0.48/0.62 <=> ! [C] : % 0.48/0.62 ( in(C,A) % 0.48/0.62 => in(C,B) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(d3_xboole_0,axiom, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( C = set_intersection2(A,B) % 0.48/0.62 <=> ! [D] : % 0.48/0.62 ( in(D,C) % 0.48/0.62 <=> ( in(D,A) % 0.48/0.62 & in(D,B) ) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(d7_xboole_0,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( disjoint(A,B) % 0.48/0.62 <=> set_intersection2(A,B) = empty_set ) ). % 0.48/0.62 % 0.48/0.62 fof(dt_k1_xboole_0,axiom, % 0.48/0.62 $true ). % 0.48/0.62 % 0.48/0.62 fof(dt_k2_xboole_0,axiom, % 0.48/0.62 $true ). % 0.48/0.62 % 0.48/0.62 fof(dt_k3_xboole_0,axiom, % 0.48/0.62 $true ). % 0.48/0.62 % 0.48/0.62 fof(fc1_xboole_0,axiom, % 0.48/0.62 empty(empty_set) ). % 0.48/0.62 % 0.48/0.62 fof(fc2_xboole_0,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( ~ empty(A) % 0.48/0.62 => ~ empty(set_union2(A,B)) ) ). % 0.48/0.62 % 0.48/0.62 fof(fc3_xboole_0,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( ~ empty(A) % 0.48/0.62 => ~ empty(set_union2(B,A)) ) ). % 0.48/0.62 % 0.48/0.62 fof(idempotence_k2_xboole_0,axiom, % 0.48/0.62 ! [A,B] : set_union2(A,A) = A ). % 0.48/0.62 % 0.48/0.62 fof(idempotence_k3_xboole_0,axiom, % 0.48/0.62 ! [A,B] : set_intersection2(A,A) = A ). % 0.48/0.62 % 0.48/0.62 fof(rc1_xboole_0,axiom, % 0.48/0.62 ? [A] : empty(A) ). % 0.48/0.62 % 0.48/0.62 fof(rc2_xboole_0,axiom, % 0.48/0.62 ? [A] : ~ empty(A) ). % 0.48/0.62 % 0.48/0.62 fof(reflexivity_r1_tarski,axiom, % 0.48/0.62 ! [A,B] : subset(A,A) ). % 0.48/0.62 % 0.48/0.62 fof(symmetry_r1_xboole_0,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( disjoint(A,B) % 0.48/0.62 => disjoint(B,A) ) ). % 0.48/0.62 % 0.48/0.62 fof(t12_xboole_1,lemma, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( subset(A,B) % 0.48/0.62 => set_union2(A,B) = B ) ). % 0.48/0.62 % 0.48/0.62 fof(t17_xboole_1,lemma, % 0.48/0.62 ! [A,B] : subset(set_intersection2(A,B),A) ). % 0.48/0.62 % 0.48/0.62 fof(t19_xboole_1,lemma, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( ( subset(A,B) % 0.48/0.62 & subset(A,C) ) % 0.48/0.62 => subset(A,set_intersection2(B,C)) ) ). % 0.48/0.62 % 0.48/0.62 fof(t1_boole,axiom, % 0.48/0.62 ! [A] : set_union2(A,empty_set) = A ). % 0.48/0.62 % 0.48/0.62 fof(t1_xboole_1,lemma, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( ( subset(A,B) % 0.48/0.62 & subset(B,C) ) % 0.48/0.62 => subset(A,C) ) ). % 0.48/0.62 % 0.48/0.62 fof(t26_xboole_1,lemma, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( subset(A,B) % 0.48/0.62 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ). % 0.48/0.62 % 0.48/0.62 fof(t28_xboole_1,conjecture, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( subset(A,B) % 0.48/0.62 => set_intersection2(A,B) = A ) ). % 0.48/0.62 % 0.48/0.62 fof(t2_boole,axiom, % 0.48/0.62 ! [A] : set_intersection2(A,empty_set) = empty_set ). % 0.48/0.62 % 0.48/0.62 fof(t2_xboole_1,lemma, % 0.48/0.62 ! [A] : subset(empty_set,A) ). % 0.48/0.62 % 0.48/0.62 fof(t3_xboole_0,lemma, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( ~ ( ~ disjoint(A,B) % 0.48/0.62 & ! [C] : % 0.48/0.62 ~ ( in(C,A) % 0.48/0.62 & in(C,B) ) ) % 0.48/0.62 & ~ ( ? [C] : % 0.48/0.62 ( in(C,A) % 0.48/0.62 & in(C,B) ) % 0.48/0.62 & disjoint(A,B) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(t3_xboole_1,lemma, % 0.48/0.62 ! [A] : % 0.48/0.62 ( subset(A,empty_set) % 0.48/0.62 => A = empty_set ) ). % 0.48/0.62 % 0.48/0.62 fof(t4_xboole_0,lemma, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ( ~ ( ~ disjoint(A,B) % 0.48/0.62 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.48/0.62 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.48/0.62 & disjoint(A,B) ) ) ). % 0.48/0.62 % 0.48/0.62 fof(t6_boole,axiom, % 0.48/0.62 ! [A] : % 0.48/0.62 ( empty(A) % 0.48/0.62 => A = empty_set ) ). % 0.48/0.62 % 0.48/0.62 fof(t7_boole,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ~ ( in(A,B) % 0.48/0.62 & empty(B) ) ). % 0.48/0.62 % 0.48/0.62 fof(t7_xboole_1,lemma, % 0.48/0.62 ! [A,B] : subset(A,set_union2(A,B)) ). % 0.48/0.62 % 0.48/0.62 fof(t8_boole,axiom, % 0.48/0.62 ! [A,B] : % 0.48/0.62 ~ ( empty(A) % 0.48/0.62 & A != B % 0.48/0.62 & empty(B) ) ). % 0.48/0.62 % 0.48/0.62 fof(t8_xboole_1,lemma, % 0.48/0.62 ! [A,B,C] : % 0.48/0.62 ( ( subset(A,B) % 0.48/0.62 & subset(C,B) ) % 0.48/0.62 => subset(set_union2(A,C),B) ) ). % 0.48/0.62 % 0.48/0.62 %------------------------------------------------------------------------------ % 0.48/0.62 %------------------------------------------- % 0.48/0.62 % Proof found % 0.48/0.62 % SZS status Theorem for theBenchmark % 0.48/0.62 % SZS output start Proof % 0.48/0.62 %ClaNum:82(EqnAxiom:27) % 0.48/0.62 %VarNum:269(SingletonVarNum:114) % 0.48/0.62 %MaxLitNum:4 % 0.48/0.62 %MaxfuncDepth:1 % 0.48/0.62 %SharedTerms:11 % 0.48/0.62 %goalClause: 30 42 % 0.48/0.62 %singleGoalClaCount:2 % 0.48/0.62 [28]P1(a1) % 0.48/0.62 [29]P1(a2) % 0.48/0.62 [30]P3(a8,a10) % 0.48/0.62 [41]~P1(a9) % 0.48/0.62 [42]~E(f11(a8,a10),a8) % 0.48/0.62 [32]P3(a1,x321) % 0.48/0.62 [34]P3(x341,x341) % 0.48/0.62 [31]E(f11(x311,a1),a1) % 0.48/0.62 [33]E(f13(x331,a1),x331) % 0.48/0.62 [35]E(f13(x351,x351),x351) % 0.48/0.62 [36]E(f11(x361,x361),x361) % 0.48/0.62 [37]E(f13(x371,x372),f13(x372,x371)) % 0.48/0.62 [38]E(f11(x381,x382),f11(x382,x381)) % 0.48/0.62 [39]P3(x391,f13(x391,x392)) % 0.48/0.62 [40]P3(f11(x401,x402),x401) % 0.48/0.62 [43]~P1(x431)+E(x431,a1) % 0.48/0.62 [47]~P3(x471,a1)+E(x471,a1) % 0.48/0.62 [48]P4(f3(x481),x481)+E(x481,a1) % 0.48/0.62 [46]~E(x461,x462)+P3(x461,x462) % 0.48/0.62 [49]~P4(x492,x491)+~E(x491,a1) % 0.48/0.62 [50]~P1(x501)+~P4(x502,x501) % 0.48/0.62 [53]~P2(x532,x531)+P2(x531,x532) % 0.48/0.62 [55]~P4(x552,x551)+~P4(x551,x552) % 0.48/0.62 [51]~P2(x511,x512)+E(f11(x511,x512),a1) % 0.48/0.62 [52]P2(x521,x522)+~E(f11(x521,x522),a1) % 0.48/0.62 [54]~P3(x541,x542)+E(f13(x541,x542),x542) % 0.48/0.62 [57]P1(x571)+~P1(f13(x572,x571)) % 0.48/0.62 [58]P1(x581)+~P1(f13(x581,x582)) % 0.48/0.62 [59]P3(x591,x592)+P4(f5(x591,x592),x591) % 0.48/0.62 [60]P2(x601,x602)+P4(f12(x601,x602),x602) % 0.48/0.62 [61]P2(x611,x612)+P4(f12(x611,x612),x611) % 0.48/0.62 [70]P3(x701,x702)+~P4(f5(x701,x702),x702) % 0.48/0.62 [71]P2(x711,x712)+P4(f4(x711,x712),f11(x711,x712)) % 0.48/0.62 [75]~P2(x751,x752)+~P4(x753,f11(x751,x752)) % 0.48/0.62 [76]~P3(x761,x763)+P3(f11(x761,x762),f11(x763,x762)) % 0.48/0.62 [44]~P1(x442)+~P1(x441)+E(x441,x442) % 0.48/0.62 [56]~P3(x562,x561)+~P3(x561,x562)+E(x561,x562) % 0.48/0.62 [62]~P3(x623,x622)+P4(x621,x622)+~P4(x621,x623) % 0.48/0.62 [63]~P3(x631,x633)+P3(x631,x632)+~P3(x633,x632) % 0.48/0.62 [68]~P2(x683,x682)+~P4(x681,x682)+~P4(x681,x683) % 0.48/0.62 [73]~P3(x731,x733)+~P3(x731,x732)+P3(x731,f11(x732,x733)) % 0.48/0.62 [74]~P3(x742,x743)+~P3(x741,x743)+P3(f13(x741,x742),x743) % 0.48/0.62 [77]P4(f7(x772,x773,x771),x771)+P4(f7(x772,x773,x771),x773)+E(x771,f11(x772,x773)) % 0.48/0.62 [78]P4(f7(x782,x783,x781),x781)+P4(f7(x782,x783,x781),x782)+E(x781,f11(x782,x783)) % 0.48/0.62 [80]~P4(f6(x802,x803,x801),x801)+~P4(f6(x802,x803,x801),x803)+E(x801,f13(x802,x803)) % 0.48/0.62 [81]~P4(f6(x812,x813,x811),x811)+~P4(f6(x812,x813,x811),x812)+E(x811,f13(x812,x813)) % 0.48/0.62 [64]~P4(x641,x644)+P4(x641,x642)+~E(x642,f13(x643,x644)) % 0.48/0.62 [65]~P4(x651,x653)+P4(x651,x652)+~E(x652,f13(x653,x654)) % 0.48/0.62 [66]~P4(x661,x663)+P4(x661,x662)+~E(x663,f11(x664,x662)) % 0.48/0.62 [67]~P4(x671,x673)+P4(x671,x672)+~E(x673,f11(x672,x674)) % 0.48/0.62 [79]P4(f6(x792,x793,x791),x791)+P4(f6(x792,x793,x791),x793)+P4(f6(x792,x793,x791),x792)+E(x791,f13(x792,x793)) % 0.48/0.62 [82]~P4(f7(x822,x823,x821),x821)+~P4(f7(x822,x823,x821),x823)+~P4(f7(x822,x823,x821),x822)+E(x821,f11(x822,x823)) % 0.48/0.62 [69]~P4(x691,x694)+P4(x691,x692)+P4(x691,x693)+~E(x694,f13(x693,x692)) % 0.48/0.62 [72]~P4(x721,x724)+~P4(x721,x723)+P4(x721,x722)+~E(x722,f11(x723,x724)) % 0.48/0.62 %EqnAxiom % 0.48/0.62 [1]E(x11,x11) % 0.48/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.48/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.48/0.62 [4]~E(x41,x42)+E(f11(x41,x43),f11(x42,x43)) % 0.48/0.62 [5]~E(x51,x52)+E(f11(x53,x51),f11(x53,x52)) % 0.48/0.62 [6]~E(x61,x62)+E(f13(x61,x63),f13(x62,x63)) % 0.48/0.62 [7]~E(x71,x72)+E(f13(x73,x71),f13(x73,x72)) % 0.48/0.62 [8]~E(x81,x82)+E(f7(x81,x83,x84),f7(x82,x83,x84)) % 0.48/0.62 [9]~E(x91,x92)+E(f7(x93,x91,x94),f7(x93,x92,x94)) % 0.48/0.62 [10]~E(x101,x102)+E(f7(x103,x104,x101),f7(x103,x104,x102)) % 0.48/0.62 [11]~E(x111,x112)+E(f6(x111,x113,x114),f6(x112,x113,x114)) % 0.48/0.62 [12]~E(x121,x122)+E(f6(x123,x121,x124),f6(x123,x122,x124)) % 0.48/0.62 [13]~E(x131,x132)+E(f6(x133,x134,x131),f6(x133,x134,x132)) % 0.48/0.62 [14]~E(x141,x142)+E(f5(x141,x143),f5(x142,x143)) % 0.48/0.62 [15]~E(x151,x152)+E(f5(x153,x151),f5(x153,x152)) % 0.48/0.62 [16]~E(x161,x162)+E(f12(x161,x163),f12(x162,x163)) % 0.48/0.62 [17]~E(x171,x172)+E(f12(x173,x171),f12(x173,x172)) % 0.48/0.62 [18]~E(x181,x182)+E(f4(x181,x183),f4(x182,x183)) % 0.48/0.62 [19]~E(x191,x192)+E(f4(x193,x191),f4(x193,x192)) % 0.48/0.62 [20]~E(x201,x202)+E(f3(x201),f3(x202)) % 0.48/0.62 [21]~P1(x211)+P1(x212)+~E(x211,x212) % 0.48/0.62 [22]P4(x222,x223)+~E(x221,x222)+~P4(x221,x223) % 0.48/0.62 [23]P4(x233,x232)+~E(x231,x232)+~P4(x233,x231) % 0.48/0.62 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243) % 0.48/0.62 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251) % 0.48/0.62 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263) % 0.48/0.62 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271) % 0.48/0.62 % 0.48/0.62 %------------------------------------------- % 0.48/0.62 cnf(84,plain, % 0.48/0.62 (~P4(x841,a1)), % 0.48/0.62 inference(equality_inference,[],[49])). % 0.48/0.62 cnf(87,plain, % 0.48/0.62 (~P4(x871,f11(x872,x873))+P4(x871,x873)), % 0.48/0.62 inference(equality_inference,[],[66])). % 0.48/0.62 cnf(88,plain, % 0.48/0.62 (~P4(x881,f11(x882,x883))+P4(x881,x882)), % 0.48/0.62 inference(equality_inference,[],[67])). % 0.48/0.62 cnf(107,plain, % 0.48/0.62 (~P4(x1071,a1)), % 0.48/0.62 inference(rename_variables,[],[84])). % 0.48/0.62 cnf(118,plain, % 0.48/0.62 ($false), % 0.48/0.62 inference(scs_inference,[],[30,42,34,84,107,39,40,35,36,29,2,49,59,87,88,50,52,60,61,56,63,73]), % 0.48/0.62 ['proof']). % 0.48/0.62 % SZS output end Proof % 0.48/0.62 % Total time :0.000000s %------------------------------------------------------------------------------