%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU040+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n029.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 15:00:54 EDT 2024 % Result : Theorem 1.43s 1.56s % Output : CNFRefutation 1.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU040+1 : TPTP v8.2.0. Released v3.2.0. % 0.00/0.06 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.05/0.25 % Computer : n029.cluster.edu % 0.05/0.25 % Model : x86_64 x86_64 % 0.05/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.05/0.25 % Memory : 8042.1875MB % 0.05/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.05/0.25 % CPULimit : 300 % 0.05/0.25 % WCLimit : 300 % 0.05/0.25 % DateTime : Fri Jun 21 11:16:38 EDT 2024 % 0.05/0.25 % CPUTime : % 0.10/0.46 start to proof:theBenchmark % 1.43/1.54 %------------------------------------------- % 1.43/1.54 % File :CSE---1.7 % 1.43/1.54 % Problem :theBenchmark % 1.43/1.54 % Transform :cnf % 1.43/1.54 % Format :tptp:raw % 1.43/1.54 % Command :java -jar mcs_scs.jar %d %s % 1.43/1.54 % 1.43/1.54 % Result :Theorem 1.030000s % 1.43/1.54 % Output :CNFRefutation 1.030000s % 1.43/1.54 %------------------------------------------- % 1.43/1.55 %------------------------------------------------------------------------------ % 1.43/1.55 % File : SEU040+1 : TPTP v8.2.0. Released v3.2.0. % 1.43/1.55 % Domain : Set theory % 1.43/1.55 % Problem : Functions and their basic properties, theorem 76 % 1.43/1.55 % Version : [Urb06] axioms : Especial. % 1.43/1.55 % English : % 1.43/1.55 % 1.43/1.55 % Refs : [Byl90] Bylinski (1990), Functions and Their Basic Properties % 1.43/1.55 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 1.43/1.55 % Source : [Urb06] % 1.43/1.55 % Names : funct_1__t76_funct_1 [Urb06] % 1.43/1.55 % 1.43/1.55 % Status : Theorem % 1.43/1.55 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.00 v3.2.0 % 1.43/1.55 % Syntax : Number of formulae : 38 ( 6 unt; 0 def) % 1.43/1.55 % Number of atoms : 92 ( 2 equ) % 1.43/1.55 % Maximal formula atoms : 6 ( 2 avg) % 1.43/1.55 % Number of connectives : 68 ( 14 ~; 1 |; 33 &) % 1.43/1.55 % ( 1 <=>; 19 =>; 0 <=; 0 <~>) % 1.43/1.55 % Maximal formula depth : 7 ( 4 avg) % 1.43/1.55 % Maximal term depth : 3 ( 1 avg) % 1.43/1.55 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty) % 1.43/1.55 % Number of functors : 5 ( 5 usr; 1 con; 0-2 aty) % 1.43/1.55 % Number of variables : 55 ( 44 !; 11 ?) % 1.43/1.55 % SPC : FOF_THM_RFO_SEQ % 1.43/1.55 % 1.43/1.55 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 1.43/1.55 % library, www.mizar.org % 1.43/1.55 %------------------------------------------------------------------------------ % 1.43/1.55 fof(antisymmetry_r2_hidden,axiom, % 1.43/1.55 ! [A,B] : % 1.43/1.55 ( in(A,B) % 1.43/1.55 => ~ in(B,A) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc4_relat_1,axiom, % 1.43/1.55 ( empty(empty_set) % 1.43/1.55 & relation(empty_set) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc12_relat_1,axiom, % 1.43/1.55 ( empty(empty_set) % 1.43/1.55 & relation(empty_set) % 1.43/1.55 & relation_empty_yielding(empty_set) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc1_xboole_0,axiom, % 1.43/1.55 empty(empty_set) ). % 1.43/1.55 % 1.43/1.55 fof(t1_subset,axiom, % 1.43/1.55 ! [A,B] : % 1.43/1.55 ( in(A,B) % 1.43/1.55 => element(A,B) ) ). % 1.43/1.55 % 1.43/1.55 fof(t4_subset,axiom, % 1.43/1.55 ! [A,B,C] : % 1.43/1.55 ( ( in(A,B) % 1.43/1.55 & element(B,powerset(C)) ) % 1.43/1.55 => element(A,C) ) ). % 1.43/1.55 % 1.43/1.55 fof(t5_subset,axiom, % 1.43/1.55 ! [A,B,C] : % 1.43/1.55 ~ ( in(A,B) % 1.43/1.55 & element(B,powerset(C)) % 1.43/1.55 & empty(C) ) ). % 1.43/1.55 % 1.43/1.55 fof(t8_boole,axiom, % 1.43/1.55 ! [A,B] : % 1.43/1.55 ~ ( empty(A) % 1.43/1.55 & A != B % 1.43/1.55 & empty(B) ) ). % 1.43/1.55 % 1.43/1.55 fof(existence_m1_subset_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ? [B] : element(B,A) ). % 1.43/1.55 % 1.43/1.55 fof(cc1_funct_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( empty(A) % 1.43/1.55 => function(A) ) ). % 1.43/1.55 % 1.43/1.55 fof(cc2_funct_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( ( relation(A) % 1.43/1.55 & empty(A) % 1.43/1.55 & function(A) ) % 1.43/1.55 => ( relation(A) % 1.43/1.55 & function(A) % 1.43/1.55 & one_to_one(A) ) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc1_subset_1,axiom, % 1.43/1.55 ! [A] : ~ empty(powerset(A)) ). % 1.43/1.55 % 1.43/1.55 fof(fc5_relat_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( ( ~ empty(A) % 1.43/1.55 & relation(A) ) % 1.43/1.55 => ~ empty(relation_dom(A)) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc6_relat_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( ( ~ empty(A) % 1.43/1.55 & relation(A) ) % 1.43/1.55 => ~ empty(relation_rng(A)) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc7_relat_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( empty(A) % 1.43/1.55 => ( empty(relation_dom(A)) % 1.43/1.55 & relation(relation_dom(A)) ) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc8_relat_1,axiom, % 1.43/1.55 ! [A] : % 1.43/1.55 ( empty(A) % 1.43/1.55 => ( empty(relation_rng(A)) % 1.43/1.55 & relation(relation_rng(A)) ) ) ). % 1.43/1.55 % 1.43/1.55 fof(fc13_relat_1,axiom, % 1.43/1.55 ! [A,B] : % 1.43/1.55 ( ( relation(A) % 1.43/1.55 & relation_empty_yielding(A) ) % 1.43/1.55 => ( relation(relation_dom_restriction(A,B)) % 1.43/1.55 & relation_empty_yielding(relation_dom_restriction(A,B)) ) ) ). % 1.43/1.55 % 1.43/1.55 fof(cc1_relat_1,axiom, % 1.43/1.56 ! [A] : % 1.43/1.56 ( empty(A) % 1.43/1.56 => relation(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(t2_subset,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( element(A,B) % 1.43/1.56 => ( empty(B) % 1.43/1.56 | in(A,B) ) ) ). % 1.43/1.56 % 1.43/1.56 fof(t6_boole,axiom, % 1.43/1.56 ! [A] : % 1.43/1.56 ( empty(A) % 1.43/1.56 => A = empty_set ) ). % 1.43/1.56 % 1.43/1.56 fof(t7_boole,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ~ ( in(A,B) % 1.43/1.56 & empty(B) ) ). % 1.43/1.56 % 1.43/1.56 fof(reflexivity_r1_tarski,axiom, % 1.43/1.56 ! [A,B] : subset(A,A) ). % 1.43/1.56 % 1.43/1.56 fof(dt_k7_relat_1,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( relation(A) % 1.43/1.56 => relation(relation_dom_restriction(A,B)) ) ). % 1.43/1.56 % 1.43/1.56 fof(fc4_funct_1,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( ( relation(A) % 1.43/1.56 & function(A) ) % 1.43/1.56 => ( relation(relation_dom_restriction(A,B)) % 1.43/1.56 & function(relation_dom_restriction(A,B)) ) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc1_funct_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( relation(A) % 1.43/1.56 & function(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc2_funct_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( relation(A) % 1.43/1.56 & empty(A) % 1.43/1.56 & function(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc3_funct_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( relation(A) % 1.43/1.56 & function(A) % 1.43/1.56 & one_to_one(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc1_subset_1,axiom, % 1.43/1.56 ! [A] : % 1.43/1.56 ( ~ empty(A) % 1.43/1.56 => ? [B] : % 1.43/1.56 ( element(B,powerset(A)) % 1.43/1.56 & ~ empty(B) ) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc2_subset_1,axiom, % 1.43/1.56 ! [A] : % 1.43/1.56 ? [B] : % 1.43/1.56 ( element(B,powerset(A)) % 1.43/1.56 & empty(B) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc1_relat_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( empty(A) % 1.43/1.56 & relation(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc2_relat_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( ~ empty(A) % 1.43/1.56 & relation(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc3_relat_1,axiom, % 1.43/1.56 ? [A] : % 1.43/1.56 ( relation(A) % 1.43/1.56 & relation_empty_yielding(A) ) ). % 1.43/1.56 % 1.43/1.56 fof(rc1_xboole_0,axiom, % 1.43/1.56 ? [A] : empty(A) ). % 1.43/1.56 % 1.43/1.56 fof(rc2_xboole_0,axiom, % 1.43/1.56 ? [A] : ~ empty(A) ). % 1.43/1.56 % 1.43/1.56 fof(t3_subset,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( element(A,powerset(B)) % 1.43/1.56 <=> subset(A,B) ) ). % 1.43/1.56 % 1.43/1.56 fof(t76_funct_1,conjecture, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( ( relation(B) % 1.43/1.56 & function(B) ) % 1.43/1.56 => ( subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) % 1.43/1.56 & subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ) ) ). % 1.43/1.56 % 1.43/1.56 fof(t89_relat_1,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( relation(B) % 1.43/1.56 => subset(relation_dom(relation_dom_restriction(B,A)),relation_dom(B)) ) ). % 1.43/1.56 % 1.43/1.56 fof(t99_relat_1,axiom, % 1.43/1.56 ! [A,B] : % 1.43/1.56 ( relation(B) % 1.43/1.56 => subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ) ). % 1.43/1.56 % 1.43/1.56 %------------------------------------------------------------------------------ % 1.43/1.56 %------------------------------------------- % 1.43/1.56 % Proof found % 1.43/1.56 % SZS status Theorem for theBenchmark % 1.43/1.56 % SZS output start Proof % 1.43/1.56 %ClaNum:80(EqnAxiom:22) % 1.43/1.56 %VarNum:95(SingletonVarNum:47) % 1.43/1.56 %MaxLitNum:4 % 1.43/1.56 %MaxfuncDepth:2 % 1.43/1.56 %SharedTerms:39 % 1.43/1.56 %goalClause: 37 43 80 % 1.43/1.56 %singleGoalClaCount:2 % 1.43/1.56 [25]P1(a1) % 1.43/1.56 [26]P1(a2) % 1.43/1.56 [27]P1(a9) % 1.43/1.56 [28]P1(a3) % 1.43/1.56 [30]P3(a1) % 1.43/1.56 [31]P3(a4) % 1.43/1.56 [32]P3(a2) % 1.43/1.56 [33]P3(a10) % 1.43/1.56 [34]P3(a9) % 1.43/1.56 [35]P3(a13) % 1.43/1.56 [36]P3(a14) % 1.43/1.56 [37]P3(a5) % 1.43/1.56 [38]P7(a1) % 1.43/1.56 [39]P7(a14) % 1.43/1.56 [40]P4(a4) % 1.43/1.56 [41]P4(a2) % 1.43/1.56 [42]P4(a10) % 1.43/1.56 [43]P4(a5) % 1.43/1.56 [44]P5(a10) % 1.43/1.56 [49]~P1(a13) % 1.43/1.56 [50]~P1(a6) % 1.43/1.56 [46]P8(x461,x461) % 1.43/1.56 [45]P1(f11(x451)) % 1.43/1.56 [47]P2(f8(x471),x471) % 1.43/1.56 [48]P2(f11(x481),f15(x481)) % 1.43/1.56 [51]~P1(f15(x511)) % 1.43/1.56 [80]~P8(f17(f18(a5,a7)),f17(a5))+~P8(f16(f18(a5,a7)),f16(a5)) % 1.43/1.56 [52]~P1(x521)+E(x521,a1) % 1.43/1.56 [53]~P1(x531)+P3(x531) % 1.43/1.56 [54]~P1(x541)+P4(x541) % 1.43/1.56 [56]~P1(x561)+P1(f16(x561)) % 1.43/1.56 [57]~P1(x571)+P1(f17(x571)) % 1.43/1.56 [58]~P1(x581)+P3(f16(x581)) % 1.43/1.56 [59]~P1(x591)+P3(f17(x591)) % 1.43/1.56 [60]P1(x601)+~P1(f12(x601)) % 1.43/1.56 [65]P1(x651)+P2(f12(x651),f15(x651)) % 1.43/1.56 [64]~P1(x641)+~P6(x642,x641) % 1.43/1.56 [66]~P6(x661,x662)+P2(x661,x662) % 1.43/1.56 [74]~P6(x742,x741)+~P6(x741,x742) % 1.43/1.56 [67]~P3(x671)+P3(f18(x671,x672)) % 1.43/1.56 [69]~P8(x691,x692)+P2(x691,f15(x692)) % 1.43/1.56 [75]P8(x751,x752)+~P2(x751,f15(x752)) % 1.43/1.56 [78]~P3(x781)+P8(f16(f18(x781,x782)),f16(x781)) % 1.43/1.56 [79]~P3(x791)+P8(f17(f18(x791,x792)),f17(x791)) % 1.43/1.56 [62]~P3(x621)+P1(x621)+~P1(f16(x621)) % 1.43/1.56 [63]~P3(x631)+P1(x631)+~P1(f17(x631)) % 1.43/1.56 [55]~P1(x552)+~P1(x551)+E(x551,x552) % 1.43/1.56 [68]~P2(x682,x681)+P1(x681)+P6(x682,x681) % 1.43/1.56 [72]~P3(x721)+~P7(x721)+P7(f18(x721,x722)) % 1.43/1.56 [73]~P3(x731)+~P4(x731)+P4(f18(x731,x732)) % 1.43/1.56 [76]~P1(x761)+~P6(x762,x763)+~P2(x763,f15(x761)) % 1.43/1.56 [77]P2(x771,x772)+~P6(x771,x773)+~P2(x773,f15(x772)) % 1.43/1.56 [61]~P1(x611)+~P3(x611)+~P4(x611)+P5(x611) % 1.43/1.56 %EqnAxiom % 1.43/1.56 [1]E(x11,x11) % 1.43/1.56 [2]E(x22,x21)+~E(x21,x22) % 1.43/1.56 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.43/1.56 [4]~E(x41,x42)+E(f11(x41),f11(x42)) % 1.43/1.56 [5]~E(x51,x52)+E(f8(x51),f8(x52)) % 1.43/1.56 [6]~E(x61,x62)+E(f17(x61),f17(x62)) % 1.43/1.56 [7]~E(x71,x72)+E(f15(x71),f15(x72)) % 1.43/1.56 [8]~E(x81,x82)+E(f18(x81,x83),f18(x82,x83)) % 1.43/1.56 [9]~E(x91,x92)+E(f18(x93,x91),f18(x93,x92)) % 1.43/1.56 [10]~E(x101,x102)+E(f16(x101),f16(x102)) % 1.43/1.56 [11]~E(x111,x112)+E(f12(x111),f12(x112)) % 1.43/1.56 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 1.43/1.56 [13]P8(x132,x133)+~E(x131,x132)+~P8(x131,x133) % 1.43/1.56 [14]P8(x143,x142)+~E(x141,x142)+~P8(x143,x141) % 1.43/1.56 [15]P6(x152,x153)+~E(x151,x152)+~P6(x151,x153) % 1.43/1.56 [16]P6(x163,x162)+~E(x161,x162)+~P6(x163,x161) % 1.43/1.56 [17]~P3(x171)+P3(x172)+~E(x171,x172) % 1.43/1.56 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183) % 1.43/1.56 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191) % 1.43/1.56 [20]~P7(x201)+P7(x202)+~E(x201,x202) % 1.43/1.56 [21]~P4(x211)+P4(x212)+~E(x211,x212) % 1.43/1.56 [22]~P5(x221)+P5(x222)+~E(x221,x222) % 1.43/1.56 % 1.43/1.56 %------------------------------------------- % 1.43/1.56 cnf(591,plain, % 1.43/1.56 (P2(f16(f18(a5,x5911)),f15(f16(a5)))), % 1.43/1.56 inference(scs_inference,[],[37,69,78])). % 1.43/1.56 cnf(592,plain, % 1.43/1.56 (P8(f16(f18(a5,x5921)),f16(a5))), % 1.43/1.56 inference(scs_inference,[],[591,75])). % 1.43/1.56 cnf(610,plain, % 1.43/1.56 (~P8(f17(f18(a5,a7)),f17(a5))), % 1.43/1.56 inference(scs_inference,[],[592,80])). % 1.43/1.56 cnf(624,plain, % 1.43/1.56 ($false), % 1.43/1.56 inference(scs_inference,[],[37,610,79]), % 1.43/1.56 ['proof']). % 1.43/1.56 % SZS output end Proof % 1.43/1.56 % Total time :1.030000s %------------------------------------------------------------------------------