%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU010+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n027.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 15:00:50 EDT 2024 % Result : Theorem 5.85s 5.94s % Output : CNFRefutation 5.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU010+1 : TPTP v8.2.0. Released v3.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n027.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 15:49:38 EDT 2024 % 0.12/0.33 % CPUTime : % 0.50/0.56 start to proof:theBenchmark % 5.85/5.92 %------------------------------------------- % 5.85/5.92 % File :CSE---1.7 % 5.85/5.92 % Problem :theBenchmark % 5.85/5.92 % Transform :cnf % 5.85/5.92 % Format :tptp:raw % 5.85/5.92 % Command :java -jar mcs_scs.jar %d %s % 5.85/5.92 % 5.85/5.92 % Result :Theorem 5.330000s % 5.85/5.92 % Output :CNFRefutation 5.330000s % 5.85/5.92 %------------------------------------------- % 5.85/5.93 %------------------------------------------------------------------------------ % 5.85/5.93 % File : SEU010+1 : TPTP v8.2.0. Released v3.2.0. % 5.85/5.93 % Domain : Set theory % 5.85/5.93 % Problem : Functions and their basic properties, theorem 42 % 5.85/5.93 % Version : [Urb06] axioms : Especial. % 5.85/5.93 % English : % 5.85/5.93 % 5.85/5.93 % Refs : [Byl90] Bylinski (1990), Functions and Their Basic Properties % 5.85/5.93 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 5.85/5.93 % Source : [Urb06] % 5.85/5.93 % Names : funct_1__t42_funct_1 [Urb06] % 5.85/5.93 % 5.85/5.93 % Status : Theorem % 5.85/5.93 % Rating : 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.30 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0 % 5.85/5.93 % Syntax : Number of formulae : 38 ( 7 unt; 0 def) % 5.85/5.93 % Number of atoms : 92 ( 6 equ) % 5.85/5.93 % Maximal formula atoms : 6 ( 2 avg) % 5.85/5.93 % Number of connectives : 68 ( 14 ~; 1 |; 31 &) % 5.85/5.93 % ( 1 <=>; 21 =>; 0 <=; 0 <~>) % 5.85/5.93 % Maximal formula depth : 7 ( 4 avg) % 5.85/5.93 % Maximal term depth : 4 ( 1 avg) % 5.85/5.93 % Number of predicates : 8 ( 7 usr; 0 prp; 1-2 aty) % 5.85/5.93 % Number of functors : 6 ( 6 usr; 1 con; 0-2 aty) % 5.85/5.93 % Number of variables : 55 ( 46 !; 9 ?) % 5.85/5.93 % SPC : FOF_THM_RFO_SEQ % 5.85/5.93 % 5.85/5.93 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 5.85/5.93 % library, www.mizar.org % 5.85/5.93 %------------------------------------------------------------------------------ % 5.85/5.93 fof(antisymmetry_r2_hidden,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ( in(A,B) % 5.85/5.93 => ~ in(B,A) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc4_relat_1,axiom, % 5.85/5.93 ( empty(empty_set) % 5.85/5.93 & relation(empty_set) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc12_relat_1,axiom, % 5.85/5.93 ( empty(empty_set) % 5.85/5.93 & relation(empty_set) % 5.85/5.93 & relation_empty_yielding(empty_set) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc1_xboole_0,axiom, % 5.85/5.93 empty(empty_set) ). % 5.85/5.93 % 5.85/5.93 fof(t1_subset,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ( in(A,B) % 5.85/5.93 => element(A,B) ) ). % 5.85/5.93 % 5.85/5.93 fof(t4_subset,axiom, % 5.85/5.93 ! [A,B,C] : % 5.85/5.93 ( ( in(A,B) % 5.85/5.93 & element(B,powerset(C)) ) % 5.85/5.93 => element(A,C) ) ). % 5.85/5.93 % 5.85/5.93 fof(t5_subset,axiom, % 5.85/5.93 ! [A,B,C] : % 5.85/5.93 ~ ( in(A,B) % 5.85/5.93 & element(B,powerset(C)) % 5.85/5.93 & empty(C) ) ). % 5.85/5.93 % 5.85/5.93 fof(existence_m1_subset_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ? [B] : element(B,A) ). % 5.85/5.93 % 5.85/5.93 fof(cc1_funct_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( empty(A) % 5.85/5.93 => function(A) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc1_subset_1,axiom, % 5.85/5.93 ! [A] : ~ empty(powerset(A)) ). % 5.85/5.93 % 5.85/5.93 fof(fc5_relat_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( ( ~ empty(A) % 5.85/5.93 & relation(A) ) % 5.85/5.93 => ~ empty(relation_dom(A)) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc6_relat_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( ( ~ empty(A) % 5.85/5.93 & relation(A) ) % 5.85/5.93 => ~ empty(relation_rng(A)) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc7_relat_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( empty(A) % 5.85/5.93 => ( empty(relation_dom(A)) % 5.85/5.93 & relation(relation_dom(A)) ) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc8_relat_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( empty(A) % 5.85/5.93 => ( empty(relation_rng(A)) % 5.85/5.93 & relation(relation_rng(A)) ) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc9_relat_1,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ( ( empty(A) % 5.85/5.93 & relation(B) ) % 5.85/5.93 => ( empty(relation_composition(A,B)) % 5.85/5.93 & relation(relation_composition(A,B)) ) ) ). % 5.85/5.93 % 5.85/5.93 fof(fc10_relat_1,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ( ( empty(A) % 5.85/5.93 & relation(B) ) % 5.85/5.93 => ( empty(relation_composition(B,A)) % 5.85/5.93 & relation(relation_composition(B,A)) ) ) ). % 5.85/5.93 % 5.85/5.93 fof(cc1_relat_1,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( empty(A) % 5.85/5.93 => relation(A) ) ). % 5.85/5.93 % 5.85/5.93 fof(t2_subset,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ( element(A,B) % 5.85/5.93 => ( empty(B) % 5.85/5.93 | in(A,B) ) ) ). % 5.85/5.93 % 5.85/5.93 fof(t6_boole,axiom, % 5.85/5.93 ! [A] : % 5.85/5.93 ( empty(A) % 5.85/5.93 => A = empty_set ) ). % 5.85/5.93 % 5.85/5.93 fof(t7_boole,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ~ ( in(A,B) % 5.85/5.93 & empty(B) ) ). % 5.85/5.93 % 5.85/5.93 fof(t8_boole,axiom, % 5.85/5.93 ! [A,B] : % 5.85/5.93 ~ ( empty(A) % 5.85/5.93 & A != B % 5.85/5.93 & empty(B) ) ). % 5.85/5.93 % 5.85/5.93 fof(reflexivity_r1_tarski,axiom, % 5.85/5.94 ! [A,B] : subset(A,A) ). % 5.85/5.94 % 5.85/5.94 fof(dt_k5_relat_1,axiom, % 5.85/5.94 ! [A,B] : % 5.85/5.94 ( ( relation(A) % 5.85/5.94 & relation(B) ) % 5.85/5.94 => relation(relation_composition(A,B)) ) ). % 5.85/5.94 % 5.85/5.94 fof(dt_k6_relat_1,axiom, % 5.85/5.94 ! [A] : relation(identity_relation(A)) ). % 5.85/5.94 % 5.85/5.94 fof(fc1_funct_1,axiom, % 5.85/5.94 ! [A,B] : % 5.85/5.94 ( ( relation(A) % 5.85/5.94 & function(A) % 5.85/5.94 & relation(B) % 5.85/5.94 & function(B) ) % 5.85/5.94 => ( relation(relation_composition(A,B)) % 5.85/5.94 & function(relation_composition(A,B)) ) ) ). % 5.85/5.94 % 5.85/5.94 fof(fc2_funct_1,axiom, % 5.85/5.94 ! [A] : % 5.85/5.94 ( relation(identity_relation(A)) % 5.85/5.94 & function(identity_relation(A)) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc1_funct_1,axiom, % 5.85/5.94 ? [A] : % 5.85/5.94 ( relation(A) % 5.85/5.94 & function(A) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc1_subset_1,axiom, % 5.85/5.94 ! [A] : % 5.85/5.94 ( ~ empty(A) % 5.85/5.94 => ? [B] : % 5.85/5.94 ( element(B,powerset(A)) % 5.85/5.94 & ~ empty(B) ) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc2_subset_1,axiom, % 5.85/5.94 ! [A] : % 5.85/5.94 ? [B] : % 5.85/5.94 ( element(B,powerset(A)) % 5.85/5.94 & empty(B) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc1_relat_1,axiom, % 5.85/5.94 ? [A] : % 5.85/5.94 ( empty(A) % 5.85/5.94 & relation(A) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc2_relat_1,axiom, % 5.85/5.94 ? [A] : % 5.85/5.94 ( ~ empty(A) % 5.85/5.94 & relation(A) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc3_relat_1,axiom, % 5.85/5.94 ? [A] : % 5.85/5.94 ( relation(A) % 5.85/5.94 & relation_empty_yielding(A) ) ). % 5.85/5.94 % 5.85/5.94 fof(rc1_xboole_0,axiom, % 5.85/5.94 ? [A] : empty(A) ). % 5.85/5.94 % 5.85/5.94 fof(rc2_xboole_0,axiom, % 5.85/5.94 ? [A] : ~ empty(A) ). % 5.85/5.94 % 5.85/5.94 fof(t3_subset,axiom, % 5.85/5.94 ! [A,B] : % 5.85/5.94 ( element(A,powerset(B)) % 5.85/5.94 <=> subset(A,B) ) ). % 5.85/5.94 % 5.85/5.94 fof(t42_funct_1,conjecture, % 5.85/5.94 ! [A] : % 5.85/5.94 ( ( relation(A) % 5.85/5.94 & function(A) ) % 5.85/5.94 => ( relation_composition(identity_relation(relation_dom(A)),A) = A % 5.85/5.94 & relation_composition(A,identity_relation(relation_rng(A))) = A ) ) ). % 5.85/5.94 % 5.85/5.94 fof(t77_relat_1,axiom, % 5.85/5.94 ! [A,B] : % 5.85/5.94 ( relation(B) % 5.85/5.94 => ( subset(relation_dom(B),A) % 5.85/5.94 => relation_composition(identity_relation(A),B) = B ) ) ). % 5.85/5.94 % 5.85/5.94 fof(t79_relat_1,axiom, % 5.85/5.94 ! [A,B] : % 5.85/5.94 ( relation(B) % 5.85/5.94 => ( subset(relation_rng(B),A) % 5.85/5.94 => relation_composition(B,identity_relation(A)) = B ) ) ). % 5.85/5.94 % 5.85/5.94 %------------------------------------------------------------------------------ % 5.85/5.94 %------------------------------------------- % 5.85/5.94 % Proof found % 5.85/5.94 % SZS status Theorem for theBenchmark % 5.85/5.94 % SZS output start Proof % 5.85/5.94 %ClaNum:78(EqnAxiom:22) % 5.85/5.94 %VarNum:112(SingletonVarNum:54) % 5.85/5.94 %MaxLitNum:5 % 5.85/5.94 %MaxfuncDepth:3 % 5.85/5.94 %SharedTerms:31 % 5.85/5.94 %goalClause: 34 38 78 % 5.85/5.94 %singleGoalClaCount:2 % 5.85/5.94 [25]P1(a1) % 5.85/5.94 [26]P1(a2) % 5.85/5.94 [27]P1(a8) % 5.85/5.94 [29]P3(a1) % 5.85/5.94 [30]P3(a3) % 5.85/5.94 [31]P3(a2) % 5.85/5.94 [32]P3(a9) % 5.85/5.94 [33]P3(a10) % 5.85/5.94 [34]P3(a4) % 5.85/5.94 [35]P6(a1) % 5.85/5.94 [36]P6(a10) % 5.85/5.94 [37]P4(a3) % 5.85/5.94 [38]P4(a4) % 5.85/5.94 [46]~P1(a9) % 5.85/5.94 [47]~P1(a12) % 5.85/5.94 [43]P7(x431,x431) % 5.85/5.94 [39]P1(f6(x391)) % 5.85/5.94 [41]P3(f11(x411)) % 5.85/5.94 [42]P4(f11(x421)) % 5.85/5.94 [44]P2(f5(x441),x441) % 5.85/5.94 [45]P2(f6(x451),f13(x451)) % 5.85/5.94 [48]~P1(f13(x481)) % 5.85/5.94 [78]~E(f15(a4,f11(f16(a4))),a4)+~E(f15(f11(f14(a4)),a4),a4) % 5.85/5.94 [49]~P1(x491)+E(x491,a1) % 5.85/5.94 [50]~P1(x501)+P3(x501) % 5.85/5.94 [51]~P1(x511)+P4(x511) % 5.85/5.94 [53]~P1(x531)+P1(f14(x531)) % 5.85/5.94 [54]~P1(x541)+P1(f16(x541)) % 5.85/5.94 [55]~P1(x551)+P3(f14(x551)) % 5.85/5.94 [56]~P1(x561)+P3(f16(x561)) % 5.85/5.94 [57]P1(x571)+~P1(f7(x571)) % 5.85/5.94 [61]P1(x611)+P2(f7(x611),f13(x611)) % 5.85/5.94 [60]~P1(x601)+~P5(x602,x601) % 5.85/5.94 [62]~P5(x621,x622)+P2(x621,x622) % 5.85/5.94 [70]~P5(x702,x701)+~P5(x701,x702) % 5.85/5.94 [64]~P7(x641,x642)+P2(x641,f13(x642)) % 5.85/5.94 [71]P7(x711,x712)+~P2(x711,f13(x712)) % 5.85/5.94 [58]~P3(x581)+P1(x581)+~P1(f14(x581)) % 5.85/5.94 [59]~P3(x591)+P1(x591)+~P1(f16(x591)) % 5.85/5.94 [52]~P1(x522)+~P1(x521)+E(x521,x522) % 5.85/5.94 [63]~P2(x632,x631)+P1(x631)+P5(x632,x631) % 5.85/5.94 [65]~P1(x652)+~P3(x651)+P1(f15(x651,x652)) % 5.85/5.94 [66]~P1(x661)+~P3(x662)+P1(f15(x661,x662)) % 5.85/5.94 [67]~P1(x672)+~P3(x671)+P3(f15(x671,x672)) % 5.85/5.94 [68]~P1(x681)+~P3(x682)+P3(f15(x681,x682)) % 5.85/5.94 [69]~P3(x692)+~P3(x691)+P3(f15(x691,x692)) % 5.85/5.94 [74]~P3(x741)+~P7(f16(x741),x742)+E(f15(x741,f11(x742)),x741) % 5.85/5.94 [75]~P3(x752)+~P7(f14(x752),x751)+E(f15(f11(x751),x752),x752) % 5.85/5.94 [76]~P1(x761)+~P5(x762,x763)+~P2(x763,f13(x761)) % 5.85/5.94 [77]P2(x771,x772)+~P5(x771,x773)+~P2(x773,f13(x772)) % 5.85/5.94 [73]~P3(x732)+~P3(x731)+~P4(x732)+~P4(x731)+P4(f15(x731,x732)) % 5.85/5.94 %EqnAxiom % 5.85/5.94 [1]E(x11,x11) % 5.85/5.94 [2]E(x22,x21)+~E(x21,x22) % 5.85/5.94 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 5.85/5.94 [4]~E(x41,x42)+E(f6(x41),f6(x42)) % 5.85/5.94 [5]~E(x51,x52)+E(f11(x51),f11(x52)) % 5.85/5.94 [6]~E(x61,x62)+E(f14(x61),f14(x62)) % 5.85/5.94 [7]~E(x71,x72)+E(f15(x71,x73),f15(x72,x73)) % 5.85/5.94 [8]~E(x81,x82)+E(f15(x83,x81),f15(x83,x82)) % 5.85/5.94 [9]~E(x91,x92)+E(f5(x91),f5(x92)) % 5.85/5.94 [10]~E(x101,x102)+E(f16(x101),f16(x102)) % 5.85/5.94 [11]~E(x111,x112)+E(f13(x111),f13(x112)) % 5.85/5.94 [12]~E(x121,x122)+E(f7(x121),f7(x122)) % 5.85/5.94 [13]~P1(x131)+P1(x132)+~E(x131,x132) % 5.85/5.94 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 5.85/5.94 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 5.85/5.94 [16]P5(x162,x163)+~E(x161,x162)+~P5(x161,x163) % 5.85/5.94 [17]P5(x173,x172)+~E(x171,x172)+~P5(x173,x171) % 5.85/5.94 [18]~P3(x181)+P3(x182)+~E(x181,x182) % 5.85/5.94 [19]P7(x192,x193)+~E(x191,x192)+~P7(x191,x193) % 5.85/5.94 [20]P7(x203,x202)+~E(x201,x202)+~P7(x203,x201) % 5.85/5.94 [21]~P4(x211)+P4(x212)+~E(x211,x212) % 5.85/5.94 [22]~P6(x221)+P6(x222)+~E(x221,x222) % 5.85/5.94 % 5.85/5.94 %------------------------------------------- % 5.85/5.94 cnf(927,plain, % 5.85/5.94 (~E(f15(f11(f14(a4)),a4),a4)), % 5.85/5.94 inference(scs_inference,[],[43,34,78,74])). % 5.85/5.94 cnf(928,plain, % 5.85/5.94 ($false), % 5.85/5.94 inference(scs_inference,[],[927,34,43,75]), % 5.85/5.94 ['proof']). % 5.85/5.94 % SZS output end Proof % 5.85/5.94 % Total time :5.330000s %------------------------------------------------------------------------------