%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU080+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 : n025.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 15:01:00 EDT 2024 % Result : Theorem 0.61s 0.71s % Output : CNFRefutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU080+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n025.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Jun 21 16:06:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.42/0.62 start to proof:theBenchmark % 0.61/0.69 %------------------------------------------- % 0.61/0.69 % File :CSE---1.7 % 0.61/0.69 % Problem :theBenchmark % 0.61/0.69 % Transform :cnf % 0.61/0.69 % Format :tptp:raw % 0.61/0.69 % Command :java -jar mcs_scs.jar %d %s % 0.61/0.69 % 0.61/0.69 % Result :Theorem 0.020000s % 0.61/0.69 % Output :CNFRefutation 0.020000s % 0.61/0.69 %------------------------------------------- % 0.61/0.70 %------------------------------------------------------------------------------ % 0.61/0.70 % File : SEU080+1 : TPTP v8.2.0. Released v3.2.0. % 0.61/0.70 % Domain : Set theory % 0.61/0.70 % Problem : Functions and their basic properties, theorem 161 % 0.61/0.70 % Version : [Urb06] axioms : Especial. % 0.61/0.70 % English : % 0.61/0.70 % 0.61/0.70 % Refs : [Byl90] Bylinski (1990), Functions and Their Basic Properties % 0.61/0.70 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.61/0.70 % Source : [Urb06] % 0.61/0.70 % Names : funct_1__t161_funct_1 [Urb06] % 0.61/0.70 % 0.61/0.70 % Status : Theorem % 0.61/0.70 % Rating : 0.14 v8.2.0, 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.23 v6.0.0, 0.30 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.05 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0 % 0.61/0.70 % Syntax : Number of formulae : 33 ( 6 unt; 0 def) % 0.61/0.70 % Number of atoms : 82 ( 5 equ) % 0.61/0.70 % Maximal formula atoms : 6 ( 2 avg) % 0.61/0.70 % Number of connectives : 61 ( 12 ~; 1 |; 31 &) % 0.61/0.70 % ( 2 <=>; 15 =>; 0 <=; 0 <~>) % 0.61/0.70 % Maximal formula depth : 8 ( 4 avg) % 0.61/0.70 % Maximal term depth : 2 ( 1 avg) % 0.61/0.70 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty) % 0.61/0.70 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty) % 0.61/0.70 % Number of variables : 49 ( 38 !; 11 ?) % 0.61/0.70 % SPC : FOF_THM_RFO_SEQ % 0.61/0.70 % 0.61/0.70 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.61/0.70 % library, www.mizar.org % 0.61/0.70 %------------------------------------------------------------------------------ % 0.61/0.70 fof(antisymmetry_r2_hidden,axiom, % 0.61/0.70 ! [A,B] : % 0.61/0.70 ( in(A,B) % 0.61/0.70 => ~ in(B,A) ) ). % 0.61/0.70 % 0.61/0.70 fof(cc1_funct_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( empty(A) % 0.61/0.70 => function(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(cc1_relat_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( empty(A) % 0.61/0.70 => relation(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(cc2_funct_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( ( relation(A) % 0.61/0.70 & empty(A) % 0.61/0.70 & function(A) ) % 0.61/0.70 => ( relation(A) % 0.61/0.70 & function(A) % 0.61/0.70 & one_to_one(A) ) ) ). % 0.61/0.70 % 0.61/0.70 fof(d10_xboole_0,axiom, % 0.61/0.70 ! [A,B] : % 0.61/0.70 ( A = B % 0.61/0.70 <=> ( subset(A,B) % 0.61/0.70 & subset(B,A) ) ) ). % 0.61/0.70 % 0.61/0.70 fof(existence_m1_subset_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ? [B] : element(B,A) ). % 0.61/0.70 % 0.61/0.70 fof(fc12_relat_1,axiom, % 0.61/0.70 ( empty(empty_set) % 0.61/0.70 & relation(empty_set) % 0.61/0.70 & relation_empty_yielding(empty_set) ) ). % 0.61/0.70 % 0.61/0.70 fof(fc1_subset_1,axiom, % 0.61/0.70 ! [A] : ~ empty(powerset(A)) ). % 0.61/0.70 % 0.61/0.70 fof(fc1_xboole_0,axiom, % 0.61/0.70 empty(empty_set) ). % 0.61/0.70 % 0.61/0.70 fof(fc4_relat_1,axiom, % 0.61/0.70 ( empty(empty_set) % 0.61/0.70 & relation(empty_set) ) ). % 0.61/0.70 % 0.61/0.70 fof(fc6_relat_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( ( ~ empty(A) % 0.61/0.70 & relation(A) ) % 0.61/0.70 => ~ empty(relation_rng(A)) ) ). % 0.61/0.70 % 0.61/0.70 fof(fc8_relat_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( empty(A) % 0.61/0.70 => ( empty(relation_rng(A)) % 0.61/0.70 & relation(relation_rng(A)) ) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc1_funct_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( relation(A) % 0.61/0.70 & function(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc1_relat_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( empty(A) % 0.61/0.70 & relation(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc1_subset_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ( ~ empty(A) % 0.61/0.70 => ? [B] : % 0.61/0.70 ( element(B,powerset(A)) % 0.61/0.70 & ~ empty(B) ) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc1_xboole_0,axiom, % 0.61/0.70 ? [A] : empty(A) ). % 0.61/0.70 % 0.61/0.70 fof(rc2_funct_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( relation(A) % 0.61/0.70 & empty(A) % 0.61/0.70 & function(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc2_relat_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( ~ empty(A) % 0.61/0.70 & relation(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc2_subset_1,axiom, % 0.61/0.70 ! [A] : % 0.61/0.70 ? [B] : % 0.61/0.70 ( element(B,powerset(A)) % 0.61/0.70 & empty(B) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc2_xboole_0,axiom, % 0.61/0.70 ? [A] : ~ empty(A) ). % 0.61/0.70 % 0.61/0.70 fof(rc3_funct_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( relation(A) % 0.61/0.70 & function(A) % 0.61/0.70 & one_to_one(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(rc3_relat_1,axiom, % 0.61/0.70 ? [A] : % 0.61/0.70 ( relation(A) % 0.61/0.70 & relation_empty_yielding(A) ) ). % 0.61/0.70 % 0.61/0.70 fof(reflexivity_r1_tarski,axiom, % 0.61/0.70 ! [A,B] : subset(A,A) ). % 0.61/0.70 % 0.61/0.70 fof(t158_funct_1,axiom, % 0.61/0.70 ! [A,B,C] : % 0.61/0.70 ( ( relation(C) % 0.61/0.70 & function(C) ) % 0.61/0.70 => ( ( subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) % 0.61/0.70 & subset(A,relation_rng(C)) ) % 0.61/0.70 => subset(A,B) ) ) ). % 0.61/0.70 % 0.61/0.70 fof(t161_funct_1,conjecture, % 0.61/0.70 ! [A,B,C] : % 0.61/0.70 ( ( relation(C) % 0.61/0.70 & function(C) ) % 0.61/0.70 => ( ( relation_inverse_image(C,A) = relation_inverse_image(C,B) % 0.61/0.70 & subset(A,relation_rng(C)) % 0.61/0.70 & subset(B,relation_rng(C)) ) % 0.61/0.70 => A = B ) ) ). % 0.61/0.70 % 0.61/0.70 fof(t1_subset,axiom, % 0.61/0.70 ! [A,B] : % 0.61/0.70 ( in(A,B) % 0.61/0.70 => element(A,B) ) ). % 0.61/0.70 % 0.61/0.70 fof(t2_subset,axiom, % 0.61/0.71 ! [A,B] : % 0.61/0.71 ( element(A,B) % 0.61/0.71 => ( empty(B) % 0.61/0.71 | in(A,B) ) ) ). % 0.61/0.71 % 0.61/0.71 fof(t3_subset,axiom, % 0.61/0.71 ! [A,B] : % 0.61/0.71 ( element(A,powerset(B)) % 0.61/0.71 <=> subset(A,B) ) ). % 0.61/0.71 % 0.61/0.71 fof(t4_subset,axiom, % 0.61/0.71 ! [A,B,C] : % 0.61/0.71 ( ( in(A,B) % 0.61/0.71 & element(B,powerset(C)) ) % 0.61/0.71 => element(A,C) ) ). % 0.61/0.71 % 0.61/0.71 fof(t5_subset,axiom, % 0.61/0.71 ! [A,B,C] : % 0.61/0.71 ~ ( in(A,B) % 0.61/0.71 & element(B,powerset(C)) % 0.61/0.71 & empty(C) ) ). % 0.61/0.71 % 0.61/0.71 fof(t6_boole,axiom, % 0.61/0.71 ! [A] : % 0.61/0.71 ( empty(A) % 0.61/0.71 => A = empty_set ) ). % 0.61/0.71 % 0.61/0.71 fof(t7_boole,axiom, % 0.61/0.71 ! [A,B] : % 0.61/0.71 ~ ( in(A,B) % 0.61/0.71 & empty(B) ) ). % 0.61/0.71 % 0.61/0.71 fof(t8_boole,axiom, % 0.61/0.71 ! [A,B] : % 0.61/0.71 ~ ( empty(A) % 0.61/0.71 & A != B % 0.61/0.71 & empty(B) ) ). % 0.61/0.71 % 0.61/0.71 %------------------------------------------------------------------------------ % 0.61/0.71 %------------------------------------------- % 0.61/0.71 % Proof found % 0.61/0.71 % SZS status Theorem for theBenchmark % 0.61/0.71 % SZS output start Proof % 0.61/0.71 %ClaNum:76(EqnAxiom:21) % 0.61/0.71 %VarNum:89(SingletonVarNum:41) % 0.61/0.71 %MaxLitNum:5 % 0.61/0.71 %MaxfuncDepth:1 % 0.61/0.71 %SharedTerms:40 % 0.61/0.71 %goalClause: 31 40 46 47 49 51 % 0.61/0.71 %singleGoalClaCount:6 % 0.61/0.71 [24]P1(a1) % 0.61/0.71 [25]P1(a2) % 0.61/0.71 [26]P1(a10) % 0.61/0.71 [27]P1(a12) % 0.61/0.71 [28]P3(a3) % 0.61/0.71 [29]P3(a12) % 0.61/0.71 [30]P3(a4) % 0.61/0.71 [31]P3(a5) % 0.61/0.71 [33]P4(a1) % 0.61/0.71 [34]P4(a3) % 0.61/0.71 [35]P4(a2) % 0.61/0.71 [36]P4(a12) % 0.61/0.71 [37]P4(a13) % 0.61/0.71 [38]P4(a4) % 0.61/0.71 [39]P4(a6) % 0.61/0.71 [40]P4(a5) % 0.61/0.71 [41]P5(a4) % 0.61/0.71 [42]P7(a1) % 0.61/0.71 [43]P7(a6) % 0.61/0.71 [51]~E(a8,a7) % 0.61/0.71 [52]~P1(a13) % 0.61/0.71 [53]~P1(a18) % 0.61/0.71 [46]P8(a7,f15(a5)) % 0.61/0.71 [47]P8(a8,f15(a5)) % 0.61/0.71 [49]E(f16(a5,a8),f16(a5,a7)) % 0.61/0.71 [45]P8(x451,x451) % 0.61/0.71 [44]P1(f14(x441)) % 0.61/0.71 [48]P2(f9(x481),x481) % 0.61/0.71 [50]P2(f14(x501),f17(x501)) % 0.61/0.71 [54]~P1(f17(x541)) % 0.61/0.71 [55]~P1(x551)+E(x551,a1) % 0.61/0.71 [56]~P1(x561)+P3(x561) % 0.61/0.71 [57]~P1(x571)+P4(x571) % 0.61/0.71 [59]~P1(x591)+P1(f15(x591)) % 0.61/0.71 [60]~P1(x601)+P4(f15(x601)) % 0.61/0.71 [63]P1(x631)+~P1(f11(x631)) % 0.61/0.71 [67]P1(x671)+P2(f11(x671),f17(x671)) % 0.61/0.71 [62]~E(x621,x622)+P8(x621,x622) % 0.61/0.71 [66]~P1(x661)+~P6(x662,x661) % 0.61/0.71 [68]~P6(x681,x682)+P2(x681,x682) % 0.61/0.71 [71]~P6(x712,x711)+~P6(x711,x712) % 0.61/0.71 [70]~P8(x701,x702)+P2(x701,f17(x702)) % 0.61/0.71 [72]P8(x721,x722)+~P2(x721,f17(x722)) % 0.61/0.71 [65]~P4(x651)+P1(x651)+~P1(f15(x651)) % 0.61/0.71 [58]~P1(x582)+~P1(x581)+E(x581,x582) % 0.61/0.71 [69]~P2(x692,x691)+P1(x691)+P6(x692,x691) % 0.61/0.71 [73]~P8(x732,x731)+~P8(x731,x732)+E(x731,x732) % 0.61/0.71 [74]~P1(x741)+~P6(x742,x743)+~P2(x743,f17(x741)) % 0.61/0.71 [75]P2(x751,x752)+~P6(x751,x753)+~P2(x753,f17(x752)) % 0.61/0.71 [64]~P1(x641)+~P3(x641)+~P4(x641)+P5(x641) % 0.61/0.71 [76]~P4(x763)+P8(x761,x762)+~P3(x763)+~P8(x761,f15(x763))+~P8(f16(x763,x761),f16(x763,x762)) % 0.61/0.71 %EqnAxiom % 0.61/0.71 [1]E(x11,x11) % 0.61/0.71 [2]E(x22,x21)+~E(x21,x22) % 0.61/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.61/0.71 [4]~E(x41,x42)+E(f14(x41),f14(x42)) % 0.61/0.71 [5]~E(x51,x52)+E(f15(x51),f15(x52)) % 0.61/0.71 [6]~E(x61,x62)+E(f16(x61,x63),f16(x62,x63)) % 0.61/0.71 [7]~E(x71,x72)+E(f16(x73,x71),f16(x73,x72)) % 0.61/0.71 [8]~E(x81,x82)+E(f9(x81),f9(x82)) % 0.61/0.71 [9]~E(x91,x92)+E(f17(x91),f17(x92)) % 0.61/0.71 [10]~E(x101,x102)+E(f11(x101),f11(x102)) % 0.61/0.71 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 0.61/0.71 [12]P8(x122,x123)+~E(x121,x122)+~P8(x121,x123) % 0.61/0.71 [13]P8(x133,x132)+~E(x131,x132)+~P8(x133,x131) % 0.61/0.71 [14]P6(x142,x143)+~E(x141,x142)+~P6(x141,x143) % 0.61/0.71 [15]P6(x153,x152)+~E(x151,x152)+~P6(x153,x151) % 0.61/0.71 [16]~P4(x161)+P4(x162)+~E(x161,x162) % 0.61/0.71 [17]~P3(x171)+P3(x172)+~E(x171,x172) % 0.61/0.71 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183) % 0.61/0.71 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191) % 0.61/0.71 [20]~P5(x201)+P5(x202)+~E(x201,x202) % 0.61/0.71 [21]~P7(x211)+P7(x212)+~E(x211,x212) % 0.61/0.71 % 0.61/0.71 %------------------------------------------- % 0.61/0.71 cnf(82,plain, % 0.61/0.71 (P2(f9(x821),x821)), % 0.61/0.71 inference(rename_variables,[],[48])). % 0.61/0.71 cnf(84,plain, % 0.61/0.71 (P8(f16(a5,a7),f16(a5,a8))), % 0.61/0.71 inference(scs_inference,[],[49,45,48,24,2,66,72,12])). % 0.61/0.71 cnf(85,plain, % 0.61/0.71 (P8(x851,x851)), % 0.61/0.71 inference(rename_variables,[],[45])). % 0.61/0.71 cnf(86,plain, % 0.61/0.71 (P8(f16(a5,a8),f16(a5,a7))), % 0.61/0.71 inference(scs_inference,[],[49,45,85,48,24,2,66,72,12,13])). % 0.61/0.71 cnf(89,plain, % 0.61/0.71 (P2(f9(x891),x891)), % 0.61/0.71 inference(rename_variables,[],[48])). % 0.61/0.71 cnf(90,plain, % 0.61/0.71 (P6(f9(a13),a13)), % 0.61/0.71 inference(scs_inference,[],[49,45,85,48,82,89,24,52,2,66,72,12,13,19,69])). % 0.61/0.71 cnf(91,plain, % 0.61/0.71 (P2(f9(x911),x911)), % 0.61/0.71 inference(rename_variables,[],[48])). % 0.61/0.71 cnf(93,plain, % 0.61/0.71 (~P6(x931,f9(f17(a1)))), % 0.61/0.71 inference(scs_inference,[],[49,45,85,48,82,89,91,24,52,2,66,72,12,13,19,69,74])). % 0.61/0.71 cnf(105,plain, % 0.61/0.71 (P8(f14(x1051),x1051)), % 0.61/0.71 inference(scs_inference,[],[50,72])). % 0.61/0.71 cnf(109,plain, % 0.61/0.71 (~P6(x1091,f14(a2))), % 0.61/0.71 inference(scs_inference,[],[50,25,72,66,74])). % 0.61/0.71 cnf(112,plain, % 0.61/0.71 (P6(f9(a18),a18)), % 0.61/0.71 inference(scs_inference,[],[50,25,53,48,72,66,74,69])). % 0.61/0.71 cnf(122,plain, % 0.61/0.71 (~P8(a7,a8)), % 0.61/0.71 inference(scs_inference,[],[31,40,51,47,49,86,93,50,90,25,53,48,72,66,74,69,15,76,71,21,73])). % 0.61/0.71 cnf(141,plain, % 0.61/0.71 (P2(f9(x1411),x1411)), % 0.61/0.71 inference(rename_variables,[],[48])). % 0.61/0.71 cnf(147,plain, % 0.61/0.71 (P8(f14(x1471),x1471)), % 0.61/0.71 inference(rename_variables,[],[105])). % 0.61/0.71 cnf(152,plain, % 0.61/0.71 ($false), % 0.61/0.71 inference(scs_inference,[],[31,49,40,46,84,122,105,147,109,112,26,54,48,141,66,74,69,12,15,13,76]), % 0.61/0.71 ['proof']). % 0.61/0.71 % SZS output end Proof % 0.61/0.71 % Total time :0.020000s %------------------------------------------------------------------------------