%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU169+1 : 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 : n017.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 15:01:31 EDT 2024 % Result : Theorem 26.55s 26.59s % Output : CNFRefutation 26.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU169+1 : TPTP v8.2.0. Released v3.3.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n017.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 11:22:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.53/0.56 start to proof:theBenchmark % 26.53/26.58 %------------------------------------------- % 26.53/26.58 % File :CSE---1.7 % 26.53/26.58 % Problem :theBenchmark % 26.53/26.58 % Transform :cnf % 26.55/26.58 % Format :tptp:raw % 26.55/26.58 % Command :java -jar mcs_scs.jar %d %s % 26.55/26.58 % 26.55/26.58 % Result :Theorem 25.980000s % 26.55/26.58 % Output :CNFRefutation 25.980000s % 26.55/26.58 %------------------------------------------- % 26.55/26.59 %------------------------------------------------------------------------------ % 26.55/26.59 % File : SEU169+1 : TPTP v8.2.0. Released v3.3.0. % 26.55/26.59 % Domain : Set theory % 26.55/26.59 % Problem : MPTP bushy problem l3_subset_1 % 26.55/26.59 % Version : [Urb07] axioms : Especial. % 26.55/26.59 % English : % 26.55/26.59 % 26.55/26.59 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 26.55/26.59 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 26.55/26.59 % Source : [Urb07] % 26.55/26.59 % Names : bushy-l3_subset_1 [Urb07] % 26.55/26.59 % 26.55/26.59 % Status : Theorem % 26.55/26.59 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.13 v7.0.0, 0.07 v6.4.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.27 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.3.0 % 26.55/26.59 % Syntax : Number of formulae : 18 ( 9 unt; 0 def) % 26.55/26.59 % Number of atoms : 36 ( 3 equ) % 26.55/26.59 % Maximal formula atoms : 6 ( 2 avg) % 26.55/26.59 % Number of connectives : 27 ( 9 ~; 0 |; 5 &) % 26.55/26.59 % ( 5 <=>; 8 =>; 0 <=; 0 <~>) % 26.55/26.59 % Maximal formula depth : 7 ( 4 avg) % 26.55/26.59 % Maximal term depth : 2 ( 1 avg) % 26.55/26.59 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty) % 26.55/26.59 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty) % 26.55/26.59 % Number of variables : 27 ( 23 !; 4 ?) % 26.55/26.59 % SPC : FOF_THM_RFO_SEQ % 26.55/26.59 % 26.55/26.59 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 26.55/26.59 % library, www.mizar.org % 26.55/26.59 %------------------------------------------------------------------------------ % 26.55/26.59 fof(antisymmetry_r2_hidden,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ( in(A,B) % 26.55/26.59 => ~ in(B,A) ) ). % 26.55/26.59 % 26.55/26.59 fof(d1_zfmisc_1,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ( B = powerset(A) % 26.55/26.59 <=> ! [C] : % 26.55/26.59 ( in(C,B) % 26.55/26.59 <=> subset(C,A) ) ) ). % 26.55/26.59 % 26.55/26.59 fof(d2_subset_1,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ( ( ~ empty(A) % 26.55/26.59 => ( element(B,A) % 26.55/26.59 <=> in(B,A) ) ) % 26.55/26.59 & ( empty(A) % 26.55/26.59 => ( element(B,A) % 26.55/26.59 <=> empty(B) ) ) ) ). % 26.55/26.59 % 26.55/26.59 fof(d3_tarski,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ( subset(A,B) % 26.55/26.59 <=> ! [C] : % 26.55/26.59 ( in(C,A) % 26.55/26.59 => in(C,B) ) ) ). % 26.55/26.59 % 26.55/26.59 fof(dt_k1_xboole_0,axiom, % 26.55/26.59 $true ). % 26.55/26.59 % 26.55/26.59 fof(dt_k1_zfmisc_1,axiom, % 26.55/26.59 $true ). % 26.55/26.59 % 26.55/26.59 fof(dt_m1_subset_1,axiom, % 26.55/26.59 $true ). % 26.55/26.59 % 26.55/26.59 fof(existence_m1_subset_1,axiom, % 26.55/26.59 ! [A] : % 26.55/26.59 ? [B] : element(B,A) ). % 26.55/26.59 % 26.55/26.59 fof(fc1_subset_1,axiom, % 26.55/26.59 ! [A] : ~ empty(powerset(A)) ). % 26.55/26.59 % 26.55/26.59 fof(fc1_xboole_0,axiom, % 26.55/26.59 empty(empty_set) ). % 26.55/26.59 % 26.55/26.59 fof(l3_subset_1,conjecture, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ( element(B,powerset(A)) % 26.55/26.59 => ! [C] : % 26.55/26.59 ( in(C,B) % 26.55/26.59 => in(C,A) ) ) ). % 26.55/26.59 % 26.55/26.59 fof(rc1_subset_1,axiom, % 26.55/26.59 ! [A] : % 26.55/26.59 ( ~ empty(A) % 26.55/26.59 => ? [B] : % 26.55/26.59 ( element(B,powerset(A)) % 26.55/26.59 & ~ empty(B) ) ) ). % 26.55/26.59 % 26.55/26.59 fof(rc1_xboole_0,axiom, % 26.55/26.59 ? [A] : empty(A) ). % 26.55/26.59 % 26.55/26.59 fof(rc2_xboole_0,axiom, % 26.55/26.59 ? [A] : ~ empty(A) ). % 26.55/26.59 % 26.55/26.59 fof(reflexivity_r1_tarski,axiom, % 26.55/26.59 ! [A,B] : subset(A,A) ). % 26.55/26.59 % 26.55/26.59 fof(t6_boole,axiom, % 26.55/26.59 ! [A] : % 26.55/26.59 ( empty(A) % 26.55/26.59 => A = empty_set ) ). % 26.55/26.59 % 26.55/26.59 fof(t7_boole,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ~ ( in(A,B) % 26.55/26.59 & empty(B) ) ). % 26.55/26.59 % 26.55/26.59 fof(t8_boole,axiom, % 26.55/26.59 ! [A,B] : % 26.55/26.59 ~ ( empty(A) % 26.55/26.59 & A != B % 26.55/26.59 & empty(B) ) ). % 26.55/26.59 % 26.55/26.59 %------------------------------------------------------------------------------ % 26.55/26.59 %------------------------------------------- % 26.55/26.59 % Proof found % 26.55/26.59 % SZS status Theorem for theBenchmark % 26.55/26.59 % SZS output start Proof % 26.55/26.59 %ClaNum:43(EqnAxiom:17) % 26.55/26.59 %VarNum:85(SingletonVarNum:37) % 26.55/26.59 %MaxLitNum:3 % 26.55/26.59 %MaxfuncDepth:1 % 26.55/26.59 %SharedTerms:13 % 26.55/26.59 %goalClause: 20 22 26 % 26.55/26.59 %singleGoalClaCount:3 % 26.55/26.59 [18]P1(a1) % 26.55/26.59 [19]P1(a2) % 26.55/26.59 [20]P3(a3,a4) % 26.55/26.59 [24]~P1(a11) % 26.55/26.59 [26]~P3(a3,a5) % 26.55/26.59 [22]P2(a4,f10(a5)) % 26.55/26.59 [21]P4(x211,x211) % 26.55/26.59 [23]P2(f6(x231),x231) % 26.55/26.59 [25]~P1(f10(x251)) % 26.55/26.59 [27]~P1(x271)+E(x271,a1) % 26.55/26.59 [29]P1(x291)+~P1(f9(x291)) % 26.55/26.59 [32]P1(x321)+P2(f9(x321),f10(x321)) % 26.55/26.59 [31]~P1(x311)+~P3(x312,x311) % 26.55/26.59 [36]~P3(x362,x361)+~P3(x361,x362) % 26.55/26.59 [39]P4(x391,x392)+P3(f7(x391,x392),x391) % 26.55/26.59 [41]P4(x411,x412)+~P3(f7(x411,x412),x412) % 26.55/26.59 [28]~P1(x282)+~P1(x281)+E(x281,x282) % 26.55/26.59 [30]~P1(x302)+~P1(x301)+P2(x301,x302) % 26.55/26.59 [33]~P2(x331,x332)+P1(x331)+~P1(x332) % 26.55/26.59 [34]~P2(x342,x341)+P1(x341)+P3(x342,x341) % 26.55/26.59 [35]~P3(x352,x351)+P1(x351)+P2(x352,x351) % 26.55/26.59 [42]P3(f8(x422,x421),x421)+P4(f8(x422,x421),x422)+E(x421,f10(x422)) % 26.55/26.59 [43]~P3(f8(x432,x431),x431)+~P4(f8(x432,x431),x432)+E(x431,f10(x432)) % 26.55/26.59 [40]~P4(x403,x402)+P3(x401,x402)+~P3(x401,x403) % 26.55/26.59 [37]~P4(x371,x373)+P3(x371,x372)+~E(x372,f10(x373)) % 26.55/26.60 [38]~P3(x381,x383)+P4(x381,x382)+~E(x383,f10(x382)) % 26.55/26.60 %EqnAxiom % 26.55/26.60 [1]E(x11,x11) % 26.55/26.60 [2]E(x22,x21)+~E(x21,x22) % 26.55/26.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 26.55/26.60 [4]~E(x41,x42)+E(f10(x41),f10(x42)) % 26.55/26.60 [5]~E(x51,x52)+E(f6(x51),f6(x52)) % 26.55/26.60 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63)) % 26.55/26.60 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72)) % 26.55/26.60 [8]~E(x81,x82)+E(f9(x81),f9(x82)) % 26.55/26.60 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93)) % 26.55/26.60 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102)) % 26.55/26.60 [11]~P1(x111)+P1(x112)+~E(x111,x112) % 26.55/26.60 [12]P4(x122,x123)+~E(x121,x122)+~P4(x121,x123) % 26.55/26.60 [13]P4(x133,x132)+~E(x131,x132)+~P4(x133,x131) % 26.55/26.60 [14]P3(x142,x143)+~E(x141,x142)+~P3(x141,x143) % 26.55/26.60 [15]P3(x153,x152)+~E(x151,x152)+~P3(x153,x151) % 26.55/26.60 [16]P2(x162,x163)+~E(x161,x162)+~P2(x161,x163) % 26.55/26.60 [17]P2(x173,x172)+~E(x171,x172)+~P2(x173,x171) % 26.55/26.60 % 26.55/26.60 %------------------------------------------- % 26.55/26.60 cnf(45,plain, % 26.55/26.60 (~P3(x451,f10(x452))+P4(x451,x452)), % 26.55/26.60 inference(equality_inference,[],[38])). % 26.55/26.60 cnf(46,plain, % 26.55/26.60 (~P3(x461,a1)), % 26.55/26.60 inference(scs_inference,[],[18,31])). % 26.55/26.60 cnf(55,plain, % 26.55/26.60 (P3(f6(a11),a11)), % 26.55/26.60 inference(scs_inference,[],[20,26,23,18,24,31,36,39,33,15,34])). % 26.55/26.60 cnf(72,plain, % 26.55/26.60 (P3(a4,f10(a5))), % 26.55/26.60 inference(scs_inference,[],[22,46,55,19,25,36,31,15,34])). % 26.55/26.60 cnf(117,plain, % 26.55/26.60 (~E(f10(a5),a1)), % 26.55/26.60 inference(scs_inference,[],[46,72,15])). % 26.55/26.60 cnf(148,plain, % 26.55/26.60 (P4(f8(a5,a1),a5)), % 26.55/26.60 inference(scs_inference,[],[117,46,2,42])). % 26.55/26.60 cnf(1864,plain, % 26.55/26.60 ($false), % 26.55/26.60 inference(scs_inference,[],[20,26,148,72,40,12,45]), % 26.55/26.60 ['proof']). % 26.55/26.60 % SZS output end Proof % 26.55/26.60 % Total time :25.980000s %------------------------------------------------------------------------------