%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET691+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 14:22:15 EDT 2024
% Result : Theorem 1.07s 1.14s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET691+4 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n019.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 : Sun Jun 23 13:32:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.52/0.56 start to proof:theBenchmark
% 1.07/1.13 %-------------------------------------------
% 1.07/1.13 % File :CSE---1.7
% 1.07/1.13 % Problem :theBenchmark
% 1.07/1.13 % Transform :cnf
% 1.07/1.13 % Format :tptp:raw
% 1.07/1.13 % Command :java -jar mcs_scs.jar %d %s
% 1.07/1.13
% 1.07/1.13 % Result :Theorem 0.530000s
% 1.07/1.13 % Output :CNFRefutation 0.530000s
% 1.07/1.13 %-------------------------------------------
% 1.07/1.14 %--------------------------------------------------------------------------
% 1.07/1.14 % File : SET691+4 : TPTP v8.2.0. Released v2.2.0.
% 1.07/1.14 % Domain : Set Theory (Naive)
% 1.07/1.14 % Problem : A set is a subset of empty set if and only if it is equal to it
% 1.07/1.14 % Version : [Pas99] axioms.
% 1.07/1.14 % English :
% 1.07/1.14
% 1.07/1.14 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 1.07/1.14 % Source : [Pas99]
% 1.07/1.14 % Names :
% 1.07/1.14
% 1.07/1.14 % Status : Theorem
% 1.07/1.14 % Rating : 0.06 v8.2.0, 0.08 v7.5.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.00 v2.2.1
% 1.07/1.14 % Syntax : Number of formulae : 12 ( 1 unt; 0 def)
% 1.07/1.14 % Number of atoms : 31 ( 3 equ)
% 1.07/1.14 % Maximal formula atoms : 3 ( 2 avg)
% 1.07/1.14 % Number of connectives : 21 ( 2 ~; 2 |; 4 &)
% 1.07/1.14 % ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% 1.07/1.14 % Maximal formula depth : 7 ( 5 avg)
% 1.07/1.14 % Maximal term depth : 2 ( 1 avg)
% 1.07/1.14 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 1.07/1.14 % Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% 1.07/1.14 % Number of variables : 29 ( 28 !; 1 ?)
% 1.07/1.14 % SPC : FOF_THM_RFO_SEQ
% 1.07/1.14
% 1.07/1.14 % Comments :
% 1.07/1.14 %--------------------------------------------------------------------------
% 1.07/1.14 %----Include set theory definitions
% 1.07/1.14 include('Axioms/SET006+0.ax').
% 1.07/1.14 %--------------------------------------------------------------------------
% 1.07/1.14 %----Extended version of SET063
% 1.07/1.14 fof(thI16,conjecture,
% 1.07/1.14 ! [A] :
% 1.07/1.14 ( subset(A,empty_set)
% 1.07/1.14 <=> equal_set(A,empty_set) ) ).
% 1.07/1.14
% 1.07/1.14 %--------------------------------------------------------------------------
% 1.07/1.14 %-------------------------------------------
% 1.07/1.14 % Proof found
% 1.07/1.14 % SZS status Theorem for theBenchmark
% 1.07/1.14 % SZS output start Proof
% 1.07/1.14 %ClaNum:58(EqnAxiom:27)
% 1.07/1.14 %VarNum:147(SingletonVarNum:72)
% 1.07/1.14 %MaxLitNum:3
% 1.07/1.14 %MaxfuncDepth:1
% 1.07/1.14 %SharedTerms:6
% 1.07/1.14 %goalClause: 29 32
% 1.07/1.14 [28]~P1(x281,a1)
% 1.07/1.14 [29]P3(a3,a1)+P2(a3,a1)
% 1.07/1.14 [32]~P3(a3,a1)+~P2(a3,a1)
% 1.07/1.14 [33]~P2(x332,x331)+P3(x331,x332)
% 1.07/1.14 [34]~P2(x341,x342)+P3(x341,x342)
% 1.07/1.14 [30]~E(x301,x302)+P1(x301,f7(x302))
% 1.07/1.14 [31]E(x311,x312)+~P1(x311,f7(x312))
% 1.07/1.14 [35]~P3(x351,x352)+P1(x351,f8(x352))
% 1.07/1.14 [38]P3(x381,x382)+~P1(x381,f8(x382))
% 1.07/1.14 [39]P3(x391,x392)+P1(f4(x391,x392),x391)
% 1.07/1.14 [42]P1(f5(x421,x422),x422)+P1(x421,f10(x422))
% 1.07/1.14 [48]~P1(x481,f13(x482))+P1(x481,f6(x481,x482))
% 1.07/1.14 [49]~P1(x491,f13(x492))+P1(f6(x491,x492),x492)
% 1.07/1.14 [54]P3(x541,x542)+~P1(f4(x541,x542),x542)
% 1.07/1.14 [55]~P1(x551,f5(x551,x552))+P1(x551,f10(x552))
% 1.07/1.14 [36]~E(x361,x363)+P1(x361,f11(x362,x363))
% 1.07/1.14 [37]~E(x371,x372)+P1(x371,f11(x372,x373))
% 1.07/1.14 [43]~P1(x431,x433)+P1(x431,f12(x432,x433))
% 1.07/1.14 [44]~P1(x441,x442)+P1(x441,f12(x442,x443))
% 1.07/1.14 [51]P1(x511,x512)+~P1(x511,f9(x513,x512))
% 1.07/1.14 [52]P1(x521,x522)+~P1(x521,f9(x522,x523))
% 1.07/1.14 [53]P1(x531,x532)+~P1(x531,f2(x532,x533))
% 1.07/1.14 [57]~P1(x571,x572)+~P1(x571,f2(x573,x572))
% 1.07/1.14 [41]~P3(x412,x411)+~P3(x411,x412)+P2(x411,x412)
% 1.07/1.14 [40]~P1(x401,x403)+P1(x401,x402)+~P3(x403,x402)
% 1.07/1.14 [45]~P1(x453,x452)+~P1(x451,x453)+P1(x451,f13(x452))
% 1.07/1.14 [46]E(x461,x462)+E(x461,x463)+~P1(x461,f11(x463,x462))
% 1.07/1.14 [47]P1(x471,x472)+~P1(x472,x473)+~P1(x471,f10(x473))
% 1.07/1.14 [50]~P1(x501,x503)+P1(x501,x502)+P1(x501,f2(x503,x502))
% 1.07/1.14 [56]~P1(x561,x563)+~P1(x561,x562)+P1(x561,f9(x562,x563))
% 1.07/1.14 [58]P1(x581,x582)+P1(x581,x583)+~P1(x581,f12(x583,x582))
% 1.07/1.14 %EqnAxiom
% 1.07/1.14 [1]E(x11,x11)
% 1.07/1.14 [2]E(x22,x21)+~E(x21,x22)
% 1.07/1.14 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.07/1.14 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 1.07/1.14 [5]~E(x51,x52)+E(f12(x51,x53),f12(x52,x53))
% 1.07/1.14 [6]~E(x61,x62)+E(f12(x63,x61),f12(x63,x62))
% 1.07/1.14 [7]~E(x71,x72)+E(f8(x71),f8(x72))
% 1.07/1.14 [8]~E(x81,x82)+E(f11(x81,x83),f11(x82,x83))
% 1.07/1.14 [9]~E(x91,x92)+E(f11(x93,x91),f11(x93,x92))
% 1.07/1.14 [10]~E(x101,x102)+E(f10(x101),f10(x102))
% 1.07/1.14 [11]~E(x111,x112)+E(f5(x111,x113),f5(x112,x113))
% 1.07/1.14 [12]~E(x121,x122)+E(f5(x123,x121),f5(x123,x122))
% 1.07/1.14 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 1.07/1.14 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 1.07/1.14 [15]~E(x151,x152)+E(f2(x151,x153),f2(x152,x153))
% 1.07/1.14 [16]~E(x161,x162)+E(f2(x163,x161),f2(x163,x162))
% 1.07/1.14 [17]~E(x171,x172)+E(f9(x171,x173),f9(x172,x173))
% 1.07/1.14 [18]~E(x181,x182)+E(f9(x183,x181),f9(x183,x182))
% 1.07/1.14 [19]~E(x191,x192)+E(f13(x191),f13(x192))
% 1.07/1.14 [20]~E(x201,x202)+E(f6(x201,x203),f6(x202,x203))
% 1.07/1.14 [21]~E(x211,x212)+E(f6(x213,x211),f6(x213,x212))
% 1.07/1.14 [22]P1(x222,x223)+~E(x221,x222)+~P1(x221,x223)
% 1.07/1.14 [23]P1(x233,x232)+~E(x231,x232)+~P1(x233,x231)
% 1.07/1.14 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243)
% 1.07/1.14 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251)
% 1.07/1.14 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263)
% 1.07/1.14 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271)
% 1.07/1.14
% 1.07/1.14 %-------------------------------------------
% 1.07/1.14 cnf(62,plain,
% 1.07/1.14 (P3(a1,x621)),
% 1.07/1.14 inference(scs_inference,[],[28,39])).
% 1.07/1.14 cnf(343,plain,
% 1.07/1.14 (P3(a3,a1)),
% 1.07/1.14 inference(scs_inference,[],[29,34])).
% 1.07/1.14 cnf(344,plain,
% 1.07/1.14 (~P2(a3,a1)),
% 1.07/1.14 inference(scs_inference,[],[343,32])).
% 1.07/1.14 cnf(351,plain,
% 1.07/1.14 (P2(a3,a1)),
% 1.07/1.14 inference(scs_inference,[],[343,62,28,40,41])).
% 1.07/1.14 cnf(364,plain,
% 1.07/1.14 ($false),
% 1.07/1.14 inference(scs_inference,[],[344,351]),
% 1.07/1.14 ['proof']).
% 1.07/1.14 % SZS output end Proof
% 1.07/1.14 % Total time :0.530000s
%------------------------------------------------------------------------------