%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET347+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 : n023.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 14:21:23 EDT 2024
% Result : Theorem 0.59s 0.66s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET347+4 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.35 % Computer : n023.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Jun 23 16:55:53 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.55/0.61 start to proof:theBenchmark
% 0.59/0.66 %-------------------------------------------
% 0.59/0.66 % File :CSE---1.7
% 0.59/0.66 % Problem :theBenchmark
% 0.59/0.66 % Transform :cnf
% 0.59/0.66 % Format :tptp:raw
% 0.59/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.59/0.66
% 0.59/0.66 % Result :Theorem 0.000000s
% 0.59/0.66 % Output :CNFRefutation 0.000000s
% 0.59/0.66 %-------------------------------------------
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 % File : SET347+4 : TPTP v8.2.0. Released v2.2.0.
% 0.59/0.66 % Domain : Set Theory (Naive)
% 0.59/0.66 % Problem : Sum of the empty set is the empty set
% 0.59/0.66 % Version : [Pas99] axioms.
% 0.59/0.66 % English :
% 0.59/0.66
% 0.59/0.66 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 0.59/0.66 % Source : [Pas99]
% 0.59/0.66 % Names :
% 0.59/0.66
% 0.59/0.66 % Status : Theorem
% 0.59/0.66 % Rating : 0.11 v8.2.0, 0.14 v8.1.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.21 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.17 v4.0.0, 0.21 v3.7.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.25 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% 0.59/0.66 % Syntax : Number of formulae : 12 ( 2 unt; 0 def)
% 0.59/0.66 % Number of atoms : 30 ( 3 equ)
% 0.59/0.66 % Maximal formula atoms : 3 ( 2 avg)
% 0.59/0.66 % Number of connectives : 20 ( 2 ~; 2 |; 4 &)
% 0.59/0.66 % ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% 0.59/0.66 % Maximal formula depth : 7 ( 5 avg)
% 0.59/0.66 % Maximal term depth : 2 ( 1 avg)
% 0.59/0.66 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 0.59/0.66 % Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% 0.59/0.66 % Number of variables : 28 ( 27 !; 1 ?)
% 0.59/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.59/0.66
% 0.59/0.66 % Comments :
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 %----Include set theory definitions
% 0.59/0.66 include('Axioms/SET006+0.ax').
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 fof(thI38,conjecture,
% 0.59/0.66 equal_set(sum(empty_set),empty_set) ).
% 0.59/0.66
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 %-------------------------------------------
% 0.59/0.66 % Proof found
% 0.59/0.66 % SZS status Theorem for theBenchmark
% 0.59/0.66 % SZS output start Proof
% 0.59/0.66 %ClaNum:57(EqnAxiom:27)
% 0.59/0.66 %VarNum:147(SingletonVarNum:72)
% 0.59/0.66 %MaxLitNum:3
% 0.59/0.66 %MaxfuncDepth:1
% 0.59/0.66 %SharedTerms:3
% 0.59/0.66 %goalClause: 29
% 0.59/0.66 %singleGoalClaCount:1
% 0.59/0.66 [29]~P2(f3(a1),a1)
% 0.59/0.66 [28]~P1(x281,a1)
% 0.59/0.66 [32]~P2(x322,x321)+P3(x321,x322)
% 0.59/0.66 [33]~P2(x331,x332)+P3(x331,x332)
% 0.59/0.66 [30]~E(x301,x302)+P1(x301,f4(x302))
% 0.59/0.66 [31]E(x311,x312)+~P1(x311,f4(x312))
% 0.59/0.66 [34]~P3(x341,x342)+P1(x341,f5(x342))
% 0.59/0.66 [37]P3(x371,x372)+~P1(x371,f5(x372))
% 0.59/0.66 [38]P3(x381,x382)+P1(f6(x381,x382),x381)
% 0.59/0.66 [41]P1(f7(x411,x412),x412)+P1(x411,f10(x412))
% 0.59/0.66 [47]~P1(x471,f3(x472))+P1(x471,f8(x471,x472))
% 0.59/0.66 [48]~P1(x481,f3(x482))+P1(f8(x481,x482),x482)
% 0.59/0.66 [53]P3(x531,x532)+~P1(f6(x531,x532),x532)
% 0.59/0.66 [54]~P1(x541,f7(x541,x542))+P1(x541,f10(x542))
% 0.59/0.66 [35]~E(x351,x353)+P1(x351,f11(x352,x353))
% 0.59/0.66 [36]~E(x361,x362)+P1(x361,f11(x362,x363))
% 0.59/0.66 [42]~P1(x421,x423)+P1(x421,f12(x422,x423))
% 0.59/0.66 [43]~P1(x431,x432)+P1(x431,f12(x432,x433))
% 0.59/0.66 [50]P1(x501,x502)+~P1(x501,f9(x503,x502))
% 0.59/0.66 [51]P1(x511,x512)+~P1(x511,f9(x512,x513))
% 0.59/0.66 [52]P1(x521,x522)+~P1(x521,f2(x522,x523))
% 0.59/0.66 [56]~P1(x561,x562)+~P1(x561,f2(x563,x562))
% 0.59/0.66 [40]~P3(x402,x401)+~P3(x401,x402)+P2(x401,x402)
% 0.59/0.66 [39]~P1(x391,x393)+P1(x391,x392)+~P3(x393,x392)
% 0.59/0.66 [44]~P1(x443,x442)+~P1(x441,x443)+P1(x441,f3(x442))
% 0.59/0.66 [45]E(x451,x452)+E(x451,x453)+~P1(x451,f11(x453,x452))
% 0.59/0.66 [46]P1(x461,x462)+~P1(x462,x463)+~P1(x461,f10(x463))
% 0.59/0.66 [49]~P1(x491,x493)+P1(x491,x492)+P1(x491,f2(x493,x492))
% 0.59/0.66 [55]~P1(x551,x553)+~P1(x551,x552)+P1(x551,f9(x552,x553))
% 0.59/0.66 [57]P1(x571,x572)+P1(x571,x573)+~P1(x571,f12(x573,x572))
% 0.59/0.66 %EqnAxiom
% 0.59/0.66 [1]E(x11,x11)
% 0.59/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.59/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.59/0.66 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.59/0.66 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 0.59/0.66 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.59/0.66 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.59/0.66 [8]~E(x81,x82)+E(f5(x81),f5(x82))
% 0.59/0.66 [9]~E(x91,x92)+E(f11(x91,x93),f11(x92,x93))
% 0.59/0.66 [10]~E(x101,x102)+E(f11(x103,x101),f11(x103,x102))
% 0.59/0.66 [11]~E(x111,x112)+E(f2(x111,x113),f2(x112,x113))
% 0.59/0.66 [12]~E(x121,x122)+E(f2(x123,x121),f2(x123,x122))
% 0.59/0.66 [13]~E(x131,x132)+E(f6(x131,x133),f6(x132,x133))
% 0.59/0.66 [14]~E(x141,x142)+E(f6(x143,x141),f6(x143,x142))
% 0.59/0.66 [15]~E(x151,x152)+E(f9(x151,x153),f9(x152,x153))
% 0.59/0.66 [16]~E(x161,x162)+E(f9(x163,x161),f9(x163,x162))
% 0.59/0.66 [17]~E(x171,x172)+E(f10(x171),f10(x172))
% 0.59/0.66 [18]~E(x181,x182)+E(f8(x181,x183),f8(x182,x183))
% 0.59/0.66 [19]~E(x191,x192)+E(f8(x193,x191),f8(x193,x192))
% 0.59/0.66 [20]~E(x201,x202)+E(f12(x201,x203),f12(x202,x203))
% 0.59/0.66 [21]~E(x211,x212)+E(f12(x213,x211),f12(x213,x212))
% 0.59/0.66 [22]P1(x222,x223)+~E(x221,x222)+~P1(x221,x223)
% 0.59/0.66 [23]P1(x233,x232)+~E(x231,x232)+~P1(x233,x231)
% 0.59/0.66 [24]P2(x242,x243)+~E(x241,x242)+~P2(x241,x243)
% 0.59/0.66 [25]P2(x253,x252)+~E(x251,x252)+~P2(x253,x251)
% 0.59/0.66 [26]P3(x262,x263)+~E(x261,x262)+~P3(x261,x263)
% 0.59/0.66 [27]P3(x273,x272)+~E(x271,x272)+~P3(x273,x271)
% 0.59/0.66
% 0.59/0.66 %-------------------------------------------
% 0.59/0.67 cnf(61,plain,
% 0.59/0.67 (P3(a1,x611)),
% 0.59/0.67 inference(scs_inference,[],[28,38])).
% 0.59/0.67 cnf(62,plain,
% 0.59/0.67 (~P1(x621,a1)),
% 0.59/0.67 inference(rename_variables,[],[28])).
% 0.59/0.67 cnf(64,plain,
% 0.59/0.67 (~P1(x641,f3(a1))),
% 0.59/0.67 inference(scs_inference,[],[28,62,38,48])).
% 0.59/0.67 cnf(80,plain,
% 0.59/0.67 (~P1(x801,f3(a1))),
% 0.59/0.67 inference(rename_variables,[],[64])).
% 0.59/0.67 cnf(85,plain,
% 0.59/0.67 ($false),
% 0.59/0.67 inference(scs_inference,[],[29,61,64,80,38,48,40]),
% 0.59/0.67 ['proof']).
% 0.59/0.67 % SZS output end Proof
% 0.59/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------