%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET027+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 14:20:10 EDT 2024
% Result : Theorem 0.55s 0.67s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET027+4 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n026.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 13:55:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.52/0.58 start to proof:theBenchmark
% 0.55/0.66 %-------------------------------------------
% 0.55/0.66 % File :CSE---1.7
% 0.55/0.66 % Problem :theBenchmark
% 0.55/0.66 % Transform :cnf
% 0.55/0.66 % Format :tptp:raw
% 0.55/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.66
% 0.55/0.66 % Result :Theorem 0.040000s
% 0.55/0.66 % Output :CNFRefutation 0.040000s
% 0.55/0.66 %-------------------------------------------
% 0.55/0.67 %--------------------------------------------------------------------------
% 0.55/0.67 % File : SET027+4 : TPTP v8.2.0. Released v2.2.0.
% 0.55/0.67 % Domain : Set Theory (Naive)
% 0.55/0.67 % Problem : Transitivity of subset
% 0.55/0.67 % Version : [Pas99] axioms.
% 0.55/0.67 % English :
% 0.55/0.67
% 0.55/0.67 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 0.55/0.67 % Source : [Pas99]
% 0.55/0.67 % Names :
% 0.55/0.67
% 0.55/0.67 % Status : Theorem
% 0.55/0.67 % Rating : 0.11 v7.5.0, 0.09 v7.4.0, 0.17 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.10 v5.0.0, 0.08 v4.1.0, 0.04 v4.0.0, 0.08 v3.7.0, 0.15 v3.5.0, 0.11 v3.3.0, 0.00 v3.2.0, 0.09 v3.1.0, 0.00 v2.2.1
% 0.55/0.67 % Syntax : Number of formulae : 12 ( 1 unt; 0 def)
% 0.55/0.67 % Number of atoms : 32 ( 3 equ)
% 0.55/0.67 % Maximal formula atoms : 3 ( 2 avg)
% 0.55/0.67 % Number of connectives : 22 ( 2 ~; 2 |; 5 &)
% 0.55/0.67 % ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% 0.55/0.67 % Maximal formula depth : 7 ( 5 avg)
% 0.55/0.67 % Maximal term depth : 2 ( 1 avg)
% 0.55/0.67 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 0.55/0.67 % Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% 0.55/0.67 % Number of variables : 31 ( 30 !; 1 ?)
% 0.55/0.67 % SPC : FOF_THM_RFO_SEQ
% 0.55/0.67
% 0.55/0.67 % Comments :
% 0.55/0.67 %--------------------------------------------------------------------------
% 0.55/0.67 %----Include set theory definitions
% 0.55/0.67 include('Axioms/SET006+0.ax').
% 0.55/0.67 %--------------------------------------------------------------------------
% 0.55/0.67 fof(thI03,conjecture,
% 0.55/0.67 ! [A,B,C] :
% 0.55/0.67 ( ( subset(A,B)
% 0.55/0.67 & subset(B,C) )
% 0.55/0.67 => subset(A,C) ) ).
% 0.55/0.67
% 0.55/0.67 %--------------------------------------------------------------------------
% 0.55/0.67 %-------------------------------------------
% 0.55/0.67 % Proof found
% 0.55/0.67 % SZS status Theorem for theBenchmark
% 0.55/0.67 % SZS output start Proof
% 0.55/0.67 %ClaNum:59(EqnAxiom:27)
% 0.55/0.67 %VarNum:147(SingletonVarNum:72)
% 0.55/0.67 %MaxLitNum:3
% 0.55/0.67 %MaxfuncDepth:1
% 0.55/0.67 %SharedTerms:7
% 0.55/0.67 %goalClause: 28 29 30
% 0.55/0.67 %singleGoalClaCount:3
% 0.55/0.67 [28]P1(a1,a7)
% 0.55/0.67 [29]P1(a7,a8)
% 0.55/0.67 [30]~P1(a1,a8)
% 0.55/0.67 [31]~P2(x311,a2)
% 0.55/0.67 [34]~P3(x342,x341)+P1(x341,x342)
% 0.55/0.67 [35]~P3(x351,x352)+P1(x351,x352)
% 0.55/0.67 [32]~E(x321,x322)+P2(x321,f9(x322))
% 0.55/0.67 [33]E(x331,x332)+~P2(x331,f9(x332))
% 0.55/0.67 [36]~P1(x361,x362)+P2(x361,f10(x362))
% 0.55/0.67 [39]P1(x391,x392)+~P2(x391,f10(x392))
% 0.55/0.67 [40]P1(x401,x402)+P2(f4(x401,x402),x401)
% 0.55/0.67 [43]P2(f5(x431,x432),x432)+P2(x431,f12(x432))
% 0.55/0.67 [49]~P2(x491,f15(x492))+P2(x491,f6(x491,x492))
% 0.55/0.67 [50]~P2(x501,f15(x502))+P2(f6(x501,x502),x502)
% 0.55/0.67 [55]P1(x551,x552)+~P2(f4(x551,x552),x552)
% 0.55/0.67 [56]~P2(x561,f5(x561,x562))+P2(x561,f12(x562))
% 0.55/0.67 [37]~E(x371,x373)+P2(x371,f13(x372,x373))
% 0.55/0.67 [38]~E(x381,x382)+P2(x381,f13(x382,x383))
% 0.55/0.67 [44]~P2(x441,x443)+P2(x441,f14(x442,x443))
% 0.55/0.67 [45]~P2(x451,x452)+P2(x451,f14(x452,x453))
% 0.55/0.67 [52]P2(x521,x522)+~P2(x521,f11(x523,x522))
% 0.55/0.67 [53]P2(x531,x532)+~P2(x531,f11(x532,x533))
% 0.55/0.67 [54]P2(x541,x542)+~P2(x541,f3(x542,x543))
% 0.55/0.67 [58]~P2(x581,x582)+~P2(x581,f3(x583,x582))
% 0.55/0.67 [42]~P1(x422,x421)+~P1(x421,x422)+P3(x421,x422)
% 0.55/0.67 [41]~P2(x411,x413)+P2(x411,x412)+~P1(x413,x412)
% 0.55/0.67 [46]~P2(x463,x462)+~P2(x461,x463)+P2(x461,f15(x462))
% 0.55/0.67 [47]E(x471,x472)+E(x471,x473)+~P2(x471,f13(x473,x472))
% 0.55/0.67 [48]P2(x481,x482)+~P2(x482,x483)+~P2(x481,f12(x483))
% 0.55/0.67 [51]~P2(x511,x513)+P2(x511,x512)+P2(x511,f3(x513,x512))
% 0.55/0.67 [57]~P2(x571,x573)+~P2(x571,x572)+P2(x571,f11(x572,x573))
% 0.55/0.67 [59]P2(x591,x592)+P2(x591,x593)+~P2(x591,f14(x593,x592))
% 0.55/0.67 %EqnAxiom
% 0.55/0.67 [1]E(x11,x11)
% 0.55/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.67 [4]~E(x41,x42)+E(f9(x41),f9(x42))
% 0.55/0.67 [5]~E(x51,x52)+E(f14(x51,x53),f14(x52,x53))
% 0.55/0.67 [6]~E(x61,x62)+E(f14(x63,x61),f14(x63,x62))
% 0.55/0.67 [7]~E(x71,x72)+E(f10(x71),f10(x72))
% 0.55/0.67 [8]~E(x81,x82)+E(f13(x81,x83),f13(x82,x83))
% 0.55/0.67 [9]~E(x91,x92)+E(f13(x93,x91),f13(x93,x92))
% 0.55/0.67 [10]~E(x101,x102)+E(f12(x101),f12(x102))
% 0.55/0.67 [11]~E(x111,x112)+E(f5(x111,x113),f5(x112,x113))
% 0.55/0.67 [12]~E(x121,x122)+E(f5(x123,x121),f5(x123,x122))
% 0.55/0.67 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 0.55/0.67 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 0.55/0.67 [15]~E(x151,x152)+E(f3(x151,x153),f3(x152,x153))
% 0.55/0.67 [16]~E(x161,x162)+E(f3(x163,x161),f3(x163,x162))
% 0.55/0.67 [17]~E(x171,x172)+E(f11(x171,x173),f11(x172,x173))
% 0.55/0.67 [18]~E(x181,x182)+E(f11(x183,x181),f11(x183,x182))
% 0.55/0.67 [19]~E(x191,x192)+E(f15(x191),f15(x192))
% 0.55/0.67 [20]~E(x201,x202)+E(f6(x201,x203),f6(x202,x203))
% 0.55/0.67 [21]~E(x211,x212)+E(f6(x213,x211),f6(x213,x212))
% 0.55/0.67 [22]P1(x222,x223)+~E(x221,x222)+~P1(x221,x223)
% 0.55/0.67 [23]P1(x233,x232)+~E(x231,x232)+~P1(x233,x231)
% 0.55/0.67 [24]P2(x242,x243)+~E(x241,x242)+~P2(x241,x243)
% 0.55/0.67 [25]P2(x253,x252)+~E(x251,x252)+~P2(x253,x251)
% 0.55/0.67 [26]P3(x262,x263)+~E(x261,x262)+~P3(x261,x263)
% 0.55/0.67 [27]P3(x273,x272)+~E(x271,x272)+~P3(x273,x271)
% 0.55/0.67
% 0.55/0.67 %-------------------------------------------
% 0.55/0.67 cnf(60,plain,
% 0.55/0.67 (P2(x601,f9(x601))),
% 0.55/0.67 inference(equality_inference,[],[32])).
% 0.55/0.67 cnf(61,plain,
% 0.55/0.67 (P2(x611,f13(x612,x611))),
% 0.55/0.67 inference(equality_inference,[],[37])).
% 0.55/0.67 cnf(67,plain,
% 0.55/0.67 (P1(a2,x671)),
% 0.55/0.67 inference(scs_inference,[],[30,31,34,35,40])).
% 0.55/0.67 cnf(68,plain,
% 0.55/0.67 (~P2(x681,a2)),
% 0.55/0.67 inference(rename_variables,[],[31])).
% 0.55/0.67 cnf(70,plain,
% 0.55/0.67 (~P2(x701,f15(a2))),
% 0.55/0.67 inference(scs_inference,[],[30,31,68,34,35,40,50])).
% 0.55/0.67 cnf(71,plain,
% 0.55/0.67 (~P2(x711,a2)),
% 0.55/0.67 inference(rename_variables,[],[31])).
% 0.55/0.67 cnf(79,plain,
% 0.55/0.67 (~P2(x791,a1)+P2(x791,a7)),
% 0.55/0.67 inference(scs_inference,[],[28,29,30,60,31,68,71,34,35,40,50,42,22,23,25,41])).
% 0.55/0.67 cnf(88,plain,
% 0.55/0.67 (~P2(x881,f15(a2))),
% 0.55/0.67 inference(rename_variables,[],[70])).
% 0.55/0.67 cnf(91,plain,
% 0.55/0.67 (~P2(x911,f15(a2))),
% 0.55/0.67 inference(rename_variables,[],[70])).
% 0.55/0.67 cnf(94,plain,
% 0.55/0.67 (P1(a2,x941)),
% 0.55/0.67 inference(rename_variables,[],[67])).
% 0.55/0.67 cnf(95,plain,
% 0.55/0.67 (~P1(x951,x952)+P3(x951,x952)+~P1(x952,x951)),
% 0.55/0.67 inference(rename_variables,[],[42])).
% 0.55/0.67 cnf(103,plain,
% 0.55/0.68 (~P2(x1031,a7)+P2(x1031,a8)),
% 0.55/0.68 inference(scs_inference,[],[28,29,30,61,70,88,91,67,94,40,50,42,22,25,95,26,41])).
% 0.55/0.68 cnf(140,plain,
% 0.55/0.68 (~P2(f4(a1,a8),a7)),
% 0.55/0.68 inference(scs_inference,[],[30,103,55])).
% 0.55/0.68 cnf(143,plain,
% 0.55/0.68 ($false),
% 0.55/0.68 inference(scs_inference,[],[30,140,79,40]),
% 0.55/0.68 ['proof']).
% 0.55/0.68 % SZS output end Proof
% 0.55/0.68 % Total time :0.040000s
%------------------------------------------------------------------------------