TSTP Solution File: SET095+4 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n016.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 : Thu Aug 31 14:28:40 EDT 2023
% Result : Theorem 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.18/0.34 % Computer : n016.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sat Aug 26 15:02:27 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 % File :CSE---1.6
% 0.20/0.67 % Problem :theBenchmark
% 0.20/0.67 % Transform :cnf
% 0.20/0.67 % Format :tptp:raw
% 0.20/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.67
% 0.20/0.67 % Result :Theorem 0.060000s
% 0.20/0.67 % Output :CNFRefutation 0.060000s
% 0.20/0.67 %-------------------------------------------
% 0.20/0.68 %--------------------------------------------------------------------------
% 0.20/0.68 % File : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.20/0.68 % Domain : Set Theory (Naive)
% 0.20/0.68 % Problem : If X is in Y, then the singleton containing X is a subset of Y
% 0.20/0.68 % Version : [Pas99] axioms.
% 0.20/0.68 % English :
% 0.20/0.68
% 0.20/0.68 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 0.20/0.68 % Source : [Pas99]
% 0.20/0.68 % Names :
% 0.20/0.68
% 0.20/0.68 % Status : Theorem
% 0.20/0.68 % Rating : 0.17 v7.5.0, 0.16 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.21 v6.2.0, 0.20 v6.1.0, 0.27 v6.0.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.09 v3.1.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.12 v2.4.0, 0.00 v2.2.1
% 0.20/0.68 % Syntax : Number of formulae : 12 ( 1 unt; 0 def)
% 0.20/0.68 % Number of atoms : 31 ( 3 equ)
% 0.20/0.68 % Maximal formula atoms : 3 ( 2 avg)
% 0.20/0.68 % Number of connectives : 21 ( 2 ~; 2 |; 4 &)
% 0.20/0.68 % ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.68 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.68 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.68 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 0.20/0.68 % Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% 0.20/0.68 % Number of variables : 30 ( 29 !; 1 ?)
% 0.20/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.68
% 0.20/0.68 % Comments :
% 0.20/0.68 %--------------------------------------------------------------------------
% 0.20/0.68 %----Include set theory definitions
% 0.20/0.68 include('Axioms/SET006+0.ax').
% 0.20/0.68 %--------------------------------------------------------------------------
% 0.20/0.68 fof(thI44,conjecture,
% 0.20/0.68 ! [A,X] :
% 0.20/0.68 ( member(X,A)
% 0.20/0.68 => subset(singleton(X),A) ) ).
% 0.20/0.68
% 0.20/0.68 %--------------------------------------------------------------------------
% 0.20/0.68 %-------------------------------------------
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark
% 0.20/0.68 % SZS output start Proof
% 0.20/0.68 %ClaNum:58(EqnAxiom:27)
% 0.20/0.68 %VarNum:147(SingletonVarNum:72)
% 0.20/0.68 %MaxLitNum:3
% 0.20/0.68 %MaxfuncDepth:1
% 0.20/0.68 %SharedTerms:6
% 0.20/0.68 %goalClause: 28 30
% 0.20/0.68 %singleGoalClaCount:2
% 0.20/0.68 [28]P1(a1,a2)
% 0.20/0.68 [30]~P3(f8(a1),a2)
% 0.20/0.68 [29]~P1(x291,a3)
% 0.20/0.68 [33]~P2(x332,x331)+P3(x331,x332)
% 0.20/0.68 [34]~P2(x341,x342)+P3(x341,x342)
% 0.20/0.68 [31]~E(x311,x312)+P1(x311,f8(x312))
% 0.20/0.68 [32]E(x321,x322)+~P1(x321,f8(x322))
% 0.20/0.68 [35]~P3(x351,x352)+P1(x351,f9(x352))
% 0.20/0.68 [38]P3(x381,x382)+~P1(x381,f9(x382))
% 0.20/0.68 [39]P3(x391,x392)+P1(f5(x391,x392),x391)
% 0.20/0.68 [42]P1(f6(x421,x422),x422)+P1(x421,f11(x422))
% 0.20/0.68 [48]~P1(x481,f14(x482))+P1(x481,f7(x481,x482))
% 0.20/0.68 [49]~P1(x491,f14(x492))+P1(f7(x491,x492),x492)
% 0.20/0.68 [54]P3(x541,x542)+~P1(f5(x541,x542),x542)
% 0.20/0.68 [55]~P1(x551,f6(x551,x552))+P1(x551,f11(x552))
% 0.20/0.68 [36]~E(x361,x363)+P1(x361,f12(x362,x363))
% 0.20/0.68 [37]~E(x371,x372)+P1(x371,f12(x372,x373))
% 0.20/0.68 [43]~P1(x431,x433)+P1(x431,f13(x432,x433))
% 0.20/0.68 [44]~P1(x441,x442)+P1(x441,f13(x442,x443))
% 0.20/0.68 [51]P1(x511,x512)+~P1(x511,f10(x513,x512))
% 0.20/0.68 [52]P1(x521,x522)+~P1(x521,f10(x522,x523))
% 0.20/0.68 [53]P1(x531,x532)+~P1(x531,f4(x532,x533))
% 0.20/0.68 [57]~P1(x571,x572)+~P1(x571,f4(x573,x572))
% 0.20/0.68 [41]~P3(x412,x411)+~P3(x411,x412)+P2(x411,x412)
% 0.20/0.68 [40]~P1(x401,x403)+P1(x401,x402)+~P3(x403,x402)
% 0.20/0.68 [45]~P1(x453,x452)+~P1(x451,x453)+P1(x451,f14(x452))
% 0.20/0.68 [46]E(x461,x462)+E(x461,x463)+~P1(x461,f12(x463,x462))
% 0.20/0.68 [47]P1(x471,x472)+~P1(x472,x473)+~P1(x471,f11(x473))
% 0.20/0.68 [50]~P1(x501,x503)+P1(x501,x502)+P1(x501,f4(x503,x502))
% 0.20/0.68 [56]~P1(x561,x563)+~P1(x561,x562)+P1(x561,f10(x562,x563))
% 0.20/0.68 [58]P1(x581,x582)+P1(x581,x583)+~P1(x581,f13(x583,x582))
% 0.20/0.68 %EqnAxiom
% 0.20/0.68 [1]E(x11,x11)
% 0.20/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.68 [4]~E(x41,x42)+E(f8(x41),f8(x42))
% 0.20/0.68 [5]~E(x51,x52)+E(f13(x51,x53),f13(x52,x53))
% 0.20/0.68 [6]~E(x61,x62)+E(f13(x63,x61),f13(x63,x62))
% 0.20/0.68 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73))
% 0.20/0.68 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82))
% 0.20/0.68 [9]~E(x91,x92)+E(f9(x91),f9(x92))
% 0.20/0.68 [10]~E(x101,x102)+E(f12(x101,x103),f12(x102,x103))
% 0.20/0.68 [11]~E(x111,x112)+E(f12(x113,x111),f12(x113,x112))
% 0.20/0.68 [12]~E(x121,x122)+E(f10(x121,x123),f10(x122,x123))
% 0.20/0.68 [13]~E(x131,x132)+E(f10(x133,x131),f10(x133,x132))
% 0.20/0.68 [14]~E(x141,x142)+E(f5(x141,x143),f5(x142,x143))
% 0.20/0.68 [15]~E(x151,x152)+E(f5(x153,x151),f5(x153,x152))
% 0.20/0.68 [16]~E(x161,x162)+E(f7(x161,x163),f7(x162,x163))
% 0.20/0.68 [17]~E(x171,x172)+E(f7(x173,x171),f7(x173,x172))
% 0.20/0.68 [18]~E(x181,x182)+E(f11(x181),f11(x182))
% 0.20/0.68 [19]~E(x191,x192)+E(f6(x191,x193),f6(x192,x193))
% 0.20/0.68 [20]~E(x201,x202)+E(f6(x203,x201),f6(x203,x202))
% 0.20/0.68 [21]~E(x211,x212)+E(f14(x211),f14(x212))
% 0.20/0.68 [22]P1(x222,x223)+~E(x221,x222)+~P1(x221,x223)
% 0.20/0.68 [23]P1(x233,x232)+~E(x231,x232)+~P1(x233,x231)
% 0.20/0.68 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243)
% 0.20/0.68 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251)
% 0.20/0.68 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263)
% 0.20/0.68 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271)
% 0.20/0.68
% 0.20/0.68 %-------------------------------------------
% 0.20/0.69 cnf(59,plain,
% 0.20/0.69 (~P2(f8(a1),a2)),
% 0.20/0.69 inference(scs_inference,[],[30,34])).
% 0.20/0.69 cnf(61,plain,
% 0.20/0.69 (P3(a3,x611)),
% 0.20/0.69 inference(scs_inference,[],[29,30,34,33,39])).
% 0.20/0.69 cnf(62,plain,
% 0.20/0.69 (~P1(x621,a3)),
% 0.20/0.69 inference(rename_variables,[],[29])).
% 0.20/0.69 cnf(65,plain,
% 0.20/0.69 (~P1(x651,a3)),
% 0.20/0.69 inference(rename_variables,[],[29])).
% 0.20/0.69 cnf(67,plain,
% 0.20/0.69 (~E(a3,f8(a1))),
% 0.20/0.69 inference(scs_inference,[],[29,62,30,34,33,39,49,24])).
% 0.20/0.69 cnf(68,plain,
% 0.20/0.69 (~E(a2,a3)),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,30,34,33,39,49,24,23])).
% 0.20/0.69 cnf(69,plain,
% 0.20/0.69 (~P1(x691,a3)),
% 0.20/0.69 inference(rename_variables,[],[29])).
% 0.20/0.69 cnf(70,plain,
% 0.20/0.69 (~E(f8(a1),a3)),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,30,34,33,39,49,24,23,2])).
% 0.20/0.69 cnf(73,plain,
% 0.20/0.69 (~P1(x731,f4(a3,x732))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,30,34,33,39,49,24,23,2,57,53])).
% 0.20/0.69 cnf(77,plain,
% 0.20/0.69 (~P1(x771,f10(x772,a3))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,30,34,33,39,49,24,23,2,57,53,52,51])).
% 0.20/0.69 cnf(83,plain,
% 0.20/0.69 (~P1(f8(a1),f9(a2))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38])).
% 0.20/0.69 cnf(91,plain,
% 0.20/0.69 (P1(x911,f11(a3))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38,35,32,54,42])).
% 0.20/0.69 cnf(92,plain,
% 0.20/0.69 (~P1(x921,a3)),
% 0.20/0.69 inference(rename_variables,[],[29])).
% 0.20/0.69 cnf(95,plain,
% 0.20/0.69 (~E(a1,f5(f8(a1),a2))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38,35,32,54,42,27,22])).
% 0.20/0.69 cnf(96,plain,
% 0.20/0.69 (~P3(a2,a3)),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,92,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38,35,32,54,42,27,22,40])).
% 0.20/0.69 cnf(97,plain,
% 0.20/0.69 (~P1(x971,a3)),
% 0.20/0.69 inference(rename_variables,[],[29])).
% 0.20/0.69 cnf(99,plain,
% 0.20/0.69 (~P1(x991,f11(f9(a2)))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,92,97,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38,35,32,54,42,27,22,40,47])).
% 0.20/0.69 cnf(101,plain,
% 0.20/0.69 (P1(a1,f14(f11(a3)))),
% 0.20/0.69 inference(scs_inference,[],[28,29,62,65,69,92,97,30,34,33,39,49,24,23,2,57,53,52,51,44,43,38,35,32,54,42,27,22,40,47,45])).
% 0.20/0.69 cnf(118,plain,
% 0.20/0.69 (P1(x1181,f11(a3))),
% 0.20/0.69 inference(rename_variables,[],[91])).
% 0.20/0.69 cnf(124,plain,
% 0.20/0.69 (P3(x1241,f11(a3))),
% 0.20/0.69 inference(scs_inference,[],[29,91,118,83,101,70,48,47,58,46,54])).
% 0.20/0.69 cnf(130,plain,
% 0.20/0.69 (P3(a3,x1301)),
% 0.20/0.69 inference(rename_variables,[],[61])).
% 0.20/0.69 cnf(132,plain,
% 0.20/0.69 (~P1(x1321,f4(a3,x1322))),
% 0.20/0.69 inference(rename_variables,[],[73])).
% 0.20/0.69 cnf(144,plain,
% 0.20/0.69 (E(f5(f8(a1),a2),a1)),
% 0.20/0.69 inference(scs_inference,[],[28,29,30,73,132,99,91,118,96,59,61,130,83,101,70,48,47,58,46,54,42,24,23,50,39,26,25,41,38,32])).
% 0.20/0.69 cnf(146,plain,
% 0.20/0.69 (~E(f6(x1461,f9(a2)),f8(a1))),
% 0.20/0.69 inference(scs_inference,[],[28,29,30,73,132,99,91,118,96,59,61,130,83,95,101,70,48,47,58,46,54,42,24,23,50,39,26,25,41,38,32,2,22])).
% 0.20/0.69 cnf(162,plain,
% 0.20/0.69 (~P1(x1621,f10(x1622,a3))),
% 0.20/0.69 inference(rename_variables,[],[77])).
% 0.20/0.69 cnf(169,plain,
% 0.20/0.69 (P3(x1691,f11(f10(x1692,a3)))),
% 0.20/0.69 inference(scs_inference,[],[67,77,162,124,146,68,96,41,38,32,42,2,39,3,54])).
% 0.20/0.69 cnf(179,plain,
% 0.20/0.69 ($false),
% 0.20/0.69 inference(scs_inference,[],[30,169,95,96,144,25,39,2]),
% 0.20/0.69 ['proof']).
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time :0.060000s
%------------------------------------------------------------------------------