TSTP Solution File: SET884+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n006.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 14:31:34 EDT 2023
% Result : Theorem 66.92s 67.02s
% Output : CNFRefutation 66.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 15:45:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 66.92/67.01 %-------------------------------------------
% 66.92/67.01 % File :CSE---1.6
% 66.92/67.01 % Problem :theBenchmark
% 66.92/67.01 % Transform :cnf
% 66.92/67.01 % Format :tptp:raw
% 66.92/67.01 % Command :java -jar mcs_scs.jar %d %s
% 66.92/67.01
% 66.92/67.01 % Result :Theorem 66.380000s
% 66.92/67.01 % Output :CNFRefutation 66.380000s
% 66.92/67.01 %-------------------------------------------
% 66.92/67.02 %------------------------------------------------------------------------------
% 66.92/67.02 % File : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% 66.92/67.02 % Domain : Set theory
% 66.92/67.02 % Problem : ~ ( subset(singleton(A),unordered_pair(B,C)) & A != B & A != C )
% 66.92/67.02 % Version : [Urb06] axioms : Especial.
% 66.92/67.02 % English :
% 66.92/67.02
% 66.92/67.02 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 66.92/67.02 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 66.92/67.02 % Source : [Urb06]
% 66.92/67.02 % Names : zfmisc_1__t25_zfmisc_1 [Urb06]
% 66.92/67.02
% 66.92/67.02 % Status : Theorem
% 66.92/67.02 % Rating : 0.22 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.26 v5.5.0, 0.19 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.00 v5.0.0, 0.17 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.21 v3.3.0, 0.14 v3.2.0
% 66.92/67.02 % Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% 66.92/67.02 % Number of atoms : 19 ( 8 equ)
% 66.92/67.02 % Maximal formula atoms : 4 ( 2 avg)
% 66.92/67.02 % Number of connectives : 15 ( 5 ~; 1 |; 2 &)
% 66.92/67.02 % ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% 66.92/67.02 % Maximal formula depth : 8 ( 5 avg)
% 66.92/67.02 % Maximal term depth : 2 ( 1 avg)
% 66.92/67.02 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 66.92/67.02 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 66.92/67.02 % Number of variables : 21 ( 19 !; 2 ?)
% 66.92/67.02 % SPC : FOF_THM_RFO_SEQ
% 66.92/67.02
% 66.92/67.02 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 66.92/67.02 % library, www.mizar.org
% 66.92/67.02 %------------------------------------------------------------------------------
% 66.92/67.02 fof(antisymmetry_r2_hidden,axiom,
% 66.92/67.02 ! [A,B] :
% 66.92/67.02 ( in(A,B)
% 66.92/67.02 => ~ in(B,A) ) ).
% 66.92/67.02
% 66.92/67.02 fof(commutativity_k2_tarski,axiom,
% 66.92/67.02 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 66.92/67.02
% 66.92/67.02 fof(d1_tarski,axiom,
% 66.92/67.02 ! [A,B] :
% 66.92/67.02 ( B = singleton(A)
% 66.92/67.02 <=> ! [C] :
% 66.92/67.02 ( in(C,B)
% 66.92/67.02 <=> C = A ) ) ).
% 66.92/67.02
% 66.92/67.02 fof(d2_tarski,axiom,
% 66.92/67.02 ! [A,B,C] :
% 66.92/67.02 ( C = unordered_pair(A,B)
% 66.92/67.02 <=> ! [D] :
% 66.92/67.02 ( in(D,C)
% 66.92/67.02 <=> ( D = A
% 66.92/67.02 | D = B ) ) ) ).
% 66.92/67.02
% 66.92/67.02 fof(d3_tarski,axiom,
% 66.92/67.02 ! [A,B] :
% 66.92/67.02 ( subset(A,B)
% 66.92/67.02 <=> ! [C] :
% 66.92/67.02 ( in(C,A)
% 66.92/67.02 => in(C,B) ) ) ).
% 66.92/67.02
% 66.92/67.02 fof(rc1_xboole_0,axiom,
% 66.92/67.02 ? [A] : empty(A) ).
% 66.92/67.02
% 66.92/67.02 fof(rc2_xboole_0,axiom,
% 66.92/67.02 ? [A] : ~ empty(A) ).
% 66.92/67.02
% 66.92/67.02 fof(reflexivity_r1_tarski,axiom,
% 66.92/67.02 ! [A,B] : subset(A,A) ).
% 66.92/67.02
% 66.92/67.02 fof(t25_zfmisc_1,conjecture,
% 66.92/67.02 ! [A,B,C] :
% 66.92/67.02 ~ ( subset(singleton(A),unordered_pair(B,C))
% 66.92/67.02 & A != B
% 66.92/67.02 & A != C ) ).
% 66.92/67.02
% 66.92/67.02 %------------------------------------------------------------------------------
% 66.92/67.02 %-------------------------------------------
% 66.92/67.02 % Proof found
% 66.92/67.02 % SZS status Theorem for theBenchmark
% 66.92/67.02 % SZS output start Proof
% 66.92/67.03 %ClaNum:39(EqnAxiom:18)
% 66.92/67.03 %VarNum:114(SingletonVarNum:43)
% 66.92/67.03 %MaxLitNum:4
% 66.92/67.03 %MaxfuncDepth:1
% 66.92/67.03 %SharedTerms:12
% 66.92/67.03 %goalClause: 22 23 24
% 66.92/67.03 %singleGoalClaCount:3
% 66.92/67.03 [19]P1(a1)
% 66.92/67.03 [23]~E(a9,a6)
% 66.92/67.03 [24]~E(a10,a6)
% 66.92/67.03 [25]~P1(a7)
% 66.92/67.03 [22]P2(f8(a6),f5(a9,a10))
% 66.92/67.03 [20]P2(x201,x201)
% 66.92/67.03 [21]E(f5(x211,x212),f5(x212,x211))
% 66.92/67.03 [30]~P3(x302,x301)+~P3(x301,x302)
% 66.92/67.03 [32]P2(x321,x322)+P3(f2(x321,x322),x321)
% 66.92/67.03 [35]P2(x351,x352)+~P3(f2(x351,x352),x352)
% 66.92/67.03 [34]E(f3(x342,x341),x342)+P3(f3(x342,x341),x341)+E(x341,f8(x342))
% 66.92/67.03 [36]~E(f3(x362,x361),x362)+~P3(f3(x362,x361),x361)+E(x361,f8(x362))
% 66.92/67.03 [33]~P2(x333,x332)+P3(x331,x332)+~P3(x331,x333)
% 66.92/67.03 [26]P3(x261,x262)+~E(x261,x263)+~E(x262,f8(x263))
% 66.92/67.03 [27]~P3(x271,x273)+E(x271,x272)+~E(x273,f8(x272))
% 66.92/67.03 [38]~E(f4(x382,x383,x381),x383)+~P3(f4(x382,x383,x381),x381)+E(x381,f5(x382,x383))
% 66.92/67.03 [39]~E(f4(x392,x393,x391),x392)+~P3(f4(x392,x393,x391),x391)+E(x391,f5(x392,x393))
% 66.92/67.03 [28]P3(x281,x282)+~E(x281,x283)+~E(x282,f5(x284,x283))
% 66.92/67.03 [29]P3(x291,x292)+~E(x291,x293)+~E(x292,f5(x293,x294))
% 66.92/67.03 [37]E(f4(x372,x373,x371),x373)+E(f4(x372,x373,x371),x372)+P3(f4(x372,x373,x371),x371)+E(x371,f5(x372,x373))
% 66.92/67.03 [31]~P3(x311,x314)+E(x311,x312)+E(x311,x313)+~E(x314,f5(x313,x312))
% 66.92/67.03 %EqnAxiom
% 66.92/67.03 [1]E(x11,x11)
% 66.92/67.03 [2]E(x22,x21)+~E(x21,x22)
% 66.92/67.03 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 66.92/67.03 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 66.92/67.03 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 66.92/67.03 [6]~E(x61,x62)+E(f4(x61,x63,x64),f4(x62,x63,x64))
% 66.92/67.03 [7]~E(x71,x72)+E(f4(x73,x71,x74),f4(x73,x72,x74))
% 66.92/67.03 [8]~E(x81,x82)+E(f4(x83,x84,x81),f4(x83,x84,x82))
% 66.92/67.03 [9]~E(x91,x92)+E(f8(x91),f8(x92))
% 66.92/67.03 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103))
% 66.92/67.03 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112))
% 66.92/67.03 [12]~E(x121,x122)+E(f2(x121,x123),f2(x122,x123))
% 66.92/67.03 [13]~E(x131,x132)+E(f2(x133,x131),f2(x133,x132))
% 66.92/67.03 [14]~P1(x141)+P1(x142)+~E(x141,x142)
% 66.92/67.03 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 66.92/67.03 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 66.92/67.03 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173)
% 66.92/67.03 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181)
% 66.92/67.03
% 66.92/67.03 %-------------------------------------------
% 66.92/67.04 cnf(40,plain,
% 66.92/67.04 (P2(f8(a6),f5(a10,a9))),
% 66.92/67.04 inference(scs_inference,[],[22,21,16])).
% 66.92/67.04 cnf(41,plain,
% 66.92/67.04 (E(f5(x411,x412),f5(x412,x411))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(42,plain,
% 66.92/67.04 (P2(f5(x421,x422),f5(x422,x421))),
% 66.92/67.04 inference(scs_inference,[],[22,20,21,41,16,15])).
% 66.92/67.04 cnf(44,plain,
% 66.92/67.04 (~P3(a9,f5(a6,a6))),
% 66.92/67.04 inference(scs_inference,[],[22,20,23,21,41,16,15,31])).
% 66.92/67.04 cnf(47,plain,
% 66.92/67.04 (~E(a6,a9)),
% 66.92/67.04 inference(scs_inference,[],[22,20,23,21,41,16,15,31,2])).
% 66.92/67.04 cnf(49,plain,
% 66.92/67.04 (~E(a1,a7)),
% 66.92/67.04 inference(scs_inference,[],[22,20,23,19,25,21,41,16,15,31,2,17,14])).
% 66.92/67.04 cnf(64,plain,
% 66.92/67.04 (~P3(x641,f8(a6))+P3(x641,f5(a9,a10))),
% 66.92/67.04 inference(scs_inference,[],[22,33])).
% 66.92/67.04 cnf(85,plain,
% 66.92/67.04 (~E(a6,a10)),
% 66.92/67.04 inference(scs_inference,[],[24,2])).
% 66.92/67.04 cnf(87,plain,
% 66.92/67.04 (P3(f5(x871,x872),x873)+~E(x873,f8(f5(x872,x871)))),
% 66.92/67.04 inference(scs_inference,[],[21,26])).
% 66.92/67.04 cnf(90,plain,
% 66.92/67.04 (P3(f5(x902,x901),f8(f5(x901,x902)))),
% 66.92/67.04 inference(equality_inference,[],[87])).
% 66.92/67.04 cnf(93,plain,
% 66.92/67.04 (~P3(f8(f5(x931,x932)),f5(x932,x931))),
% 66.92/67.04 inference(scs_inference,[],[90,30])).
% 66.92/67.04 cnf(95,plain,
% 66.92/67.04 (~E(f8(f5(x951,x952)),x951)),
% 66.92/67.04 inference(scs_inference,[],[21,90,30,29])).
% 66.92/67.04 cnf(97,plain,
% 66.92/67.04 (~E(f5(f8(x971),x972),x971)),
% 66.92/67.04 inference(scs_inference,[],[21,90,30,29,9])).
% 66.92/67.04 cnf(106,plain,
% 66.92/67.04 (~P3(a1,x1061)+~E(f5(a9,a10),f5(a6,a6))+~E(x1061,f5(a7,a7))),
% 66.92/67.04 inference(scs_inference,[],[42,44,21,90,49,30,29,9,18,64,33,28,31])).
% 66.92/67.04 cnf(112,plain,
% 66.92/67.04 (E(f5(x1121,x1122),f5(x1122,x1121))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(115,plain,
% 66.92/67.04 (P3(f5(x1151,x1152),f8(f5(x1151,x1152)))),
% 66.92/67.04 inference(scs_inference,[],[21,112,95,90,31,17])).
% 66.92/67.04 cnf(118,plain,
% 66.92/67.04 (E(f5(x1181,x1182),f5(x1182,x1181))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(120,plain,
% 66.92/67.04 (~E(f5(x1201,f8(x1202)),x1202)),
% 66.92/67.04 inference(scs_inference,[],[21,112,118,95,97,90,31,17,106,3])).
% 66.92/67.04 cnf(122,plain,
% 66.92/67.04 (E(f5(x1221,x1222),f5(x1222,x1221))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(125,plain,
% 66.92/67.04 (P3(f5(a7,a7),f5(x1251,x1252))+~E(f8(f5(a7,a7)),f8(x1252))),
% 66.92/67.04 inference(scs_inference,[],[21,112,118,122,95,97,90,31,17,106,3,27,29])).
% 66.92/67.04 cnf(133,plain,
% 66.92/67.04 (P3(f5(a7,a7),f5(x1331,f5(a7,a7)))),
% 66.92/67.04 inference(equality_inference,[],[125])).
% 66.92/67.04 cnf(135,plain,
% 66.92/67.04 (~E(f5(x1351,f8(x1352)),x1352)),
% 66.92/67.04 inference(rename_variables,[],[120])).
% 66.92/67.04 cnf(142,plain,
% 66.92/67.04 (E(f5(x1421,x1422),f5(x1422,x1421))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(145,plain,
% 66.92/67.04 (P3(f5(x1451,x1452),x1453)+~E(x1453,f5(x1454,f5(x1452,x1451)))),
% 66.92/67.04 inference(scs_inference,[],[40,21,142,93,115,120,135,133,5,30,33,18,2,15,28])).
% 66.92/67.04 cnf(151,plain,
% 66.92/67.04 (P3(f5(x1511,x1512),f5(x1513,f5(x1512,x1511)))),
% 66.92/67.04 inference(equality_inference,[],[145])).
% 66.92/67.04 cnf(156,plain,
% 66.92/67.04 (P3(f5(x1561,x1562),f5(f5(x1562,x1561),x1563))),
% 66.92/67.04 inference(scs_inference,[],[21,151,30,18])).
% 66.92/67.04 cnf(158,plain,
% 66.92/67.04 (E(f5(x1581,x1582),f5(x1582,x1581))),
% 66.92/67.04 inference(rename_variables,[],[21])).
% 66.92/67.04 cnf(159,plain,
% 66.92/67.04 (~P3(f5(f5(x1591,x1592),x1593),f5(x1592,x1591))),
% 66.92/67.04 inference(scs_inference,[],[21,158,151,30,18,17])).
% 66.92/67.04 cnf(191,plain,
% 66.92/67.04 (~P3(a1,x1911)+~E(x1911,f8(a7))),
% 66.92/67.04 inference(scs_inference,[],[21,49,159,156,17,28,30,27])).
% 66.92/67.04 cnf(193,plain,
% 66.92/67.04 (~P3(a1,f8(a7))),
% 66.92/67.04 inference(equality_inference,[],[191])).
% 66.92/67.04 cnf(286,plain,
% 66.92/67.04 (~E(a1,x2861)+~E(f8(a7),f5(x2862,x2861))),
% 66.92/67.04 inference(scs_inference,[],[193,28])).
% 66.92/67.04 cnf(307,plain,
% 66.92/67.04 (~E(f5(x3071,x3072),f8(a7))+~E(a1,x3072)),
% 66.92/67.04 inference(scs_inference,[],[286,2])).
% 66.92/67.04 cnf(318,plain,
% 66.92/67.04 (~E(f5(x3181,x3182),f8(a7))+~E(a1,x3181)),
% 66.92/67.04 inference(scs_inference,[],[21,307,3])).
% 66.92/67.04 cnf(328,plain,
% 66.92/67.04 (~P3(a6,x3281)+~E(x3281,f8(a10))),
% 66.92/67.04 inference(scs_inference,[],[85,27])).
% 66.92/67.04 cnf(333,plain,
% 66.92/67.04 (~P3(a6,f8(a10))),
% 66.92/67.04 inference(equality_inference,[],[328])).
% 66.92/67.04 cnf(337,plain,
% 66.92/67.04 (~E(f8(a7),f5(x3371,x3372))+~E(a1,x3371)),
% 66.92/67.04 inference(scs_inference,[],[318,2])).
% 66.92/67.04 cnf(345,plain,
% 66.92/67.04 (~P3(f8(a7),f5(f5(x3451,x3452),f5(x3451,x3452)))+~E(a1,x3451)),
% 66.92/67.04 inference(scs_inference,[],[21,337,31])).
% 66.92/67.04 cnf(346,plain,
% 66.92/67.04 (~P3(f8(a7),f5(f5(a1,x3461),f5(a1,x3461)))),
% 66.92/67.04 inference(equality_inference,[],[345])).
% 66.92/67.04 cnf(353,plain,
% 66.92/67.04 (~E(x3531,a9)+~E(a6,x3531)),
% 66.92/67.04 inference(scs_inference,[],[346,333,47,21,29,2,28,3])).
% 66.92/67.04 cnf(1649,plain,
% 66.92/67.04 (~P3(a6,f5(x16491,a10))+~E(x16491,a9)),
% 66.92/67.04 inference(scs_inference,[],[85,21,353,31])).
% 66.92/67.04 cnf(1650,plain,
% 66.92/67.04 (~P3(a6,f5(a9,a10))),
% 66.92/67.04 inference(equality_inference,[],[1649])).
% 66.92/67.04 cnf(1651,plain,
% 66.92/67.04 (~P3(a6,f8(a6))),
% 66.92/67.04 inference(scs_inference,[],[22,1650,33])).
% 66.92/67.04 cnf(1705,plain,
% 66.92/67.04 (~E(a6,x17051)+~E(f8(a6),f8(x17051))),
% 66.92/67.04 inference(scs_inference,[],[1651,26])).
% 66.92/67.05 cnf(1710,plain,
% 66.92/67.05 (~E(f8(x17101),f8(a6))+~E(a6,x17101)),
% 66.92/67.05 inference(scs_inference,[],[1705,2])).
% 66.92/67.05 cnf(1716,plain,
% 66.92/67.05 (~E(x17161,a6)+~E(a6,x17161)),
% 66.92/67.05 inference(scs_inference,[],[1710,9])).
% 66.92/67.05 cnf(1717,plain,
% 66.92/67.05 (~P3(a6,f5(x17171,a10))+~E(x17171,a6)),
% 66.92/67.05 inference(scs_inference,[],[21,85,1716,31])).
% 66.92/67.05 cnf(1718,plain,
% 66.92/67.05 (~P3(a6,f5(a6,a10))),
% 66.92/67.05 inference(equality_inference,[],[1717])).
% 66.92/67.05 cnf(1740,plain,
% 66.92/67.05 (~P3(a6,f5(a10,a6))),
% 66.92/67.05 inference(scs_inference,[],[1718,21,17,18])).
% 66.92/67.05 cnf(1771,plain,
% 66.92/67.05 (E(f5(x17711,x17712),f5(x17712,x17711))),
% 66.92/67.05 inference(rename_variables,[],[21])).
% 66.92/67.05 cnf(1775,plain,
% 66.92/67.05 ($false),
% 66.92/67.05 inference(scs_inference,[],[1718,21,1771,1740,28,29]),
% 66.92/67.05 ['proof']).
% 66.92/67.05 % SZS output end Proof
% 66.92/67.05 % Total time :66.380000s
%------------------------------------------------------------------------------