TSTP Solution File: SET908+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET908+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 : n002.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 14:31:39 EDT 2023
% Result : Theorem 0.23s 0.70s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.16 % Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.38 % Computer : n002.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sat Aug 26 13:50:18 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.23/0.61 start to proof:theBenchmark
% 0.23/0.69 %-------------------------------------------
% 0.23/0.69 % File :CSE---1.6
% 0.23/0.69 % Problem :theBenchmark
% 0.23/0.69 % Transform :cnf
% 0.23/0.69 % Format :tptp:raw
% 0.23/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.23/0.69
% 0.23/0.69 % Result :Theorem 0.030000s
% 0.23/0.69 % Output :CNFRefutation 0.030000s
% 0.23/0.69 %-------------------------------------------
% 0.23/0.69 %------------------------------------------------------------------------------
% 0.23/0.69 % File : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% 0.23/0.69 % Domain : Set theory
% 0.23/0.69 % Problem : union(singleton(A),B) != empty_set
% 0.23/0.69 % Version : [Urb06] axioms : Especial.
% 0.23/0.69 % English :
% 0.23/0.69
% 0.23/0.69 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.23/0.69 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.23/0.69 % Source : [Urb06]
% 0.23/0.69 % Names : zfmisc_1__t49_zfmisc_1 [Urb06]
% 0.23/0.69
% 0.23/0.69 % Status : Theorem
% 0.23/0.69 % Rating : 0.14 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.12 v6.2.0, 0.28 v6.1.0, 0.30 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0
% 0.23/0.69 % Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% 0.23/0.69 % Number of atoms : 21 ( 7 equ)
% 0.23/0.69 % Maximal formula atoms : 4 ( 1 avg)
% 0.23/0.69 % Number of connectives : 17 ( 8 ~; 1 |; 0 &)
% 0.23/0.69 % ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% 0.23/0.69 % Maximal formula depth : 8 ( 4 avg)
% 0.23/0.69 % Maximal term depth : 3 ( 1 avg)
% 0.23/0.69 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.23/0.69 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.23/0.69 % Number of variables : 23 ( 21 !; 2 ?)
% 0.23/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.23/0.69
% 0.23/0.69 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.23/0.69 % library, www.mizar.org
% 0.23/0.69 %------------------------------------------------------------------------------
% 0.23/0.69 fof(antisymmetry_r2_hidden,axiom,
% 0.23/0.69 ! [A,B] :
% 0.23/0.69 ( in(A,B)
% 0.23/0.69 => ~ in(B,A) ) ).
% 0.23/0.69
% 0.23/0.69 fof(commutativity_k2_xboole_0,axiom,
% 0.23/0.69 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.23/0.69
% 0.23/0.69 fof(d1_tarski,axiom,
% 0.23/0.69 ! [A,B] :
% 0.23/0.69 ( B = singleton(A)
% 0.23/0.69 <=> ! [C] :
% 0.23/0.69 ( in(C,B)
% 0.23/0.69 <=> C = A ) ) ).
% 0.23/0.69
% 0.23/0.69 fof(d1_xboole_0,axiom,
% 0.23/0.69 ! [A] :
% 0.23/0.69 ( A = empty_set
% 0.23/0.69 <=> ! [B] : ~ in(B,A) ) ).
% 0.23/0.69
% 0.23/0.69 fof(d2_xboole_0,axiom,
% 0.23/0.69 ! [A,B,C] :
% 0.23/0.70 ( C = set_union2(A,B)
% 0.23/0.70 <=> ! [D] :
% 0.23/0.70 ( in(D,C)
% 0.23/0.70 <=> ( in(D,A)
% 0.23/0.70 | in(D,B) ) ) ) ).
% 0.23/0.70
% 0.23/0.70 fof(fc1_xboole_0,axiom,
% 0.23/0.70 empty(empty_set) ).
% 0.23/0.70
% 0.23/0.70 fof(fc2_xboole_0,axiom,
% 0.23/0.70 ! [A,B] :
% 0.23/0.70 ( ~ empty(A)
% 0.23/0.70 => ~ empty(set_union2(A,B)) ) ).
% 0.23/0.70
% 0.23/0.70 fof(fc3_xboole_0,axiom,
% 0.23/0.70 ! [A,B] :
% 0.23/0.70 ( ~ empty(A)
% 0.23/0.70 => ~ empty(set_union2(B,A)) ) ).
% 0.23/0.70
% 0.23/0.70 fof(idempotence_k2_xboole_0,axiom,
% 0.23/0.70 ! [A,B] : set_union2(A,A) = A ).
% 0.23/0.70
% 0.23/0.70 fof(rc1_xboole_0,axiom,
% 0.23/0.70 ? [A] : empty(A) ).
% 0.23/0.70
% 0.23/0.70 fof(rc2_xboole_0,axiom,
% 0.23/0.70 ? [A] : ~ empty(A) ).
% 0.23/0.70
% 0.23/0.70 fof(t49_zfmisc_1,conjecture,
% 0.23/0.70 ! [A,B] : set_union2(singleton(A),B) != empty_set ).
% 0.23/0.70
% 0.23/0.70 %------------------------------------------------------------------------------
% 0.23/0.70 %-------------------------------------------
% 0.23/0.70 % Proof found
% 0.23/0.70 % SZS status Theorem for theBenchmark
% 0.23/0.70 % SZS output start Proof
% 0.23/0.70 %ClaNum:36(EqnAxiom:15)
% 0.23/0.70 %VarNum:111(SingletonVarNum:43)
% 0.23/0.70 %MaxLitNum:4
% 0.23/0.70 %MaxfuncDepth:2
% 0.23/0.70 %SharedTerms:11
% 0.23/0.70 %goalClause: 19
% 0.23/0.70 %singleGoalClaCount:1
% 0.23/0.70 [16]P1(a1)
% 0.23/0.70 [17]P1(a2)
% 0.23/0.70 [21]~P1(a8)
% 0.23/0.70 [19]E(f6(f10(a7),a9),a1)
% 0.23/0.70 [18]E(f6(x181,x181),x181)
% 0.23/0.70 [20]E(f6(x201,x202),f6(x202,x201))
% 0.23/0.70 [22]P2(f3(x221),x221)+E(x221,a1)
% 0.23/0.70 [23]~P2(x232,x231)+~E(x231,a1)
% 0.23/0.70 [26]~P2(x262,x261)+~P2(x261,x262)
% 0.23/0.70 [27]P1(x271)+~P1(f6(x272,x271))
% 0.23/0.70 [28]P1(x281)+~P1(f6(x281,x282))
% 0.23/0.70 [29]E(f4(x292,x291),x292)+P2(f4(x292,x291),x291)+E(x291,f10(x292))
% 0.23/0.70 [33]~E(f4(x332,x331),x332)+~P2(f4(x332,x331),x331)+E(x331,f10(x332))
% 0.23/0.70 [24]P2(x241,x242)+~E(x241,x243)+~E(x242,f10(x243))
% 0.23/0.70 [25]~P2(x251,x253)+E(x251,x252)+~E(x253,f10(x252))
% 0.23/0.70 [35]~P2(f5(x352,x353,x351),x351)+~P2(f5(x352,x353,x351),x353)+E(x351,f6(x352,x353))
% 0.23/0.70 [36]~P2(f5(x362,x363,x361),x361)+~P2(f5(x362,x363,x361),x362)+E(x361,f6(x362,x363))
% 0.23/0.70 [30]~P2(x301,x304)+P2(x301,x302)+~E(x302,f6(x303,x304))
% 0.23/0.70 [31]~P2(x311,x313)+P2(x311,x312)+~E(x312,f6(x313,x314))
% 0.23/0.70 [34]P2(f5(x342,x343,x341),x341)+P2(f5(x342,x343,x341),x343)+P2(f5(x342,x343,x341),x342)+E(x341,f6(x342,x343))
% 0.23/0.70 [32]~P2(x321,x324)+P2(x321,x322)+P2(x321,x323)+~E(x324,f6(x323,x322))
% 0.23/0.70 %EqnAxiom
% 0.23/0.70 [1]E(x11,x11)
% 0.23/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.23/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.23/0.70 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.23/0.70 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.23/0.70 [6]~E(x61,x62)+E(f10(x61),f10(x62))
% 0.23/0.70 [7]~E(x71,x72)+E(f5(x71,x73,x74),f5(x72,x73,x74))
% 0.23/0.70 [8]~E(x81,x82)+E(f5(x83,x81,x84),f5(x83,x82,x84))
% 0.23/0.70 [9]~E(x91,x92)+E(f5(x93,x94,x91),f5(x93,x94,x92))
% 0.23/0.70 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.23/0.70 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.23/0.70 [12]~E(x121,x122)+E(f3(x121),f3(x122))
% 0.23/0.70 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.23/0.70 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.23/0.70 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.23/0.70
% 0.23/0.70 %-------------------------------------------
% 0.23/0.70 cnf(38,plain,
% 0.23/0.70 (~P2(x381,f6(f10(a7),a9))),
% 0.23/0.70 inference(scs_inference,[],[19,2,23])).
% 0.23/0.70 cnf(41,plain,
% 0.23/0.70 (E(f6(x411,x411),x411)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(42,plain,
% 0.23/0.70 (~P2(x421,a9)),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,20,2,23,13,31])).
% 0.23/0.70 cnf(43,plain,
% 0.23/0.70 (E(f6(x431,x432),f6(x432,x431))),
% 0.23/0.70 inference(rename_variables,[],[20])).
% 0.23/0.70 cnf(45,plain,
% 0.23/0.70 (~P2(x451,f10(a7))),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,20,43,2,23,13,31,30])).
% 0.23/0.70 cnf(46,plain,
% 0.23/0.70 (E(f6(x461,x462),f6(x462,x461))),
% 0.23/0.70 inference(rename_variables,[],[20])).
% 0.23/0.70 cnf(48,plain,
% 0.23/0.70 (P2(f6(f10(a7),a9),f6(f10(a1),f10(a1)))),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,41,20,43,2,23,13,31,30,24])).
% 0.23/0.70 cnf(49,plain,
% 0.23/0.70 (E(f6(x491,x491),x491)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(51,plain,
% 0.23/0.70 (P2(f6(f10(a7),a9),f10(a1))),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,41,20,43,46,2,23,13,31,30,24,32])).
% 0.23/0.70 cnf(66,plain,
% 0.23/0.70 (E(f10(f6(x661,x661)),f10(x661))),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,41,49,20,43,46,2,23,13,31,30,24,32,28,27,22,12,11,10,9,8,7,6])).
% 0.23/0.70 cnf(70,plain,
% 0.23/0.70 (E(f6(x701,x701),x701)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(71,plain,
% 0.23/0.70 (~P2(f6(f3(a9),f3(a9)),f6(a9,a9))),
% 0.23/0.70 inference(scs_inference,[],[19,21,18,41,49,70,20,43,46,2,23,13,31,30,24,32,28,27,22,12,11,10,9,8,7,6,5,4,15,14])).
% 0.23/0.70 cnf(78,plain,
% 0.23/0.70 (~P2(x781,f6(f10(a7),a9))),
% 0.23/0.70 inference(rename_variables,[],[38])).
% 0.23/0.70 cnf(87,plain,
% 0.23/0.70 (~P2(x871,f10(f6(a7,a7)))),
% 0.23/0.70 inference(scs_inference,[],[66,38,78,45,48,51,31,30,2,23,4,15])).
% 0.23/0.70 cnf(88,plain,
% 0.23/0.70 (E(f10(f6(x881,x881)),f10(x881))),
% 0.23/0.70 inference(rename_variables,[],[66])).
% 0.23/0.70 cnf(90,plain,
% 0.23/0.70 (E(f6(x901,x901),x901)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(92,plain,
% 0.23/0.70 (~P2(f6(f10(a1),f10(a1)),f6(f10(a1),f10(a1)))),
% 0.23/0.70 inference(scs_inference,[],[18,90,66,71,38,78,45,48,51,31,30,2,23,4,15,24,25])).
% 0.23/0.70 cnf(93,plain,
% 0.23/0.70 (E(f6(x931,x931),x931)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(109,plain,
% 0.23/0.70 (P2(f3(a7),a7)),
% 0.23/0.70 inference(scs_inference,[],[19,16,18,90,93,21,66,88,71,38,78,45,48,51,31,30,2,23,4,15,24,25,14,5,13,3,29,26,6,32,22])).
% 0.23/0.70 cnf(112,plain,
% 0.23/0.70 (E(f6(x1121,x1122),f6(x1122,x1121))),
% 0.23/0.70 inference(rename_variables,[],[20])).
% 0.23/0.70 cnf(117,plain,
% 0.23/0.70 (E(f6(x1171,x1171),x1171)),
% 0.23/0.70 inference(rename_variables,[],[18])).
% 0.23/0.70 cnf(120,plain,
% 0.23/0.70 (~P2(x1201,f10(f6(a7,a7)))),
% 0.23/0.70 inference(rename_variables,[],[87])).
% 0.23/0.70 cnf(126,plain,
% 0.23/0.70 (~P2(x1261,f10(f6(a7,a7)))),
% 0.23/0.70 inference(rename_variables,[],[87])).
% 0.23/0.70 cnf(130,plain,
% 0.23/0.70 ($false),
% 0.23/0.70 inference(scs_inference,[],[20,112,18,117,92,87,120,126,109,42,66,31,26,23,30,32,22,6,4,24]),
% 0.23/0.70 ['proof']).
% 0.23/0.70 % SZS output end Proof
% 0.23/0.70 % Total time :0.030000s
%------------------------------------------------------------------------------