TSTP Solution File: SET974+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET974+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 : n007.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 14:31:51 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:32:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.010000s
% 0.19/0.62 % Output :CNFRefutation 0.010000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 % File : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.62 % Domain : Set theory
% 0.19/0.62 % Problem : Basic properties of sets, theorem 127
% 0.19/0.62 % Version : [Urb06] axioms : Especial.
% 0.19/0.62 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.63 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.63 % Source : [Urb06]
% 0.19/0.63 % Names : zfmisc_1__t127_zfmisc_1 [Urb06]
% 0.19/0.63
% 0.19/0.63 % Status : Theorem
% 0.19/0.63 % Rating : 0.17 v8.1.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.21 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0, 0.21 v3.2.0
% 0.19/0.63 % Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% 0.19/0.63 % Number of atoms : 22 ( 5 equ)
% 0.19/0.63 % Maximal formula atoms : 4 ( 1 avg)
% 0.19/0.63 % Number of connectives : 19 ( 9 ~; 1 |; 6 &)
% 0.19/0.63 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.63 % Maximal formula depth : 13 ( 5 avg)
% 0.19/0.63 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.63 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.19/0.63 % Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% 0.19/0.63 % Number of variables : 31 ( 28 !; 3 ?)
% 0.19/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.63
% 0.19/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.63 % library, www.mizar.org
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( in(A,B)
% 0.19/0.63 => ~ in(B,A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(commutativity_k2_tarski,axiom,
% 0.19/0.63 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.19/0.63
% 0.19/0.63 fof(commutativity_k3_xboole_0,axiom,
% 0.19/0.63 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.19/0.63
% 0.19/0.63 fof(d5_tarski,axiom,
% 0.19/0.63 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
% 0.19/0.63
% 0.19/0.63 fof(fc1_zfmisc_1,axiom,
% 0.19/0.63 ! [A,B] : ~ empty(ordered_pair(A,B)) ).
% 0.19/0.63
% 0.19/0.63 fof(idempotence_k3_xboole_0,axiom,
% 0.19/0.63 ! [A,B] : set_intersection2(A,A) = A ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_xboole_0,axiom,
% 0.19/0.63 ? [A] : empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_xboole_0,axiom,
% 0.19/0.63 ? [A] : ~ empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(symmetry_r1_xboole_0,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( disjoint(A,B)
% 0.19/0.63 => disjoint(B,A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t104_zfmisc_1,axiom,
% 0.19/0.63 ! [A,B,C,D,E] :
% 0.19/0.63 ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
% 0.19/0.63 & ! [F,G] :
% 0.19/0.63 ~ ( A = ordered_pair(F,G)
% 0.19/0.63 & in(F,set_intersection2(B,D))
% 0.19/0.63 & in(G,set_intersection2(C,E)) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t127_zfmisc_1,conjecture,
% 0.19/0.63 ! [A,B,C,D] :
% 0.19/0.63 ( ( disjoint(A,B)
% 0.19/0.63 | disjoint(C,D) )
% 0.19/0.63 => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t4_xboole_0,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( ~ ( ~ disjoint(A,B)
% 0.19/0.63 & ! [C] : ~ in(C,set_intersection2(A,B)) )
% 0.19/0.63 & ~ ( ? [C] : in(C,set_intersection2(A,B))
% 0.19/0.63 & disjoint(A,B) ) ) ).
% 0.19/0.63
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:42(EqnAxiom:27)
% 0.19/0.63 %VarNum:78(SingletonVarNum:31)
% 0.19/0.63 %MaxLitNum:2
% 0.19/0.63 %MaxfuncDepth:3
% 0.19/0.63 %SharedTerms:13
% 0.19/0.63 %goalClause: 33 35
% 0.19/0.63 %singleGoalClaCount:1
% 0.19/0.63 [28]P1(a1)
% 0.19/0.63 [32]~P1(a4)
% 0.19/0.63 [33]~P2(f2(a5,a8),f2(a9,a10))
% 0.19/0.63 [29]E(f3(x291,x291),x291)
% 0.19/0.63 [30]E(f12(x301,x302),f12(x302,x301))
% 0.19/0.63 [31]E(f3(x311,x312),f3(x312,x311))
% 0.19/0.63 [34]~P1(f12(f12(x341,x342),f13(x341)))
% 0.19/0.63 [35]P2(a5,a9)+P2(a8,a10)
% 0.19/0.63 [36]~P2(x362,x361)+P2(x361,x362)
% 0.19/0.63 [37]~P3(x372,x371)+~P3(x371,x372)
% 0.19/0.63 [38]P2(x381,x382)+P3(f11(x381,x382),f3(x381,x382))
% 0.19/0.63 [39]~P2(x391,x392)+~P3(x393,f3(x391,x392))
% 0.19/0.63 [40]P3(f6(x401,x402,x403,x404,x405),f3(x402,x404))+~P3(x401,f3(f2(x402,x403),f2(x404,x405)))
% 0.19/0.63 [41]P3(f7(x411,x412,x413,x414,x415),f3(x413,x415))+~P3(x411,f3(f2(x412,x413),f2(x414,x415)))
% 0.19/0.63 [42]~P3(x421,f3(f2(x422,x423),f2(x424,x425)))+E(f12(f12(f6(x421,x422,x423,x424,x425),f7(x421,x422,x423,x424,x425)),f13(f6(x421,x422,x423,x424,x425))),x421)
% 0.19/0.63 %EqnAxiom
% 0.19/0.63 [1]E(x11,x11)
% 0.19/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.63 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.19/0.63 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.19/0.63 [6]~E(x61,x62)+E(f12(x61,x63),f12(x62,x63))
% 0.19/0.63 [7]~E(x71,x72)+E(f12(x73,x71),f12(x73,x72))
% 0.19/0.63 [8]~E(x81,x82)+E(f6(x81,x83,x84,x85,x86),f6(x82,x83,x84,x85,x86))
% 0.19/0.63 [9]~E(x91,x92)+E(f6(x93,x91,x94,x95,x96),f6(x93,x92,x94,x95,x96))
% 0.19/0.63 [10]~E(x101,x102)+E(f6(x103,x104,x101,x105,x106),f6(x103,x104,x102,x105,x106))
% 0.19/0.63 [11]~E(x111,x112)+E(f6(x113,x114,x115,x111,x116),f6(x113,x114,x115,x112,x116))
% 0.19/0.63 [12]~E(x121,x122)+E(f6(x123,x124,x125,x126,x121),f6(x123,x124,x125,x126,x122))
% 0.19/0.63 [13]~E(x131,x132)+E(f2(x131,x133),f2(x132,x133))
% 0.19/0.63 [14]~E(x141,x142)+E(f2(x143,x141),f2(x143,x142))
% 0.19/0.63 [15]~E(x151,x152)+E(f7(x151,x153,x154,x155,x156),f7(x152,x153,x154,x155,x156))
% 0.19/0.63 [16]~E(x161,x162)+E(f7(x163,x161,x164,x165,x166),f7(x163,x162,x164,x165,x166))
% 0.19/0.63 [17]~E(x171,x172)+E(f7(x173,x174,x171,x175,x176),f7(x173,x174,x172,x175,x176))
% 0.19/0.63 [18]~E(x181,x182)+E(f7(x183,x184,x185,x181,x186),f7(x183,x184,x185,x182,x186))
% 0.19/0.63 [19]~E(x191,x192)+E(f7(x193,x194,x195,x196,x191),f7(x193,x194,x195,x196,x192))
% 0.19/0.63 [20]~E(x201,x202)+E(f13(x201),f13(x202))
% 0.19/0.63 [21]~E(x211,x212)+E(f11(x211,x213),f11(x212,x213))
% 0.19/0.63 [22]~E(x221,x222)+E(f11(x223,x221),f11(x223,x222))
% 0.19/0.63 [23]~P1(x231)+P1(x232)+~E(x231,x232)
% 0.19/0.63 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243)
% 0.19/0.63 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251)
% 0.19/0.63 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263)
% 0.19/0.63 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271)
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(43,plain,
% 0.19/0.63 (E(x431,f3(x431,x431))),
% 0.19/0.63 inference(scs_inference,[],[29,2])).
% 0.19/0.63 cnf(47,plain,
% 0.19/0.63 (E(f3(x471,x471),x471)),
% 0.19/0.63 inference(rename_variables,[],[29])).
% 0.19/0.63 cnf(56,plain,
% 0.19/0.63 (E(f2(x561,f3(x562,x562)),f2(x561,x562))),
% 0.19/0.63 inference(scs_inference,[],[33,32,29,47,2,36,23,22,21,20,19,18,17,16,15,14])).
% 0.19/0.63 cnf(67,plain,
% 0.19/0.63 (P3(f11(f2(a5,a8),f2(a9,a10)),f3(f2(a5,a8),f2(a9,a10)))),
% 0.19/0.63 inference(scs_inference,[],[33,32,29,47,2,36,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,38])).
% 0.19/0.63 cnf(70,plain,
% 0.19/0.63 (E(f3(x701,x701),x701)),
% 0.19/0.63 inference(rename_variables,[],[29])).
% 0.19/0.63 cnf(75,plain,
% 0.19/0.63 (P3(f7(f11(f2(a5,a8),f2(a9,a10)),a5,a8,a9,a10),f3(a8,a10))),
% 0.19/0.63 inference(scs_inference,[],[33,32,29,47,70,2,36,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,38,27,26,37,41])).
% 0.19/0.63 cnf(77,plain,
% 0.19/0.63 (P3(f6(f11(f2(a5,a8),f2(a9,a10)),a5,a8,a9,a10),f3(a5,a9))),
% 0.19/0.63 inference(scs_inference,[],[33,32,29,47,70,2,36,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,38,27,26,37,41,40])).
% 0.19/0.63 cnf(88,plain,
% 0.19/0.63 (E(f2(x881,f3(x882,x882)),f2(x881,x882))),
% 0.19/0.63 inference(rename_variables,[],[56])).
% 0.19/0.63 cnf(92,plain,
% 0.19/0.63 (E(f3(x921,x922),f3(x922,x921))),
% 0.19/0.63 inference(rename_variables,[],[31])).
% 0.19/0.63 cnf(94,plain,
% 0.19/0.63 (E(x941,f3(x941,x941))),
% 0.19/0.63 inference(rename_variables,[],[43])).
% 0.19/0.63 cnf(98,plain,
% 0.19/0.63 (~P2(a5,a9)),
% 0.19/0.63 inference(scs_inference,[],[33,28,31,92,34,43,94,56,88,67,77,37,27,26,25,3,24,23,39])).
% 0.19/0.63 cnf(101,plain,
% 0.19/0.63 (P2(a8,a10)),
% 0.19/0.63 inference(scs_inference,[],[98,35])).
% 0.19/0.63 cnf(115,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[75,101,39]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------