TSTP Solution File: SET847-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% 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 14:31:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n016.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 09:51:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.010000s
% 0.19/0.63 % Output :CNFRefutation 0.010000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 % File : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.63 % Domain : Set Theory
% 0.19/0.63 % Problem : Problem about Zorn's lemma
% 0.19/0.63 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.63 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.63 % Source : [Pau06]
% 0.19/0.63 % Names :
% 0.19/0.63
% 0.19/0.63 % Status : Unsatisfiable
% 0.19/0.63 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.3.0, 0.09 v6.2.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.30 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.21 v4.1.0, 0.31 v4.0.1, 0.36 v3.7.0, 0.10 v3.5.0, 0.18 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0
% 0.19/0.63 % Syntax : Number of clauses : 11 ( 4 unt; 2 nHn; 7 RR)
% 0.19/0.63 % Number of literals : 20 ( 3 equ; 10 neg)
% 0.19/0.63 % Maximal clause size : 3 ( 1 avg)
% 0.19/0.63 % Maximal term depth : 5 ( 2 avg)
% 0.19/0.63 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.19/0.63 % Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% 0.19/0.63 % Number of variables : 28 ( 6 sgn)
% 0.19/0.63 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.19/0.63
% 0.19/0.63 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.63 % of which only a small selection are required for the refutation.
% 0.19/0.63 % The mission is to find those few axioms, after which a refutation
% 0.19/0.63 % can be quite easily found. This version has only the necessary
% 0.19/0.63 % axioms.
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 cnf(cls_Set_ODiffI_0,axiom,
% 0.19/0.63 ( ~ c_in(V_c,V_A,T_a)
% 0.19/0.63 | c_in(V_c,V_B,T_a)
% 0.19/0.63 | c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Set_OemptyE_0,axiom,
% 0.19/0.63 ~ c_in(V_a,c_emptyset,T_a) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Set_Oempty__subsetI_0,axiom,
% 0.19/0.63 c_lessequals(c_emptyset,V_A,tc_set(T_a)) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Set_OsubsetI_0,axiom,
% 0.19/0.63 ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
% 0.19/0.63 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Set_Osubset__antisym_0,axiom,
% 0.19/0.63 ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
% 0.19/0.63 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 0.19/0.63 | V_A = V_B ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.19/0.63 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Zorn_OTFin__UnionI_0,axiom,
% 0.19/0.63 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
% 0.19/0.63 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Zorn_OTFin__chain__lemma4_0,axiom,
% 0.19/0.63 ( ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.63 | c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Zorn_Oequal__succ__Union_1,axiom,
% 0.19/0.63 ( ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.63 | c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(cls_Zorn_Osucc__not__equals_0,axiom,
% 0.19/0.63 ( ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a)))
% 0.19/0.63 | c_Zorn_Osucc(V_S,V_c,T_a) != V_c ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.64 ~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:38(EqnAxiom:27)
% 0.19/0.64 %VarNum:77(SingletonVarNum:28)
% 0.19/0.64 %MaxLitNum:3
% 0.19/0.64 %MaxfuncDepth:4
% 0.19/0.64 %SharedTerms:6
% 0.19/0.64 %goalClause: 31
% 0.19/0.64 %singleGoalClaCount:1
% 0.19/0.64 [31]~P2(x311,f2(a11,a9),f8(f8(a9)))
% 0.19/0.64 [30]~P2(x301,a1,x302)
% 0.19/0.64 [28]P1(a1,x281,f8(x282))
% 0.19/0.64 [29]P1(x291,x291,f8(x292))
% 0.19/0.64 [37]~P2(f6(f5(x371,x372),f8(x372)),f5(x371,x372),f8(f8(x372)))+E(f7(x371,f6(f5(x371,x372),f8(x372)),x372),f6(f5(x371,x372),f8(x372)))
% 0.19/0.64 [33]P2(f3(x331,x332,x333),x331,x333)+P1(x331,x332,f8(x333))
% 0.19/0.64 [34]~P2(x341,f5(x342,x343),f8(f8(x343)))+P2(x341,f4(x342,x343),f8(f8(x343)))
% 0.19/0.64 [36]P2(f6(x361,f8(x362)),f5(x363,x362),f8(f8(x362)))+~P1(x361,f5(x363,x362),f8(f8(f8(x362))))
% 0.19/0.64 [38]~E(f7(x381,x382,x383),x382)+~P2(x382,f10(f4(x381,x383),f2(x381,x383),f8(f8(f8(x383)))),f8(f8(x383)))
% 0.19/0.64 [32]E(x321,x322)+~P1(x322,x321,f8(x323))+~P1(x321,x322,f8(x323))
% 0.19/0.64 [35]~P2(x351,x354,x353)+P2(x351,x352,x353)+P2(x351,f10(x354,x352,f8(x353)),x353)
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f8(x41),f8(x42))
% 0.19/0.64 [5]~E(x51,x52)+E(f10(x51,x53,x54),f10(x52,x53,x54))
% 0.19/0.64 [6]~E(x61,x62)+E(f10(x63,x61,x64),f10(x63,x62,x64))
% 0.19/0.64 [7]~E(x71,x72)+E(f10(x73,x74,x71),f10(x73,x74,x72))
% 0.19/0.64 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83))
% 0.19/0.64 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92))
% 0.19/0.64 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.19/0.64 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.19/0.64 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.19/0.64 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.19/0.64 [14]~E(x141,x142)+E(f7(x141,x143,x144),f7(x142,x143,x144))
% 0.19/0.64 [15]~E(x151,x152)+E(f7(x153,x151,x154),f7(x153,x152,x154))
% 0.19/0.64 [16]~E(x161,x162)+E(f7(x163,x164,x161),f7(x163,x164,x162))
% 0.19/0.64 [17]~E(x171,x172)+E(f6(x171,x173),f6(x172,x173))
% 0.19/0.64 [18]~E(x181,x182)+E(f6(x183,x181),f6(x183,x182))
% 0.19/0.64 [19]~E(x191,x192)+E(f3(x191,x193,x194),f3(x192,x193,x194))
% 0.19/0.64 [20]~E(x201,x202)+E(f3(x203,x201,x204),f3(x203,x202,x204))
% 0.19/0.64 [21]~E(x211,x212)+E(f3(x213,x214,x211),f3(x213,x214,x212))
% 0.19/0.64 [22]P1(x222,x223,x224)+~E(x221,x222)+~P1(x221,x223,x224)
% 0.19/0.64 [23]P1(x233,x232,x234)+~E(x231,x232)+~P1(x233,x231,x234)
% 0.19/0.64 [24]P1(x243,x244,x242)+~E(x241,x242)+~P1(x243,x244,x241)
% 0.19/0.64 [25]P2(x252,x253,x254)+~E(x251,x252)+~P2(x251,x253,x254)
% 0.19/0.64 [26]P2(x263,x262,x264)+~E(x261,x262)+~P2(x263,x261,x264)
% 0.19/0.64 [27]P2(x273,x274,x272)+~E(x271,x272)+~P2(x273,x274,x271)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(39,plain,
% 0.19/0.64 (P2(f6(f5(x391,x392),f8(x392)),f5(x391,x392),f8(f8(x392)))),
% 0.19/0.64 inference(scs_inference,[],[29,36])).
% 0.19/0.64 cnf(42,plain,
% 0.19/0.64 (~P2(x421,f2(a11,a9),f8(f8(a9)))),
% 0.19/0.64 inference(rename_variables,[],[31])).
% 0.19/0.64 cnf(45,plain,
% 0.19/0.64 (~P2(x451,f2(a11,a9),f8(f8(a9)))),
% 0.19/0.64 inference(rename_variables,[],[31])).
% 0.19/0.64 cnf(47,plain,
% 0.19/0.64 (P2(f6(f5(x471,a9),f8(a9)),f4(x471,a9),f8(f8(a9)))),
% 0.19/0.64 inference(scs_inference,[],[31,42,29,36,26,2,33,34])).
% 0.19/0.64 cnf(49,plain,
% 0.19/0.64 (E(f7(x491,f6(f5(x491,a9),f8(a9)),a9),f6(f5(x491,a9),f8(a9)))),
% 0.19/0.64 inference(scs_inference,[],[31,42,29,36,26,2,33,34,37])).
% 0.19/0.64 cnf(52,plain,
% 0.19/0.64 (~P1(f5(x521,a9),f2(a11,a9),f8(f8(f8(a9))))),
% 0.19/0.64 inference(scs_inference,[],[31,42,45,29,36,26,2,33,34,37,27,32])).
% 0.19/0.64 cnf(73,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[31,28,30,39,49,47,52,38,33,26,22,35]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------