TSTP Solution File: SET848-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET848-2 : 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 : n008.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 14:31:22 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET848-2 : 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
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 11:12:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.000000s
% 0.19/0.61 % Output :CNFRefutation 0.000000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 % File : SET848-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.61 % Domain : Set Theory
% 0.19/0.61 % Problem : Problem about Zorn's lemma
% 0.19/0.61 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.61 % English :
% 0.19/0.61
% 0.19/0.61 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.61 % Source : [Pau06]
% 0.19/0.61 % Names :
% 0.19/0.61
% 0.19/0.61 % Status : Unsatisfiable
% 0.19/0.61 % 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, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.07 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0
% 0.19/0.61 % Syntax : Number of clauses : 7 ( 3 unt; 1 nHn; 5 RR)
% 0.19/0.61 % Number of literals : 12 ( 2 equ; 6 neg)
% 0.19/0.61 % Maximal clause size : 3 ( 1 avg)
% 0.19/0.61 % Maximal term depth : 5 ( 2 avg)
% 0.19/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.19/0.61 % Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% 0.19/0.61 % Number of variables : 15 ( 1 sgn)
% 0.19/0.61 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.19/0.61
% 0.19/0.61 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.61 % of which only a small selection are required for the refutation.
% 0.19/0.61 % The mission is to find those few axioms, after which a refutation
% 0.19/0.61 % can be quite easily found. This version has only the necessary
% 0.19/0.61 % axioms.
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 cnf(cls_Set_ODiffI_0,axiom,
% 0.19/0.61 ( ~ c_in(V_c,V_A,T_a)
% 0.19/0.61 | c_in(V_c,V_B,T_a)
% 0.19/0.61 | c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.19/0.61 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_OTFin__UnionI_0,axiom,
% 0.19/0.61 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
% 0.19/0.61 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_OTFin__chain__lemma4_0,axiom,
% 0.19/0.61 ( ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.61 | c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_Osucc__not__equals_0,axiom,
% 0.19/0.61 ( ~ 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)))
% 0.19/0.61 | c_Zorn_Osucc(V_S,V_c,T_a) != V_c ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.61 ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.61
% 0.19/0.62 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.62 c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ).
% 0.19/0.62
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 %ClaNum:31(EqnAxiom:24)
% 0.19/0.62 %VarNum:42(SingletonVarNum:15)
% 0.19/0.62 %MaxLitNum:3
% 0.19/0.62 %MaxfuncDepth:4
% 0.19/0.62 %SharedTerms:10
% 0.19/0.62 %goalClause: 26 27
% 0.19/0.62 %singleGoalClaCount:2
% 0.19/0.62 [27]~P2(f4(f3(a9,a2),f1(a2)),f6(a9,a2),f1(f1(a2)))
% 0.19/0.62 [26]E(f5(a9,f4(f3(a9,a2),f1(a2)),a2),f4(f3(a9,a2),f1(a2)))
% 0.19/0.62 [25]P1(x251,x251,f1(x252))
% 0.19/0.62 [28]~P2(x281,f3(x282,x283),f1(f1(x283)))+P2(x281,f7(x282,x283),f1(f1(x283)))
% 0.19/0.62 [30]P2(f4(x301,f1(x302)),f3(x303,x302),f1(f1(x302)))+~P1(x301,f3(x303,x302),f1(f1(f1(x302))))
% 0.19/0.62 [31]~E(f5(x311,x312,x313),x312)+~P2(x312,f8(f7(x311,x313),f6(x311,x313),f1(f1(f1(x313)))),f1(f1(x313)))
% 0.19/0.62 [29]~P2(x291,x294,x293)+P2(x291,x292,x293)+P2(x291,f8(x294,x292,f1(x293)),x293)
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 0.19/0.62 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.62 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.62 [7]~E(x71,x72)+E(f8(x71,x73,x74),f8(x72,x73,x74))
% 0.19/0.62 [8]~E(x81,x82)+E(f8(x83,x81,x84),f8(x83,x82,x84))
% 0.19/0.62 [9]~E(x91,x92)+E(f8(x93,x94,x91),f8(x93,x94,x92))
% 0.19/0.62 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103))
% 0.19/0.62 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112))
% 0.19/0.62 [12]~E(x121,x122)+E(f5(x121,x123,x124),f5(x122,x123,x124))
% 0.19/0.62 [13]~E(x131,x132)+E(f5(x133,x131,x134),f5(x133,x132,x134))
% 0.19/0.62 [14]~E(x141,x142)+E(f5(x143,x144,x141),f5(x143,x144,x142))
% 0.19/0.62 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.19/0.62 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.19/0.62 [17]~E(x171,x172)+E(f6(x171,x173),f6(x172,x173))
% 0.19/0.62 [18]~E(x181,x182)+E(f6(x183,x181),f6(x183,x182))
% 0.19/0.62 [19]P1(x192,x193,x194)+~E(x191,x192)+~P1(x191,x193,x194)
% 0.19/0.62 [20]P1(x203,x202,x204)+~E(x201,x202)+~P1(x203,x201,x204)
% 0.19/0.62 [21]P1(x213,x214,x212)+~E(x211,x212)+~P1(x213,x214,x211)
% 0.19/0.62 [22]P2(x222,x223,x224)+~E(x221,x222)+~P2(x221,x223,x224)
% 0.19/0.62 [23]P2(x233,x232,x234)+~E(x231,x232)+~P2(x233,x231,x234)
% 0.19/0.62 [24]P2(x243,x244,x242)+~E(x241,x242)+~P2(x243,x244,x241)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(34,plain,
% 0.19/0.62 (P1(x341,x341,f1(x342))),
% 0.19/0.62 inference(rename_variables,[],[25])).
% 0.19/0.62 cnf(36,plain,
% 0.19/0.62 (~E(f3(a9,a2),f6(a9,a2))),
% 0.19/0.62 inference(scs_inference,[],[26,27,25,2,30,23])).
% 0.19/0.62 cnf(39,plain,
% 0.19/0.62 (P1(x391,x391,f1(x392))),
% 0.19/0.62 inference(rename_variables,[],[25])).
% 0.19/0.62 cnf(42,plain,
% 0.19/0.62 (P2(f4(f3(a9,a2),f1(a2)),f7(a9,a2),f1(f1(a2)))),
% 0.19/0.62 inference(scs_inference,[],[26,27,25,34,39,2,30,23,22,20,19,28])).
% 0.19/0.62 cnf(44,plain,
% 0.19/0.62 (~P2(f4(f3(a9,a2),f1(a2)),f8(f7(a9,a2),f6(a9,a2),f1(f1(f1(a2)))),f1(f1(a2)))),
% 0.19/0.62 inference(scs_inference,[],[26,27,25,34,39,2,30,23,22,20,19,28,31])).
% 0.19/0.62 cnf(53,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[26,27,44,42,36,2,22,29]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------