TSTP Solution File: SET865-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET865-2 : 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 : n028.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 14:31:30 EDT 2023
% Result : Unsatisfiable 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET865-2 : 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
% 0.13/0.34 % Computer : n028.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 08:50:37 EDT 2023
% 0.13/0.34 % 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 : SET865-2 : 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 : 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.33 v3.7.0, 0.17 v3.3.0, 0.14 v3.2.0
% 0.19/0.61 % Syntax : Number of clauses : 8 ( 2 unt; 0 nHn; 6 RR)
% 0.19/0.61 % Number of literals : 17 ( 2 equ; 10 neg)
% 0.19/0.61 % Maximal clause size : 4 ( 2 avg)
% 0.19/0.61 % Maximal term depth : 4 ( 1 avg)
% 0.19/0.61 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.19/0.61 % Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% 0.19/0.61 % Number of variables : 16 ( 0 sgn)
% 0.19/0.61 % SPC : CNF_UNS_RFO_SEQ_HRN
% 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_conjecture_0,negated_conjecture,
% 0.19/0.61 ( c_in(c_Union(V_U,t_a),v_S,tc_set(t_a))
% 0.19/0.61 | ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.61 ( c_in(v_x(V_U),v_S,tc_set(t_a))
% 0.19/0.61 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_conjecture_2,negated_conjecture,
% 0.19/0.61 ( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
% 0.19/0.61 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_conjecture_3,negated_conjecture,
% 0.19/0.61 ( V_U != v_x(V_U)
% 0.19/0.61 | ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Set_OsubsetD_0,axiom,
% 0.19/0.61 ( ~ c_in(V_c,V_A,T_a)
% 0.19/0.61 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 0.19/0.61 | c_in(V_c,V_B,T_a) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_OHausdorff_0,axiom,
% 0.19/0.61 c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
% 0.19/0.61 ( ~ c_in(V_u,V_S,tc_set(T_a))
% 0.19/0.61 | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.61 | ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
% 0.19/0.61 | c_Union(V_c,T_a) = V_u ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
% 0.19/0.61 c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ).
% 0.19/0.61
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark
% 0.19/0.61 % SZS output start Proof
% 0.19/0.61 %ClaNum:27(EqnAxiom:19)
% 0.19/0.61 %VarNum:43(SingletonVarNum:16)
% 0.19/0.61 %MaxLitNum:4
% 0.19/0.61 %MaxfuncDepth:3
% 0.19/0.61 %SharedTerms:5
% 0.19/0.61 %goalClause: 22 23 24 25
% 0.19/0.61 [20]P1(f1(x201,x202),f3(x201,x202),f5(f5(x202)))
% 0.19/0.61 [21]P2(f3(x211,x212),f4(x211,x212),f5(f5(f5(x212))))
% 0.19/0.61 [22]~E(f7(x221),x221)+~P1(x221,a8,f5(a6))
% 0.19/0.61 [23]~P1(x231,a8,f5(a6))+P1(f7(x231),a8,f5(a6))
% 0.19/0.61 [24]P2(x241,f7(x241),f5(a6))+~P1(x241,a8,f5(a6))
% 0.19/0.61 [25]~P1(x251,f4(a8,a6),f5(f5(a6)))+P1(f2(x251,a6),a8,f5(a6))
% 0.19/0.61 [26]P1(x261,x262,x263)+~P1(x261,x264,x263)+~P2(x264,x262,f5(x263))
% 0.19/0.61 [27]~P2(f2(x271,x272),x273,f5(x272))+~P1(x273,x274,f5(x272))+E(f2(x271,x272),x273)+~P1(x271,f3(x274,x272),f5(f5(x272)))
% 0.19/0.61 %EqnAxiom
% 0.19/0.61 [1]E(x11,x11)
% 0.19/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.61 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.61 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.61 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.19/0.61 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.19/0.61 [8]~E(x81,x82)+E(f5(x81),f5(x82))
% 0.19/0.62 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 0.19/0.62 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 0.19/0.62 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.19/0.62 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.19/0.62 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.19/0.62 [14]P1(x142,x143,x144)+~E(x141,x142)+~P1(x141,x143,x144)
% 0.19/0.62 [15]P1(x153,x152,x154)+~E(x151,x152)+~P1(x153,x151,x154)
% 0.19/0.62 [16]P1(x163,x164,x162)+~E(x161,x162)+~P1(x163,x164,x161)
% 0.19/0.62 [17]P2(x172,x173,x174)+~E(x171,x172)+~P2(x171,x173,x174)
% 0.19/0.62 [18]P2(x183,x182,x184)+~E(x181,x182)+~P2(x183,x181,x184)
% 0.19/0.62 [19]P2(x193,x194,x192)+~E(x191,x192)+~P2(x193,x194,x191)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(30,plain,
% 0.19/0.62 (P1(f2(f1(a8,a6),a6),a8,f5(a6))),
% 0.19/0.62 inference(scs_inference,[],[20,21,26,25])).
% 0.19/0.62 cnf(32,plain,
% 0.19/0.62 (P2(f2(f1(a8,a6),a6),f7(f2(f1(a8,a6),a6)),f5(a6))),
% 0.19/0.62 inference(scs_inference,[],[20,21,26,25,24])).
% 0.19/0.62 cnf(34,plain,
% 0.19/0.62 (~E(f7(f2(f1(a8,a6),a6)),f2(f1(a8,a6),a6))),
% 0.19/0.62 inference(scs_inference,[],[20,21,26,25,24,22])).
% 0.19/0.62 cnf(41,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[20,34,32,30,2,23,27]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------