TSTP Solution File: SET853-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET853-2 : 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 : n019.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 14:31:25 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 : SET853-2 : 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 : n019.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 08:38:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof:theBenchmark
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % File :CSE---1.6
% 0.19/0.64 % Problem :theBenchmark
% 0.19/0.64 % Transform :cnf
% 0.19/0.64 % Format :tptp:raw
% 0.19/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.64
% 0.19/0.64 % Result :Theorem 0.010000s
% 0.19/0.64 % Output :CNFRefutation 0.010000s
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 % File : SET853-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.64 % Domain : Set Theory
% 0.19/0.64 % Problem : Problem about Zorn's lemma
% 0.19/0.64 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.64 % English :
% 0.19/0.64
% 0.19/0.64 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.64 % Source : [Pau06]
% 0.19/0.64 % Names :
% 0.19/0.64
% 0.19/0.64 % Status : Unsatisfiable
% 0.19/0.64 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.27 v6.4.0, 0.20 v6.3.0, 0.18 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.22 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.23 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.21 v3.2.0
% 0.19/0.64 % Syntax : Number of clauses : 13 ( 6 unt; 5 nHn; 11 RR)
% 0.19/0.64 % Number of literals : 35 ( 4 equ; 17 neg)
% 0.19/0.64 % Maximal clause size : 5 ( 2 avg)
% 0.19/0.64 % Maximal term depth : 3 ( 2 avg)
% 0.19/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.19/0.64 % Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% 0.19/0.64 % Number of variables : 26 ( 2 sgn)
% 0.19/0.64 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.19/0.64
% 0.19/0.64 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.64 % of which only a small selection are required for the refutation.
% 0.19/0.64 % The mission is to find those few axioms, after which a refutation
% 0.19/0.64 % can be quite easily found. This version has only the necessary
% 0.19/0.64 % axioms.
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.64 c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.64 c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_2,negated_conjecture,
% 0.19/0.64 c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_3,negated_conjecture,
% 0.19/0.64 v_xa != c_Zorn_Osucc(v_S,v_x,t_a) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_4,negated_conjecture,
% 0.19/0.64 ~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_5,negated_conjecture,
% 0.19/0.64 ( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a)))
% 0.19/0.64 | V_U = v_x
% 0.19/0.64 | ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a)))
% 0.19/0.64 | ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Set_Osubset__antisym_0,axiom,
% 0.19/0.64 ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
% 0.19/0.64 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 0.19/0.64 | V_A = V_B ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.19/0.64 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
% 0.19/0.64 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
% 0.19/0.64 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
% 0.19/0.64 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
% 0.19/0.64 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
% 0.19/0.64 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.64 | ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_Zorn_Osucc__trans_0,axiom,
% 0.19/0.64 ( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
% 0.19/0.64 | c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,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:31(EqnAxiom:18)
% 0.19/0.64 %VarNum:109(SingletonVarNum:26)
% 0.19/0.64 %MaxLitNum:5
% 0.19/0.64 %MaxfuncDepth:2
% 0.19/0.64 %SharedTerms:14
% 0.19/0.64 %goalClause: 20 21 22 23 24 27
% 0.19/0.64 %singleGoalClaCount:5
% 0.19/0.64 [23]~E(f4(a7,a6,a2),a8)
% 0.19/0.64 [20]P2(a6,f3(a7,a2),f1(f1(a2)))
% 0.19/0.64 [21]P2(a8,f3(a7,a2),f1(f1(a2)))
% 0.19/0.64 [22]P1(a8,f4(a7,a6,a2),f1(f1(a2)))
% 0.19/0.64 [24]~P1(f4(a7,a8,a2),f4(a7,a6,a2),f1(f1(a2)))
% 0.19/0.64 [19]P1(x191,x191,f1(x192))
% 0.19/0.64 [26]~P1(x261,x263,f1(f1(x264)))+P1(x261,f4(x262,x263,x264),f1(f1(x264)))
% 0.19/0.64 [25]E(x251,x252)+~P1(x252,x251,f1(x253))+~P1(x251,x252,f1(x253))
% 0.19/0.64 [27]E(x271,a6)+~P2(x271,f3(a7,a2),f1(f1(a2)))+~P1(x271,a6,f1(f1(a2)))+P1(f4(a7,x271,a2),a6,f1(f1(a2)))
% 0.19/0.64 [28]~E(f5(x284,x282,x283),x282)+~P2(x281,f3(x284,x283),f1(f1(x283)))+~P2(x282,f3(x284,x283),f1(f1(x283)))+P1(f4(x284,x282,x283),x281,f1(f1(x283)))+P1(x281,x282,f1(f1(x283)))
% 0.19/0.64 [29]P1(f5(x294,x292,x293),x292,f1(f1(x293)))+~P2(x291,f3(x294,x293),f1(f1(x293)))+~P2(x292,f3(x294,x293),f1(f1(x293)))+P1(f4(x294,x292,x293),x291,f1(f1(x293)))+P1(x291,x292,f1(f1(x293)))
% 0.19/0.64 [30]P2(f5(x304,x302,x303),f3(x304,x303),f1(f1(x303)))+~P2(x301,f3(x304,x303),f1(f1(x303)))+~P2(x302,f3(x304,x303),f1(f1(x303)))+P1(f4(x304,x302,x303),x301,f1(f1(x303)))+P1(x301,x302,f1(f1(x303)))
% 0.19/0.64 [31]~P1(f4(x314,f5(x314,x312,x313),x313),x312,f1(f1(x313)))+~P2(x311,f3(x314,x313),f1(f1(x313)))+~P2(x312,f3(x314,x313),f1(f1(x313)))+P1(f4(x314,x312,x313),x311,f1(f1(x313)))+P1(x311,x312,f1(f1(x313)))
% 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(f1(x41),f1(x42))
% 0.19/0.64 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.64 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.64 [7]~E(x71,x72)+E(f4(x71,x73,x74),f4(x72,x73,x74))
% 0.19/0.64 [8]~E(x81,x82)+E(f4(x83,x81,x84),f4(x83,x82,x84))
% 0.19/0.64 [9]~E(x91,x92)+E(f4(x93,x94,x91),f4(x93,x94,x92))
% 0.19/0.64 [10]~E(x101,x102)+E(f5(x101,x103,x104),f5(x102,x103,x104))
% 0.19/0.64 [11]~E(x111,x112)+E(f5(x113,x111,x114),f5(x113,x112,x114))
% 0.19/0.65 [12]~E(x121,x122)+E(f5(x123,x124,x121),f5(x123,x124,x122))
% 0.19/0.65 [13]P1(x132,x133,x134)+~E(x131,x132)+~P1(x131,x133,x134)
% 0.19/0.65 [14]P1(x143,x142,x144)+~E(x141,x142)+~P1(x143,x141,x144)
% 0.19/0.65 [15]P1(x153,x154,x152)+~E(x151,x152)+~P1(x153,x154,x151)
% 0.19/0.65 [16]P2(x162,x163,x164)+~E(x161,x162)+~P2(x161,x163,x164)
% 0.19/0.65 [17]P2(x173,x172,x174)+~E(x171,x172)+~P2(x173,x171,x174)
% 0.19/0.65 [18]P2(x183,x184,x182)+~E(x181,x182)+~P2(x183,x184,x181)
% 0.19/0.65
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 cnf(32,plain,
% 0.19/0.65 (~P1(f4(a7,a8,a2),a6,f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[24,26])).
% 0.19/0.65 cnf(35,plain,
% 0.19/0.65 (~E(a8,f4(a7,a8,a2))),
% 0.19/0.65 inference(scs_inference,[],[22,24,19,26,14,13])).
% 0.19/0.65 cnf(36,plain,
% 0.19/0.65 (~P1(f4(a7,a6,a2),a8,f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[23,22,24,19,26,14,13,25])).
% 0.19/0.65 cnf(41,plain,
% 0.19/0.65 (~P1(a8,a6,f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[23,22,21,24,19,26,14,13,25,2,15,8,27])).
% 0.19/0.65 cnf(53,plain,
% 0.19/0.65 (P1(x531,x531,f1(x532))),
% 0.19/0.65 inference(rename_variables,[],[19])).
% 0.19/0.65 cnf(56,plain,
% 0.19/0.65 (P1(x561,x561,f1(x562))),
% 0.19/0.65 inference(rename_variables,[],[19])).
% 0.19/0.65 cnf(61,plain,
% 0.19/0.65 (~E(f5(a7,a6,a2),a6)),
% 0.19/0.65 inference(scs_inference,[],[20,19,53,56,21,24,36,32,35,41,26,14,13,25,28])).
% 0.19/0.65 cnf(64,plain,
% 0.19/0.65 (~P1(f4(a7,f5(a7,a6,a2),a2),a6,f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[20,19,53,56,23,21,24,36,32,35,41,26,14,13,25,28,3,31])).
% 0.19/0.65 cnf(66,plain,
% 0.19/0.65 (P1(f5(a7,a6,a2),a6,f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[20,19,53,56,23,21,24,36,32,35,41,26,14,13,25,28,3,31,29])).
% 0.19/0.65 cnf(68,plain,
% 0.19/0.65 (P2(f5(a7,a6,a2),f3(a7,a2),f1(f1(a2)))),
% 0.19/0.65 inference(scs_inference,[],[20,19,53,56,23,21,24,36,32,35,41,26,14,13,25,28,3,31,29,30])).
% 0.19/0.65 cnf(74,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[68,64,66,61,27]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------