TSTP Solution File: SET851-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET851-2 : 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 : n022.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 14:31:24 EDT 2023
% Result : Unsatisfiable 0.19s 0.65s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET851-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n022.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 13:21:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 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 0.000000s
% 0.19/0.64 % Output :CNFRefutation 0.000000s
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 % File : SET851-2 : 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, 0.08 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.05 v5.4.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.06 v5.0.0, 0.00 v4.1.0, 0.08 v4.0.1, 0.09 v4.0.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0
% 0.19/0.64 % Syntax : Number of clauses : 7 ( 4 unt; 2 nHn; 5 RR)
% 0.19/0.64 % Number of literals : 12 ( 1 equ; 5 neg)
% 0.19/0.64 % Maximal clause size : 4 ( 1 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% 0.19/0.64 % Number of variables : 7 ( 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_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_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 cnf(cls_conjecture_1,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_2,negated_conjecture,
% 0.19/0.64 ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ).
% 0.19/0.64
% 0.19/0.64 cnf(cls_conjecture_3,negated_conjecture,
% 0.19/0.64 ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,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_4,negated_conjecture,
% 0.19/0.64 ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
% 0.19/0.64 | c_lessequals(v_x,v_m,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_m,tc_set(tc_set(t_a)))
% 0.19/0.64 | V_U = v_m
% 0.19/0.64 | ~ c_lessequals(V_U,v_m,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 %------------------------------------------------------------------------------
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 % Proof found
% 0.19/0.65 % SZS status Theorem for theBenchmark
% 0.19/0.65 % SZS output start Proof
% 0.19/0.65 %ClaNum:22(EqnAxiom:15)
% 0.19/0.65 %VarNum:15(SingletonVarNum:7)
% 0.19/0.65 %MaxLitNum:4
% 0.19/0.65 %MaxfuncDepth:2
% 0.19/0.65 %SharedTerms:14
% 0.19/0.65 %goalClause: 17 18 19 20 22
% 0.19/0.65 %singleGoalClaCount:3
% 0.19/0.65 [17]P2(a5,f3(a6,a2),f1(f1(a2)))
% 0.19/0.65 [18]~P1(f4(a6,a5,a2),a7,f1(f1(a2)))
% 0.19/0.65 [19]~P1(f4(a6,a7,a2),f4(a6,a5,a2),f1(f1(a2)))
% 0.19/0.65 [16]P1(x161,x161,f1(x162))
% 0.19/0.65 [20]P1(f4(a6,a7,a2),a5,f1(f1(a2)))+P1(a5,a7,f1(f1(a2)))
% 0.19/0.65 [21]~P1(x211,x213,f1(f1(x214)))+P1(x211,f4(x212,x213,x214),f1(f1(x214)))
% 0.19/0.65 [22]E(x221,a7)+~P2(x221,f3(a6,a2),f1(f1(a2)))+~P1(x221,a7,f1(f1(a2)))+P1(f4(a6,x221,a2),a7,f1(f1(a2)))
% 0.19/0.65 %EqnAxiom
% 0.19/0.65 [1]E(x11,x11)
% 0.19/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.65 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 0.19/0.65 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.65 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.65 [7]~E(x71,x72)+E(f4(x71,x73,x74),f4(x72,x73,x74))
% 0.19/0.65 [8]~E(x81,x82)+E(f4(x83,x81,x84),f4(x83,x82,x84))
% 0.19/0.65 [9]~E(x91,x92)+E(f4(x93,x94,x91),f4(x93,x94,x92))
% 0.19/0.65 [10]P1(x102,x103,x104)+~E(x101,x102)+~P1(x101,x103,x104)
% 0.19/0.65 [11]P1(x113,x112,x114)+~E(x111,x112)+~P1(x113,x111,x114)
% 0.19/0.65 [12]P1(x123,x124,x122)+~E(x121,x122)+~P1(x123,x124,x121)
% 0.19/0.65 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134)
% 0.19/0.65 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144)
% 0.19/0.65 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151)
% 0.19/0.65
% 0.19/0.65 %-------------------------------------------
% 0.19/0.65 cnf(24,plain,
% 0.19/0.65 (~E(f4(a6,a5,a2),a7)),
% 0.19/0.65 inference(scs_inference,[],[18,19,16,21,11])).
% 0.19/0.65 cnf(25,plain,
% 0.19/0.65 (P1(x251,x251,f1(x252))),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(30,plain,
% 0.19/0.65 (E(a5,a7)),
% 0.19/0.65 inference(scs_inference,[],[17,18,19,16,25,21,11,10,20,12,22])).
% 0.19/0.65 cnf(45,plain,
% 0.19/0.65 (P1(x451,x451,f1(x452))),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(48,plain,
% 0.19/0.65 (P1(x481,x481,f1(x482))),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(49,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[19,16,45,48,24,30,9,8,7,6,5,4,3,21,11,10]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.000000s
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