TSTP Solution File: SET841-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET841-2 : 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 : n015.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 14:31:18 EDT 2023
% Result : Unsatisfiable 0.19s 0.69s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET841-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n015.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
% 0.12/0.33 % DateTime : Sat Aug 26 10:21:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.61 start to proof:theBenchmark
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 % File :CSE---1.6
% 0.19/0.69 % Problem :theBenchmark
% 0.19/0.69 % Transform :cnf
% 0.19/0.69 % Format :tptp:raw
% 0.19/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.69
% 0.19/0.69 % Result :Theorem 0.020000s
% 0.19/0.69 % Output :CNFRefutation 0.020000s
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 % File : SET841-2 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.69 % Domain : Set Theory
% 0.19/0.69 % Problem : Problem about Zorn's lemma
% 0.19/0.69 % Version : [Pau06] axioms : Reduced > Especial.
% 0.19/0.69 % English :
% 0.19/0.69
% 0.19/0.69 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.19/0.69 % Source : [Pau06]
% 0.19/0.69 % Names :
% 0.19/0.69
% 0.19/0.69 % Status : Unsatisfiable
% 0.19/0.69 % 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, 0.10 v5.3.0, 0.06 v5.2.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0
% 0.19/0.69 % Syntax : Number of clauses : 7 ( 6 unt; 1 nHn; 6 RR)
% 0.19/0.69 % Number of literals : 11 ( 2 equ; 4 neg)
% 0.19/0.69 % Maximal clause size : 5 ( 1 avg)
% 0.19/0.69 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.69 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.19/0.69 % Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% 0.19/0.69 % Number of variables : 6 ( 1 sgn)
% 0.19/0.69 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.19/0.69
% 0.19/0.69 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.19/0.69 % of which only a small selection are required for the refutation.
% 0.19/0.69 % The mission is to find those few axioms, after which a refutation
% 0.19/0.69 % can be quite easily found. This version has only the necessary
% 0.19/0.69 % axioms.
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.19/0.69 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_Zorn_OTFin__subsetD_0,axiom,
% 0.19/0.69 ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.69 | ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.69 | ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
% 0.19/0.69 | c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
% 0.19/0.69 | V_n = V_m ) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_conjecture_0,negated_conjecture,
% 0.19/0.69 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_conjecture_1,negated_conjecture,
% 0.19/0.69 v_m = c_Zorn_Osucc(v_S,v_m,t_a) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_conjecture_2,negated_conjecture,
% 0.19/0.69 c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_conjecture_3,negated_conjecture,
% 0.19/0.69 c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ).
% 0.19/0.69
% 0.19/0.69 cnf(cls_conjecture_4,negated_conjecture,
% 0.19/0.69 ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ).
% 0.19/0.69
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 % Proof found
% 0.19/0.69 % SZS status Theorem for theBenchmark
% 0.19/0.69 % SZS output start Proof
% 0.19/0.69 %ClaNum:22(EqnAxiom:15)
% 0.19/0.69 %VarNum:21(SingletonVarNum:6)
% 0.19/0.69 %MaxLitNum:5
% 0.19/0.69 %MaxfuncDepth:2
% 0.19/0.69 %SharedTerms:14
% 0.19/0.69 %goalClause: 16 18 19 20 21
% 0.19/0.69 %singleGoalClaCount:5
% 0.19/0.69 [16]E(f3(a1,a6,a2),a6)
% 0.19/0.69 [18]P1(a7,a6,f5(f5(a2)))
% 0.19/0.69 [19]P2(a6,f4(a1,a2),f5(f5(a2)))
% 0.19/0.69 [20]P2(a7,f4(a1,a2),f5(f5(a2)))
% 0.19/0.69 [21]~P1(f3(a1,a7,a2),a6,f5(f5(a2)))
% 0.19/0.69 [17]P1(x171,x171,f5(x172))
% 0.19/0.69 [22]E(x221,x222)+~P1(x221,x222,f5(f5(x224)))+~P2(x222,f4(x223,x224),f5(f5(x224)))+~P2(x221,f4(x223,x224),f5(f5(x224)))+P1(f3(x223,x221,x224),x222,f5(f5(x224)))
% 0.19/0.69 %EqnAxiom
% 0.19/0.69 [1]E(x11,x11)
% 0.19/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.69 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44))
% 0.19/0.69 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54))
% 0.19/0.69 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62))
% 0.19/0.69 [7]~E(x71,x72)+E(f5(x71),f5(x72))
% 0.19/0.69 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83))
% 0.19/0.69 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92))
% 0.19/0.69 [10]P1(x102,x103,x104)+~E(x101,x102)+~P1(x101,x103,x104)
% 0.19/0.70 [11]P1(x113,x112,x114)+~E(x111,x112)+~P1(x113,x111,x114)
% 0.19/0.70 [12]P1(x123,x124,x122)+~E(x121,x122)+~P1(x123,x124,x121)
% 0.19/0.70 [13]P2(x132,x133,x134)+~E(x131,x132)+~P2(x131,x133,x134)
% 0.19/0.70 [14]P2(x143,x142,x144)+~E(x141,x142)+~P2(x143,x141,x144)
% 0.19/0.70 [15]P2(x153,x154,x152)+~E(x151,x152)+~P2(x153,x154,x151)
% 0.19/0.70
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 cnf(23,plain,
% 0.19/0.70 (E(a6,f3(a1,a6,a2))),
% 0.19/0.70 inference(scs_inference,[],[16,2])).
% 0.19/0.70 cnf(26,plain,
% 0.19/0.70 (~E(a7,f3(a1,a7,a2))),
% 0.19/0.70 inference(scs_inference,[],[16,18,19,21,2,13,11,10])).
% 0.19/0.70 cnf(27,plain,
% 0.19/0.70 (E(a7,a6)),
% 0.19/0.70 inference(scs_inference,[],[16,18,20,19,21,2,13,11,10,22])).
% 0.19/0.70 cnf(34,plain,
% 0.19/0.70 (E(f3(f3(a1,a6,a2),x341,x342),f3(a6,x341,x342))),
% 0.19/0.70 inference(scs_inference,[],[16,18,20,19,21,2,13,11,10,22,9,8,7,6,5,4])).
% 0.19/0.70 cnf(42,plain,
% 0.19/0.70 (~E(f3(a1,a6,a2),f3(a1,a7,a2))),
% 0.19/0.70 inference(scs_inference,[],[16,17,21,26,2,11,10])).
% 0.19/0.70 cnf(56,plain,
% 0.19/0.70 (E(f3(x561,a6,x562),f3(x561,f3(a1,a6,a2),x562))),
% 0.19/0.70 inference(scs_inference,[],[23,5])).
% 0.19/0.70 cnf(58,plain,
% 0.19/0.70 (P1(f3(f3(a1,a6,a2),x581,x582),f3(a6,x581,x582),f5(x583))),
% 0.19/0.70 inference(scs_inference,[],[23,17,34,5,2,11])).
% 0.19/0.70 cnf(60,plain,
% 0.19/0.70 (E(a7,f3(a1,a6,a2))),
% 0.19/0.70 inference(scs_inference,[],[23,17,34,27,5,2,11,3])).
% 0.19/0.70 cnf(67,plain,
% 0.19/0.70 (E(f3(x671,a6,x672),f3(x671,f3(a1,a6,a2),x672))),
% 0.19/0.70 inference(rename_variables,[],[56])).
% 0.19/0.70 cnf(73,plain,
% 0.19/0.70 (~E(f3(a1,a6,a2),a7)),
% 0.19/0.70 inference(scs_inference,[],[17,21,58,56,67,42,10,3,2,11,5])).
% 0.19/0.70 cnf(81,plain,
% 0.19/0.70 ($false),
% 0.19/0.70 inference(scs_inference,[],[23,60,73,56,5,3,2]),
% 0.19/0.70 ['proof']).
% 0.19/0.70 % SZS output end Proof
% 0.19/0.70 % Total time :0.020000s
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