TSTP Solution File: SET844-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET844-2 : 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 : n005.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 14:31:20 EDT 2023
% Result : Unsatisfiable 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET844-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:17:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % File :CSE---1.6
% 0.20/0.61 % Problem :theBenchmark
% 0.20/0.61 % Transform :cnf
% 0.20/0.61 % Format :tptp:raw
% 0.20/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.61
% 0.20/0.61 % Result :Theorem 0.000000s
% 0.20/0.61 % Output :CNFRefutation 0.000000s
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 % File : SET844-2 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.61 % Domain : Set Theory
% 0.20/0.61 % Problem : Problem about Zorn's lemma
% 0.20/0.61 % Version : [Pau06] axioms : Reduced > Especial.
% 0.20/0.61 % English :
% 0.20/0.61
% 0.20/0.61 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.20/0.61 % Source : [Pau06]
% 0.20/0.61 % Names :
% 0.20/0.61
% 0.20/0.61 % Status : Unsatisfiable
% 0.20/0.62 % Rating : 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
% 0.20/0.62 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 5 RR)
% 0.20/0.62 % Number of literals : 10 ( 2 equ; 5 neg)
% 0.20/0.62 % Maximal clause size : 4 ( 1 avg)
% 0.20/0.62 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.20/0.62 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% 0.20/0.62 % Number of variables : 9 ( 1 sgn)
% 0.20/0.62 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.20/0.62
% 0.20/0.62 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.20/0.62 % of which only a small selection are required for the refutation.
% 0.20/0.62 % The mission is to find those few axioms, after which a refutation
% 0.20/0.62 % can be quite easily found. This version has only the necessary
% 0.20/0.62 % axioms.
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.20/0.62 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.20/0.62
% 0.20/0.62 cnf(cls_Zorn_OTFin__UnionI_0,axiom,
% 0.20/0.62 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
% 0.20/0.62 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(cls_Zorn_Oeq__succ__upper_0,axiom,
% 0.20/0.62 ( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.20/0.62 | ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.20/0.62 | V_m != c_Zorn_Osucc(V_S,V_m,T_a)
% 0.20/0.62 | c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(cls_conjecture_0,negated_conjecture,
% 0.20/0.62 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.20/0.62
% 0.20/0.62 cnf(cls_conjecture_1,negated_conjecture,
% 0.20/0.62 v_m = c_Zorn_Osucc(v_S,v_m,t_a) ).
% 0.20/0.62
% 0.20/0.62 cnf(cls_conjecture_2,negated_conjecture,
% 0.20/0.62 ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
% 0.20/0.62
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 %ClaNum:23(EqnAxiom:17)
% 0.20/0.62 %VarNum:27(SingletonVarNum:9)
% 0.20/0.62 %MaxLitNum:4
% 0.20/0.62 %MaxfuncDepth:3
% 0.20/0.62 %SharedTerms:11
% 0.20/0.62 %goalClause: 18 20 21
% 0.20/0.62 %singleGoalClaCount:3
% 0.20/0.62 [18]E(f3(a1,a7,a2),a7)
% 0.20/0.62 [20]P2(a7,f4(a1,a2),f6(f6(a2)))
% 0.20/0.62 [21]~P1(f5(f4(a1,a2),f6(a2)),a7,f6(f6(a2)))
% 0.20/0.62 [19]P1(x191,x191,f6(x192))
% 0.20/0.62 [22]P2(f5(x221,f6(x222)),f4(x223,x222),f6(f6(x222)))+~P1(x221,f4(x223,x222),f6(f6(f6(x222))))
% 0.20/0.62 [23]~E(f3(x234,x232,x233),x232)+~P2(x231,f4(x234,x233),f6(f6(x233)))+~P2(x232,f4(x234,x233),f6(f6(x233)))+P1(x231,x232,f6(f6(x233)))
% 0.20/0.62 %EqnAxiom
% 0.20/0.62 [1]E(x11,x11)
% 0.20/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.62 [4]~E(x41,x42)+E(f3(x41,x43,x44),f3(x42,x43,x44))
% 0.20/0.62 [5]~E(x51,x52)+E(f3(x53,x51,x54),f3(x53,x52,x54))
% 0.20/0.62 [6]~E(x61,x62)+E(f3(x63,x64,x61),f3(x63,x64,x62))
% 0.20/0.62 [7]~E(x71,x72)+E(f6(x71),f6(x72))
% 0.20/0.62 [8]~E(x81,x82)+E(f4(x81,x83),f4(x82,x83))
% 0.20/0.62 [9]~E(x91,x92)+E(f4(x93,x91),f4(x93,x92))
% 0.20/0.62 [10]~E(x101,x102)+E(f5(x101,x103),f5(x102,x103))
% 0.20/0.62 [11]~E(x111,x112)+E(f5(x113,x111),f5(x113,x112))
% 0.20/0.62 [12]P1(x122,x123,x124)+~E(x121,x122)+~P1(x121,x123,x124)
% 0.20/0.62 [13]P1(x133,x132,x134)+~E(x131,x132)+~P1(x133,x131,x134)
% 0.20/0.62 [14]P1(x143,x144,x142)+~E(x141,x142)+~P1(x143,x144,x141)
% 0.20/0.62 [15]P2(x152,x153,x154)+~E(x151,x152)+~P2(x151,x153,x154)
% 0.20/0.62 [16]P2(x163,x162,x164)+~E(x161,x162)+~P2(x163,x161,x164)
% 0.20/0.62 [17]P2(x173,x174,x172)+~E(x171,x172)+~P2(x173,x174,x171)
% 0.20/0.62
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 cnf(26,plain,
% 0.20/0.62 (P1(x261,x261,f6(x262))),
% 0.20/0.62 inference(rename_variables,[],[19])).
% 0.20/0.62 cnf(30,plain,
% 0.20/0.62 (P1(x301,x301,f6(x302))),
% 0.20/0.62 inference(rename_variables,[],[19])).
% 0.20/0.62 cnf(34,plain,
% 0.20/0.62 ($false),
% 0.20/0.62 inference(scs_inference,[],[18,20,21,19,26,30,2,22,15,13,12,3,23]),
% 0.20/0.62 ['proof']).
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time :0.000000s
%------------------------------------------------------------------------------