TSTP Solution File: SET846-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET846-2 : 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 : n012.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 14:31:21 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 : SET846-2 : 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
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 15:13:55 EDT 2023
% 0.12/0.34 % 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 : SET846-2 : 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 v5.3.0, 0.05 v5.2.0, 0.00 v3.2.0
% 0.19/0.61 % Syntax : Number of clauses : 5 ( 2 unt; 0 nHn; 4 RR)
% 0.19/0.61 % Number of literals : 8 ( 0 equ; 4 neg)
% 0.19/0.61 % Maximal clause size : 2 ( 1 avg)
% 0.19/0.61 % Maximal term depth : 4 ( 2 avg)
% 0.19/0.61 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty)
% 0.19/0.61 % Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% 0.19/0.61 % Number of variables : 11 ( 1 sgn)
% 0.19/0.61 % SPC : CNF_UNS_RFO_NEQ_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_Set_OUnion__upper_0,axiom,
% 0.19/0.61 ( ~ c_in(V_B,V_A,tc_set(T_a))
% 0.19/0.61 | c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Set_Osubset__refl_0,axiom,
% 0.19/0.61 c_lessequals(V_A,V_A,tc_set(T_a)) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
% 0.19/0.61 ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.19/0.61 | c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(cls_Zorn_OTFin__UnionI_0,axiom,
% 0.19/0.61 ( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
% 0.19/0.61 | c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(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_lessequals(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),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:5(EqnAxiom:0)
% 0.19/0.61 %VarNum:29(SingletonVarNum:11)
% 0.19/0.61 %MaxLitNum:2
% 0.19/0.61 %MaxfuncDepth:3
% 0.19/0.61 %SharedTerms:8
% 0.19/0.61 %goalClause: 2
% 0.19/0.61 %singleGoalClaCount:1
% 0.19/0.61 [2]~P1(f5(a6,f4(f3(a6,a2),f1(a2)),a2),f4(f3(a6,a2),f1(a2)),f1(f1(a2)))
% 0.19/0.61 [1]P1(x11,x11,f1(x12))
% 0.19/0.61 [3]~P2(x31,x32,f1(x33))+P1(x31,f4(x32,x33),f1(x33))
% 0.19/0.61 [5]~P2(x52,f3(x51,x53),f1(f1(x53)))+P2(f5(x51,x52,x53),f3(x51,x53),f1(f1(x53)))
% 0.19/0.61 [4]P2(f4(x41,f1(x42)),f3(x43,x42),f1(f1(x42)))+~P1(x41,f3(x43,x42),f1(f1(f1(x42))))
% 0.19/0.61 %EqnAxiom
% 0.19/0.61
% 0.19/0.61 %-------------------------------------------
% 0.19/0.62 cnf(8,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[2,1,3,4,5]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.000000s
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