TSTP Solution File: SET852-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET852-2 : 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 : 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 14:31:24 EDT 2023
% Result : Unsatisfiable 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET852-2 : 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
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 10:53:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.54 start to proof:theBenchmark
% 0.21/0.57 %-------------------------------------------
% 0.21/0.57 % File :CSE---1.6
% 0.21/0.57 % Problem :theBenchmark
% 0.21/0.57 % Transform :cnf
% 0.21/0.57 % Format :tptp:raw
% 0.21/0.57 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.57
% 0.21/0.57 % Result :Theorem 0.000000s
% 0.21/0.57 % Output :CNFRefutation 0.000000s
% 0.21/0.57 %-------------------------------------------
% 0.21/0.58 %------------------------------------------------------------------------------
% 0.21/0.58 % File : SET852-2 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.58 % Domain : Set Theory
% 0.21/0.58 % Problem : Problem about Zorn's lemma
% 0.21/0.58 % Version : [Pau06] axioms : Reduced > Especial.
% 0.21/0.58 % English :
% 0.21/0.58
% 0.21/0.58 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.21/0.58 % Source : [Pau06]
% 0.21/0.58 % Names :
% 0.21/0.58
% 0.21/0.58 % Status : Unsatisfiable
% 0.21/0.58 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v4.0.0, 0.14 v3.4.0, 0.00 v3.2.0
% 0.21/0.58 % Syntax : Number of clauses : 6 ( 2 unt; 4 nHn; 5 RR)
% 0.21/0.58 % Number of literals : 14 ( 0 equ; 5 neg)
% 0.21/0.58 % Maximal clause size : 3 ( 2 avg)
% 0.21/0.58 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.58 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty)
% 0.21/0.58 % Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% 0.21/0.58 % Number of variables : 13 ( 0 sgn)
% 0.21/0.58 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.21/0.58
% 0.21/0.58 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.21/0.58 % of which only a small selection are required for the refutation.
% 0.21/0.58 % The mission is to find those few axioms, after which a refutation
% 0.21/0.58 % can be quite easily found. This version has only the necessary
% 0.21/0.58 % axioms.
% 0.21/0.58 %------------------------------------------------------------------------------
% 0.21/0.58 cnf(cls_conjecture_2,negated_conjecture,
% 0.21/0.58 ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
% 0.21/0.58
% 0.21/0.58 cnf(cls_conjecture_3,negated_conjecture,
% 0.21/0.58 ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ).
% 0.21/0.58
% 0.21/0.58 cnf(cls_conjecture_4,negated_conjecture,
% 0.21/0.58 ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
% 0.21/0.58 | c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
% 0.21/0.58 | ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ) ).
% 0.21/0.58
% 0.21/0.58 cnf(cls_Zorn_OUnion__lemma0_0,axiom,
% 0.21/0.58 ( c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a))
% 0.21/0.58 | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
% 0.21/0.58 | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
% 0.21/0.58
% 0.21/0.58 cnf(cls_Zorn_OUnion__lemma0_1,axiom,
% 0.21/0.58 ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a))
% 0.21/0.58 | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
% 0.21/0.58 | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
% 0.21/0.58
% 0.21/0.58 cnf(cls_Zorn_OUnion__lemma0_2,axiom,
% 0.21/0.58 ( ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a))
% 0.21/0.58 | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
% 0.21/0.58 | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
% 0.21/0.58
% 0.21/0.58 %------------------------------------------------------------------------------
% 0.21/0.58 %-------------------------------------------
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 %ClaNum:6(EqnAxiom:0)
% 0.21/0.58 %VarNum:45(SingletonVarNum:13)
% 0.21/0.58 %MaxLitNum:3
% 0.21/0.58 %MaxfuncDepth:2
% 0.21/0.58 %SharedTerms:10
% 0.21/0.58 %goalClause: 1 2 3
% 0.21/0.58 %singleGoalClaCount:2
% 0.21/0.58 [1]~P1(f3(a1,f6(a2)),a8,f6(f6(a2)))
% 0.21/0.58 [2]~P1(f4(a7,a8,a2),f3(a1,f6(a2)),f6(f6(a2)))
% 0.21/0.58 [3]P1(f4(a7,a8,a2),x31,f6(f6(a2)))+~P2(x31,a1,f6(f6(a2)))+P1(x31,a8,f6(f6(a2)))
% 0.21/0.58 [4]P2(f5(x44,x41,x42,x43),x42,f6(x43))+P1(x41,f3(x42,x43),f6(x43))+P1(f3(x42,x43),x44,f6(x43))
% 0.21/0.58 [5]~P1(x51,f5(x54,x51,x52,x53),f6(x53))+P1(x51,f3(x52,x53),f6(x53))+P1(f3(x52,x53),x54,f6(x53))
% 0.21/0.58 [6]~P1(f5(x64,x61,x62,x63),x64,f6(x63))+P1(x61,f3(x62,x63),f6(x63))+P1(f3(x62,x63),x64,f6(x63))
% 0.21/0.58 %EqnAxiom
% 0.21/0.58
% 0.21/0.58 %-------------------------------------------
% 0.21/0.58 cnf(7,plain,
% 0.21/0.58 (~P1(f5(a8,f4(a7,a8,a2),a1,f6(a2)),a8,f6(f6(a2)))),
% 0.21/0.58 inference(scs_inference,[],[1,2,6])).
% 0.21/0.58 cnf(8,plain,
% 0.21/0.58 (~P1(f4(a7,a8,a2),f5(a8,f4(a7,a8,a2),a1,f6(a2)),f6(f6(a2)))),
% 0.21/0.58 inference(scs_inference,[],[1,2,6,5])).
% 0.21/0.58 cnf(9,plain,
% 0.21/0.58 (P2(f5(a8,f4(a7,a8,a2),a1,f6(a2)),a1,f6(f6(a2)))),
% 0.21/0.58 inference(scs_inference,[],[1,2,6,5,4])).
% 0.21/0.58 cnf(15,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(scs_inference,[],[7,8,9,3]),
% 0.21/0.58 ['proof']).
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 % Total time :0.000000s
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