TSTP Solution File: SET842-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET842-2 : 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 : n027.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 14:31:19 EDT 2023
% Result : Unsatisfiable 61.47s 61.69s
% Output : CNFRefutation 61.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET842-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n027.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 11:15:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 61.47/61.67 %-------------------------------------------
% 61.47/61.67 % File :CSE---1.6
% 61.47/61.67 % Problem :theBenchmark
% 61.47/61.67 % Transform :cnf
% 61.47/61.67 % Format :tptp:raw
% 61.47/61.68 % Command :java -jar mcs_scs.jar %d %s
% 61.47/61.68
% 61.47/61.68 % Result :Theorem 61.000000s
% 61.47/61.68 % Output :CNFRefutation 61.000000s
% 61.47/61.68 %-------------------------------------------
% 61.47/61.68 %------------------------------------------------------------------------------
% 61.47/61.68 % File : SET842-2 : TPTP v8.1.2. Released v3.2.0.
% 61.47/61.68 % Domain : Set Theory
% 61.47/61.68 % Problem : Problem about Zorn's lemma
% 61.47/61.68 % Version : [Pau06] axioms : Reduced > Especial.
% 61.47/61.68 % English :
% 61.47/61.68
% 61.47/61.68 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 61.47/61.68 % Source : [Pau06]
% 61.47/61.68 % Names :
% 61.47/61.68
% 61.47/61.69 % Status : Unsatisfiable
% 61.47/61.69 % Rating : 0.00 v7.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v4.0.0, 0.14 v3.4.0, 0.00 v3.2.0
% 61.47/61.69 % Syntax : Number of clauses : 7 ( 1 unt; 1 nHn; 6 RR)
% 61.47/61.69 % Number of literals : 14 ( 0 equ; 7 neg)
% 61.47/61.69 % Maximal clause size : 3 ( 2 avg)
% 61.47/61.69 % Maximal term depth : 3 ( 1 avg)
% 61.47/61.69 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty)
% 61.47/61.69 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% 61.47/61.69 % Number of variables : 17 ( 0 sgn)
% 61.47/61.69 % SPC : CNF_UNS_RFO_NEQ_NHN
% 61.47/61.69
% 61.47/61.69 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 61.47/61.69 % of which only a small selection are required for the refutation.
% 61.47/61.69 % The mission is to find those few axioms, after which a refutation
% 61.47/61.69 % can be quite easily found. This version has only the necessary
% 61.47/61.69 % axioms.
% 61.47/61.69 %------------------------------------------------------------------------------
% 61.47/61.69 cnf(cls_conjecture_3,negated_conjecture,
% 61.47/61.69 ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_conjecture_4,negated_conjecture,
% 61.47/61.69 ( c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
% 61.47/61.69 | ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_Set_OUnionE_0,axiom,
% 61.47/61.69 ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
% 61.47/61.69 | c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_Set_OUnionE_1,axiom,
% 61.47/61.69 ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
% 61.47/61.69 | c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_Set_OsubsetD_0,axiom,
% 61.47/61.69 ( ~ c_in(V_c,V_A,T_a)
% 61.47/61.69 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 61.47/61.69 | c_in(V_c,V_B,T_a) ) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_Set_OsubsetI_0,axiom,
% 61.47/61.69 ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
% 61.47/61.69 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 61.47/61.69
% 61.47/61.69 cnf(cls_Set_OsubsetI_1,axiom,
% 61.47/61.69 ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
% 61.47/61.69 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 61.47/61.69
% 61.47/61.69 %------------------------------------------------------------------------------
% 61.47/61.69 %-------------------------------------------
% 61.47/61.69 % Proof found
% 61.47/61.69 % SZS status Theorem for theBenchmark
% 61.47/61.69 % SZS output start Proof
% 61.47/61.69 %ClaNum:7(EqnAxiom:0)
% 61.47/61.69 %VarNum:45(SingletonVarNum:17)
% 61.47/61.69 %MaxLitNum:3
% 61.47/61.69 %MaxfuncDepth:2
% 61.47/61.69 %SharedTerms:7
% 61.47/61.69 %goalClause: 1 2
% 61.47/61.69 %singleGoalClaCount:1
% 61.47/61.69 [1]~P1(f3(a1,f6(a2)),a7,f6(f6(a2)))
% 61.47/61.69 [2]~P2(x21,a1,f6(f6(a2)))+P1(x21,a7,f6(f6(a2)))
% 61.47/61.69 [3]P2(f4(x31,x32,x33),x31,x33)+P1(x31,x32,f6(x33))
% 61.47/61.69 [5]~P2(x51,f3(x52,x53),x53)+P2(x51,f5(x51,x52,x53),x53)
% 61.47/61.69 [6]~P2(x61,f3(x62,x63),x63)+P2(f5(x61,x62,x63),x62,f6(x63))
% 61.47/61.69 [7]~P2(f4(x71,x72,x73),x72,x73)+P1(x71,x72,f6(x73))
% 61.47/61.69 [4]P2(x41,x42,x43)+~P2(x41,x44,x43)+~P1(x44,x42,f6(x43))
% 61.47/61.69 %EqnAxiom
% 61.47/61.69
% 61.47/61.69 %-------------------------------------------
% 61.59/61.70 cnf(9,plain,
% 61.59/61.70 (~P2(f4(f3(a1,f6(a2)),a7,f6(a2)),a7,f6(a2))),
% 61.59/61.70 inference(scs_inference,[],[1,2,7])).
% 61.59/61.70 cnf(10,plain,
% 61.59/61.70 (P2(f4(f3(a1,f6(a2)),a7,f6(a2)),f3(a1,f6(a2)),f6(a2))),
% 61.59/61.70 inference(scs_inference,[],[1,2,7,3])).
% 61.59/61.70 cnf(14,plain,
% 61.59/61.70 (~P1(f5(f4(f3(a1,f6(a2)),a7,f6(a2)),a1,f6(a2)),a7,f6(f6(a2)))),
% 61.59/61.70 inference(scs_inference,[],[10,9,5,4])).
% 61.59/61.70 cnf(15,plain,
% 61.59/61.70 (P1(f5(f4(f3(a1,f6(a2)),a7,f6(a2)),a1,f6(a2)),a7,f6(f6(a2)))),
% 61.59/61.70 inference(scs_inference,[],[10,6,2])).
% 61.59/61.70 cnf(25,plain,
% 61.59/61.70 ($false),
% 61.59/61.70 inference(scs_inference,[],[15,14]),
% 61.59/61.70 ['proof']).
% 61.59/61.70 % SZS output end Proof
% 61.59/61.70 % Total time :61.000000s
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