TSTP Solution File: SET845-2 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET845-2 : 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 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET845-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n005.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 16:05:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.000000s
% 0.20/0.63 % Output :CNFRefutation 0.000000s
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 % File : SET845-2 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.63 % Domain : Set Theory
% 0.20/0.63 % Problem : Problem about Zorn's lemma
% 0.20/0.63 % Version : [Pau06] axioms : Reduced > Especial.
% 0.20/0.63 % English :
% 0.20/0.63
% 0.20/0.63 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.20/0.63 % Source : [Pau06]
% 0.20/0.63 % Names :
% 0.20/0.63
% 0.20/0.63 % Status : Unsatisfiable
% 0.20/0.63 % Rating : 0.00 v5.3.0, 0.08 v5.2.0, 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
% 0.20/0.63 % Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 6 RR)
% 0.20/0.63 % Number of literals : 11 ( 3 equ; 5 neg)
% 0.20/0.63 % Maximal clause size : 3 ( 1 avg)
% 0.20/0.63 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.63 % Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% 0.20/0.63 % Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% 0.20/0.63 % Number of variables : 12 ( 1 sgn)
% 0.20/0.63 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.20/0.63
% 0.20/0.63 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.20/0.63 % of which only a small selection are required for the refutation.
% 0.20/0.63 % The mission is to find those few axioms, after which a refutation
% 0.20/0.64 % can be quite easily found. This version has only the necessary
% 0.20/0.64 % axioms.
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 cnf(cls_Set_OUnion__upper_0,axiom,
% 0.20/0.64 ( ~ c_in(V_B,V_A,tc_set(T_a))
% 0.20/0.64 | c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_Set_Osubset__antisym_0,axiom,
% 0.20/0.64 ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
% 0.20/0.64 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 0.20/0.64 | V_A = V_B ) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
% 0.20/0.64 c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
% 0.20/0.64 ( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
% 0.20/0.64 | c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_conjecture_0,negated_conjecture,
% 0.20/0.64 c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_conjecture_1,negated_conjecture,
% 0.20/0.64 v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ).
% 0.20/0.64
% 0.20/0.64 cnf(cls_conjecture_2,negated_conjecture,
% 0.20/0.64 v_m != c_Zorn_Osucc(v_S,v_m,t_a) ).
% 0.20/0.64
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:24(EqnAxiom:17)
% 0.20/0.64 %VarNum:30(SingletonVarNum:12)
% 0.20/0.64 %MaxLitNum:3
% 0.20/0.64 %MaxfuncDepth:2
% 0.20/0.64 %SharedTerms:11
% 0.20/0.64 %goalClause: 18 19 21
% 0.20/0.64 %singleGoalClaCount:3
% 0.20/0.64 [21]~E(f5(a1,a7,a2),a7)
% 0.20/0.64 [18]E(f4(f3(a1,a2),f6(a2)),a7)
% 0.20/0.64 [19]P1(a7,f3(a1,a2),f6(f6(a2)))
% 0.20/0.64 [20]P2(x201,f5(x202,x201,x203),f6(f6(x203)))
% 0.20/0.64 [22]~P1(x221,x222,f6(x223))+P2(x221,f4(x222,x223),f6(x223))
% 0.20/0.64 [24]~P1(x242,f3(x241,x243),f6(f6(x243)))+P1(f5(x241,x242,x243),f3(x241,x243),f6(f6(x243)))
% 0.20/0.64 [23]E(x231,x232)+~P2(x232,x231,f6(x233))+~P2(x231,x232,f6(x233))
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.20/0.64 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.20/0.64 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.20/0.64 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73))
% 0.20/0.64 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82))
% 0.20/0.64 [9]~E(x91,x92)+E(f5(x91,x93,x94),f5(x92,x93,x94))
% 0.20/0.64 [10]~E(x101,x102)+E(f5(x103,x101,x104),f5(x103,x102,x104))
% 0.20/0.64 [11]~E(x111,x112)+E(f5(x113,x114,x111),f5(x113,x114,x112))
% 0.20/0.64 [12]P1(x122,x123,x124)+~E(x121,x122)+~P1(x121,x123,x124)
% 0.20/0.64 [13]P1(x133,x132,x134)+~E(x131,x132)+~P1(x133,x131,x134)
% 0.20/0.64 [14]P1(x143,x144,x142)+~E(x141,x142)+~P1(x143,x144,x141)
% 0.20/0.64 [15]P2(x152,x153,x154)+~E(x151,x152)+~P2(x151,x153,x154)
% 0.20/0.64 [16]P2(x163,x162,x164)+~E(x161,x162)+~P2(x163,x161,x164)
% 0.20/0.64 [17]P2(x173,x174,x172)+~E(x171,x172)+~P2(x173,x174,x171)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(33,plain,
% 0.20/0.64 (P1(f5(a1,a7,a2),f3(a1,a2),f6(f6(a2)))),
% 0.20/0.64 inference(scs_inference,[],[18,21,19,20,2,12,3,23,22,24])).
% 0.20/0.64 cnf(36,plain,
% 0.20/0.64 (~P2(f5(a1,a7,a2),f4(f3(a1,a2),f6(a2)),f6(f6(a2)))),
% 0.20/0.64 inference(scs_inference,[],[18,21,19,20,2,12,3,23,22,24,17,16])).
% 0.20/0.64 cnf(41,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[36,33,22]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------