TSTP Solution File: SET825-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET825-2 : 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 : n022.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 14:31:11 EDT 2023
% Result : Unsatisfiable 0.18s 0.69s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Aug 26 10:58:10 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.58 start to proof:theBenchmark
% 0.18/0.67 %-------------------------------------------
% 0.18/0.68 % File :CSE---1.6
% 0.18/0.68 % Problem :theBenchmark
% 0.18/0.68 % Transform :cnf
% 0.18/0.68 % Format :tptp:raw
% 0.18/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.68
% 0.18/0.68 % Result :Theorem 0.050000s
% 0.18/0.68 % Output :CNFRefutation 0.050000s
% 0.18/0.68 %-------------------------------------------
% 0.18/0.69 %------------------------------------------------------------------------------
% 0.18/0.69 % File : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.18/0.69 % Domain : Set Theory
% 0.18/0.69 % Problem : Problem about set theory
% 0.18/0.69 % Version : [Pau06] axioms : Reduced > Especial.
% 0.18/0.69 % English :
% 0.18/0.69
% 0.18/0.69 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 0.18/0.69 % Source : [Pau06]
% 0.18/0.69 % Names :
% 0.18/0.69
% 0.18/0.69 % Status : Unsatisfiable
% 0.18/0.69 % Rating : 0.10 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.10 v5.3.0, 0.17 v5.2.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 0.09 v4.0.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.21 v3.2.0
% 0.18/0.69 % Syntax : Number of clauses : 6 ( 3 unt; 1 nHn; 5 RR)
% 0.18/0.69 % Number of literals : 11 ( 1 equ; 5 neg)
% 0.18/0.69 % Maximal clause size : 3 ( 1 avg)
% 0.18/0.69 % Maximal term depth : 4 ( 1 avg)
% 0.18/0.69 % Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% 0.18/0.69 % Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% 0.18/0.69 % Number of variables : 7 ( 0 sgn)
% 0.18/0.69 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.18/0.69
% 0.18/0.69 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 0.18/0.69 % of which only a small selection are required for the refutation.
% 0.18/0.69 % The mission is to find those few axioms, after which a refutation
% 0.18/0.69 % can be quite easily found. This version has only the necessary
% 0.18/0.69 % axioms.
% 0.18/0.69 %------------------------------------------------------------------------------
% 0.18/0.69 cnf(cls_Relation_OIdI_0,axiom,
% 0.18/0.69 c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ).
% 0.18/0.69
% 0.18/0.69 cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
% 0.18/0.69 ( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))
% 0.18/0.69 | V_a = V_b ) ).
% 0.18/0.69
% 0.18/0.69 cnf(cls_conjecture_0,negated_conjecture,
% 0.18/0.69 v_Q(v_n) ).
% 0.18/0.69
% 0.18/0.69 cnf(cls_conjecture_1,negated_conjecture,
% 0.18/0.69 ~ v_Q(v_m) ).
% 0.18/0.69
% 0.18/0.69 cnf(cls_conjecture_2,negated_conjecture,
% 0.18/0.69 ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
% 0.18/0.69 | c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
% 0.18/0.69 | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ) ).
% 0.18/0.69
% 0.18/0.69 cnf(cls_conjecture_3,negated_conjecture,
% 0.18/0.69 ( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
% 0.18/0.69 | ~ c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
% 0.18/0.69 | ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ) ).
% 0.18/0.69
% 0.18/0.69 %------------------------------------------------------------------------------
% 0.18/0.69 %-------------------------------------------
% 0.18/0.69 % Proof found
% 0.18/0.69 % SZS status Theorem for theBenchmark
% 0.18/0.69 % SZS output start Proof
% 0.18/0.71 %ClaNum:22(EqnAxiom:16)
% 0.18/0.71 %VarNum:24(SingletonVarNum:7)
% 0.18/0.71 %MaxLitNum:3
% 0.18/0.71 %MaxfuncDepth:3
% 0.18/0.71 %SharedTerms:10
% 0.18/0.71 %goalClause: 17 19 21 22
% 0.18/0.71 %singleGoalClaCount:2
% 0.18/0.71 [17]P1(a1)
% 0.18/0.71 [19]~P1(a8)
% 0.18/0.71 [18]P2(f2(x181,x181,x182,x182),a4,f5(x182,x182))
% 0.18/0.71 [20]E(x201,x202)+~P2(f2(x201,x202,x203,x203),a4,f5(x203,x203))
% 0.18/0.71 [21]~P2(f2(a3,a3,a6,a6),x211,f5(a6,a6))+P2(f2(a1,a8,a6,a6),x211,f5(a6,a6))+P2(f2(f9(x211),f10(x211),a6,a6),x211,f5(a6,a6))
% 0.18/0.71 [22]~P2(f2(a3,a3,a6,a6),x221,f5(a6,a6))+P2(f2(a1,a8,a6,a6),x221,f5(a6,a6))+~P2(f2(f7(f9(x221)),f7(f10(x221)),a6,a6),x221,f5(a6,a6))
% 0.18/0.71 %EqnAxiom
% 0.18/0.71 [1]E(x11,x11)
% 0.18/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.71 [4]~E(x41,x42)+E(f2(x41,x43,x44,x45),f2(x42,x43,x44,x45))
% 0.18/0.71 [5]~E(x51,x52)+E(f2(x53,x51,x54,x55),f2(x53,x52,x54,x55))
% 0.18/0.71 [6]~E(x61,x62)+E(f2(x63,x64,x61,x65),f2(x63,x64,x62,x65))
% 0.18/0.71 [7]~E(x71,x72)+E(f2(x73,x74,x75,x71),f2(x73,x74,x75,x72))
% 0.18/0.71 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.18/0.71 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.18/0.71 [10]~E(x101,x102)+E(f9(x101),f9(x102))
% 0.18/0.71 [11]~E(x111,x112)+E(f7(x111),f7(x112))
% 0.18/0.71 [12]~E(x121,x122)+E(f10(x121),f10(x122))
% 0.18/0.71 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.18/0.71 [14]P2(x142,x143,x144)+~E(x141,x142)+~P2(x141,x143,x144)
% 0.18/0.71 [15]P2(x153,x152,x154)+~E(x151,x152)+~P2(x153,x151,x154)
% 0.18/0.71 [16]P2(x163,x164,x162)+~E(x161,x162)+~P2(x163,x164,x161)
% 0.18/0.71
% 0.18/0.71 %-------------------------------------------
% 0.18/0.72 cnf(23,plain,
% 0.18/0.72 (~E(a1,a8)),
% 0.18/0.72 inference(scs_inference,[],[17,19,13])).
% 0.18/0.72 cnf(26,plain,
% 0.18/0.72 (~P2(f2(a1,a8,x261,x261),a4,f5(x261,x261))),
% 0.18/0.72 inference(scs_inference,[],[23,2,20])).
% 0.18/0.72 cnf(28,plain,
% 0.18/0.72 (~E(f2(x281,x281,x282,x282),f2(a1,a8,x282,x282))),
% 0.18/0.72 inference(scs_inference,[],[18,23,2,20,14])).
% 0.18/0.72 cnf(29,plain,
% 0.18/0.72 (P2(f2(x291,x291,x292,x292),a4,f5(x292,x292))),
% 0.18/0.72 inference(rename_variables,[],[18])).
% 0.18/0.72 cnf(30,plain,
% 0.18/0.72 (~P2(f2(a1,a8,x301,x301),a4,x302)+~E(x302,f5(x301,x301))),
% 0.18/0.72 inference(scs_inference,[],[18,23,2,20,14,16])).
% 0.18/0.72 cnf(31,plain,
% 0.18/0.72 (~P2(f2(f7(f9(a4)),f7(f10(a4)),a6,a6),a4,f5(a6,a6))),
% 0.18/0.72 inference(scs_inference,[],[18,29,23,2,20,14,16,22])).
% 0.18/0.72 cnf(32,plain,
% 0.18/0.72 (P2(f2(x321,x321,x322,x322),a4,f5(x322,x322))),
% 0.18/0.72 inference(rename_variables,[],[18])).
% 0.18/0.72 cnf(34,plain,
% 0.18/0.72 (P2(f2(f9(a4),f10(a4),a6,a6),a4,f5(a6,a6))),
% 0.18/0.72 inference(scs_inference,[],[18,29,32,23,2,20,14,16,22,21])).
% 0.18/0.72 cnf(40,plain,
% 0.18/0.72 (E(f10(a4),f9(a4))),
% 0.18/0.72 inference(scs_inference,[],[34,20,2])).
% 0.18/0.72 cnf(41,plain,
% 0.18/0.72 (~E(f2(x411,x411,a6,a6),f2(f7(f9(a4)),f7(f10(a4)),a6,a6))),
% 0.18/0.72 inference(scs_inference,[],[18,34,31,20,2,14])).
% 0.18/0.72 cnf(44,plain,
% 0.18/0.72 (E(f7(f9(a4)),f7(f10(a4)))),
% 0.18/0.72 inference(scs_inference,[],[18,34,31,20,2,14,12,11])).
% 0.18/0.72 cnf(46,plain,
% 0.18/0.72 (E(f5(x461,f9(a4)),f5(x461,f10(a4)))),
% 0.18/0.72 inference(scs_inference,[],[18,34,31,20,2,14,12,11,10,9])).
% 0.18/0.72 cnf(49,plain,
% 0.18/0.72 (E(f2(x491,x492,f9(a4),x493),f2(x491,x492,f10(a4),x493))),
% 0.18/0.72 inference(scs_inference,[],[18,34,31,20,2,14,12,11,10,9,8,7,6])).
% 0.18/0.72 cnf(51,plain,
% 0.18/0.72 (E(f2(x511,f9(a4),x512,x513),f2(x511,f10(a4),x512,x513))),
% 0.18/0.72 inference(scs_inference,[],[18,34,26,31,20,2,14,12,11,10,9,8,7,6,15,5])).
% 0.18/0.72 cnf(52,plain,
% 0.18/0.72 (E(f2(f9(a4),x521,x522,x523),f2(f10(a4),x521,x522,x523))),
% 0.18/0.72 inference(scs_inference,[],[18,34,26,31,20,2,14,12,11,10,9,8,7,6,15,5,4])).
% 0.18/0.72 cnf(60,plain,
% 0.18/0.72 (~P2(f2(f2(x601,x601,x602,x602),f2(a1,a8,x602,x602),x603,x603),a4,f5(x603,x603))),
% 0.18/0.72 inference(scs_inference,[],[28,46,30,20])).
% 0.18/0.72 cnf(62,plain,
% 0.18/0.72 (~E(f2(a1,a8,x621,x621),f2(x622,x622,x621,x621))),
% 0.18/0.72 inference(scs_inference,[],[28,46,30,20,2])).
% 0.18/0.72 cnf(74,plain,
% 0.18/0.72 (E(f2(x741,x742,f10(a4),x743),f2(x741,x742,f9(a4),x743))),
% 0.18/0.72 inference(scs_inference,[],[49,2])).
% 0.18/0.72 cnf(78,plain,
% 0.18/0.72 (~E(f2(x781,x781,x782,x782),f2(f2(x783,x783,x784,x784),f2(a1,a8,x784,x784),x782,x782))),
% 0.18/0.72 inference(scs_inference,[],[18,49,62,60,2,3,14])).
% 0.18/0.72 cnf(84,plain,
% 0.18/0.72 (~E(f2(f2(x841,x841,x842,x842),f2(a1,a8,x842,x842),x843,x843),f2(x844,x844,x843,x843))),
% 0.18/0.72 inference(scs_inference,[],[78,2])).
% 0.18/0.72 cnf(85,plain,
% 0.18/0.72 (E(f2(f9(a4),f9(a4),x851,x852),f2(f10(a4),f10(a4),x851,x852))),
% 0.18/0.72 inference(scs_inference,[],[78,51,52,2,3])).
% 0.18/0.72 cnf(96,plain,
% 0.18/0.72 (E(f2(x961,x962,f10(a4),x963),f2(x961,x962,f9(a4),x963))),
% 0.18/0.72 inference(rename_variables,[],[74])).
% 0.18/0.72 cnf(108,plain,
% 0.18/0.72 ($false),
% 0.18/0.72 inference(scs_inference,[],[84,74,96,85,44,41,40,18,2,3,14,10,7,4,12,11,9,8,5]),
% 0.18/0.72 ['proof']).
% 0.18/0.72 % SZS output end Proof
% 0.18/0.72 % Total time :0.050000s
%------------------------------------------------------------------------------