TSTP Solution File: TOP004-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : TOP004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n017.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 : Fri Sep 1 05:53:20 EDT 2023
% Result : Unsatisfiable 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 23:00:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.54 start to proof:theBenchmark
% 0.19/0.58 %-------------------------------------------
% 0.19/0.58 % File :CSE---1.6
% 0.19/0.58 % Problem :theBenchmark
% 0.19/0.58 % Transform :cnf
% 0.19/0.58 % Format :tptp:raw
% 0.19/0.58 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.58
% 0.19/0.58 % Result :Theorem 0.000000s
% 0.19/0.58 % Output :CNFRefutation 0.000000s
% 0.19/0.58 %-------------------------------------------
% 0.19/0.59 %--------------------------------------------------------------------------
% 0.19/0.59 % File : TOP004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.59 % Domain : Topology
% 0.19/0.59 % Problem : Topology generated by a basis forms a topological space, part 4
% 0.19/0.59 % Version : [WM89] axioms : Incomplete > Reduced & Augmented > Incomplete.
% 0.19/0.59 % English :
% 0.19/0.59
% 0.19/0.59 % Refs : [WM89] Wick & McCune (1989), Automated Reasoning about Elemen
% 0.19/0.59 % Source : [WM89]
% 0.19/0.59 % Names : Lemma 1d [WM89]
% 0.19/0.59
% 0.19/0.59 % Status : Unsatisfiable
% 0.19/0.59 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% 0.19/0.59 % Syntax : Number of clauses : 21 ( 5 unt; 1 nHn; 17 RR)
% 0.19/0.59 % Number of literals : 59 ( 0 equ; 38 neg)
% 0.19/0.59 % Maximal clause size : 6 ( 2 avg)
% 0.19/0.59 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.59 % Number of predicates : 5 ( 5 usr; 0 prp; 2-2 aty)
% 0.19/0.59 % Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% 0.19/0.59 % Number of variables : 59 ( 6 sgn)
% 0.19/0.59 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.19/0.59
% 0.19/0.59 % Comments : The axioms in this version are known to be incomplete. To
% 0.19/0.59 % make them complete it is be necessary to add appropriate set
% 0.19/0.59 % theory axioms.
% 0.19/0.59 %--------------------------------------------------------------------------
% 0.19/0.59 %----Include Point-set topology axioms
% 0.19/0.59 % include('Axioms/TOP001-0.ax').
% 0.19/0.59 %--------------------------------------------------------------------------
% 0.19/0.59 %----Sigma (union of members).
% 0.19/0.59 cnf(union_of_members_3,axiom,
% 0.19/0.59 ( element_of_set(U,union_of_members(Vf))
% 0.19/0.59 | ~ element_of_set(U,Uu1)
% 0.19/0.59 | ~ element_of_collection(Uu1,Vf) ) ).
% 0.19/0.59
% 0.19/0.59 %----Basis for a topology
% 0.19/0.59 cnf(basis_for_topology_28,axiom,
% 0.19/0.59 ( ~ basis(X,Vf)
% 0.19/0.59 | equal_sets(union_of_members(Vf),X) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(basis_for_topology_29,axiom,
% 0.19/0.59 ( ~ basis(X,Vf)
% 0.19/0.59 | ~ element_of_set(Y,X)
% 0.19/0.59 | ~ element_of_collection(Vb1,Vf)
% 0.19/0.59 | ~ element_of_collection(Vb2,Vf)
% 0.19/0.59 | ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
% 0.19/0.59 | element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2)) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(basis_for_topology_30,axiom,
% 0.19/0.59 ( ~ basis(X,Vf)
% 0.19/0.59 | ~ element_of_set(Y,X)
% 0.19/0.59 | ~ element_of_collection(Vb1,Vf)
% 0.19/0.59 | ~ element_of_collection(Vb2,Vf)
% 0.19/0.59 | ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
% 0.19/0.59 | element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(basis_for_topology_31,axiom,
% 0.19/0.59 ( ~ basis(X,Vf)
% 0.19/0.59 | ~ element_of_set(Y,X)
% 0.19/0.59 | ~ element_of_collection(Vb1,Vf)
% 0.19/0.59 | ~ element_of_collection(Vb2,Vf)
% 0.19/0.59 | ~ element_of_set(Y,intersection_of_sets(Vb1,Vb2))
% 0.19/0.59 | subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2)) ) ).
% 0.19/0.59
% 0.19/0.59 %----Topology generated by a basis
% 0.19/0.59 cnf(topology_generated_37,axiom,
% 0.19/0.59 ( ~ element_of_collection(U,top_of_basis(Vf))
% 0.19/0.59 | ~ element_of_set(X,U)
% 0.19/0.59 | element_of_set(X,f10(Vf,U,X)) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(topology_generated_38,axiom,
% 0.19/0.59 ( ~ element_of_collection(U,top_of_basis(Vf))
% 0.19/0.59 | ~ element_of_set(X,U)
% 0.19/0.59 | element_of_collection(f10(Vf,U,X),Vf) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(topology_generated_39,axiom,
% 0.19/0.59 ( ~ element_of_collection(U,top_of_basis(Vf))
% 0.19/0.59 | ~ element_of_set(X,U)
% 0.19/0.59 | subset_sets(f10(Vf,U,X),U) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(topology_generated_40,axiom,
% 0.19/0.59 ( element_of_collection(U,top_of_basis(Vf))
% 0.19/0.59 | element_of_set(f11(Vf,U),U) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(topology_generated_41,axiom,
% 0.19/0.59 ( element_of_collection(U,top_of_basis(Vf))
% 0.19/0.59 | ~ element_of_set(f11(Vf,U),Uu11)
% 0.19/0.59 | ~ element_of_collection(Uu11,Vf)
% 0.19/0.59 | ~ subset_sets(Uu11,U) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_12,axiom,
% 0.19/0.59 ( ~ subset_sets(X,Y)
% 0.19/0.59 | ~ subset_sets(Y,Z)
% 0.19/0.59 | subset_sets(X,Z) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_13,axiom,
% 0.19/0.59 ( ~ element_of_set(Z,intersection_of_sets(X,Y))
% 0.19/0.59 | element_of_set(Z,X) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_14,axiom,
% 0.19/0.59 ( ~ element_of_set(Z,intersection_of_sets(X,Y))
% 0.19/0.59 | element_of_set(Z,Y) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_15,axiom,
% 0.19/0.59 ( element_of_set(Z,intersection_of_sets(X,Y))
% 0.19/0.59 | ~ element_of_set(Z,X)
% 0.19/0.59 | ~ element_of_set(Z,Y) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_16,axiom,
% 0.19/0.59 ( ~ subset_sets(X,Y)
% 0.19/0.59 | ~ subset_sets(U,V)
% 0.19/0.59 | subset_sets(intersection_of_sets(X,U),intersection_of_sets(Y,V)) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_17,axiom,
% 0.19/0.59 ( ~ equal_sets(X,Y)
% 0.19/0.59 | ~ element_of_set(Z,X)
% 0.19/0.59 | element_of_set(Z,Y) ) ).
% 0.19/0.59
% 0.19/0.59 cnf(set_theory_18,axiom,
% 0.19/0.59 equal_sets(intersection_of_sets(X,Y),intersection_of_sets(Y,X)) ).
% 0.19/0.59
% 0.19/0.59 cnf(lemma_1d_1,negated_conjecture,
% 0.19/0.59 basis(cx,f) ).
% 0.19/0.59
% 0.19/0.59 cnf(lemma_1d_2,negated_conjecture,
% 0.19/0.59 element_of_collection(U,top_of_basis(f)) ).
% 0.19/0.59
% 0.19/0.59 cnf(lemma_1d_3,negated_conjecture,
% 0.19/0.59 element_of_collection(V,top_of_basis(f)) ).
% 0.19/0.59
% 0.19/0.59 cnf(lemma_1d_4,negated_conjecture,
% 0.19/0.59 ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ).
% 0.19/0.59
% 0.19/0.59 %--------------------------------------------------------------------------
% 0.19/0.59 %-------------------------------------------
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark
% 0.19/0.59 % SZS output start Proof
% 0.19/0.59 %ClaNum:21(EqnAxiom:0)
% 0.19/0.59 %VarNum:144(SingletonVarNum:58)
% 0.19/0.59 %MaxLitNum:6
% 0.19/0.59 %MaxfuncDepth:1
% 0.19/0.59 %SharedTerms:4
% 0.19/0.59 %goalClause: 1 3 5
% 0.19/0.59 %singleGoalClaCount:3
% 0.19/0.59 [1]P1(a1,a2)
% 0.19/0.59 [3]P2(x31,f3(a2))
% 0.19/0.59 [4]P3(f4(x41,x42),f4(x42,x41))
% 0.19/0.59 [5]~P2(f4(x51,x52),f3(a2))
% 0.19/0.59 [6]~P1(x62,x61)+P3(f8(x61),x62)
% 0.19/0.59 [9]P4(f5(x92,x91),x91)+P2(x91,f3(x92))
% 0.19/0.59 [11]P4(x111,x112)+~P4(x111,f4(x113,x112))
% 0.19/0.59 [12]P4(x121,x122)+~P4(x121,f4(x122,x123))
% 0.19/0.59 [7]~P3(x73,x72)+P4(x71,x72)+~P4(x71,x73)
% 0.19/0.59 [8]~P5(x81,x83)+P5(x81,x82)+~P5(x83,x82)
% 0.19/0.59 [10]~P2(x103,x102)+~P4(x101,x103)+P4(x101,f8(x102))
% 0.19/0.59 [13]~P4(x131,x133)+~P4(x131,x132)+P4(x131,f4(x132,x133))
% 0.19/0.59 [16]~P4(x161,x163)+~P2(x163,f3(x162))+P4(x161,f6(x162,x163,x161))
% 0.19/0.59 [17]~P4(x173,x172)+~P2(x172,f3(x171))+P2(f6(x171,x172,x173),x171)
% 0.19/0.59 [18]~P4(x183,x182)+~P2(x182,f3(x181))+P5(f6(x181,x182,x183),x182)
% 0.19/0.59 [14]~P5(x142,x144)+~P5(x141,x143)+P5(f4(x141,x142),f4(x143,x144))
% 0.19/0.59 [15]~P5(x153,x151)+~P2(x153,x152)+~P4(f5(x152,x151),x153)+P2(x151,f3(x152))
% 0.19/0.59 [19]~P4(x191,x192)+~P2(x195,x193)+~P2(x194,x193)+~P1(x192,x193)+~P4(x191,f4(x194,x195))+P4(x191,f7(x192,x193,x191,x194,x195))
% 0.19/0.59 [20]~P4(x203,x201)+~P2(x205,x202)+~P2(x204,x202)+~P1(x201,x202)+~P4(x203,f4(x204,x205))+P2(f7(x201,x202,x203,x204,x205),x202)
% 0.19/0.59 [21]~P4(x213,x211)+~P2(x215,x212)+~P2(x214,x212)+~P1(x211,x212)+~P4(x213,f4(x214,x215))+P5(f7(x211,x212,x213,x214,x215),f4(x214,x215))
% 0.19/0.59 %EqnAxiom
% 0.19/0.59
% 0.19/0.59 %-------------------------------------------
% 0.19/0.59 cnf(22,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(scs_inference,[],[3,5]),
% 0.19/0.59 ['proof']).
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time :0.000000s
%------------------------------------------------------------------------------