TSTP Solution File: TOP001-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : TOP001-2 : 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 : n018.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 05:53:19 EDT 2023
% Result : Unsatisfiable 266.90s 271.42s
% Output : CNFRefutation 267.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : TOP001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 00:06:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.23/0.60 start to proof:theBenchmark
% 266.90/271.39 %-------------------------------------------
% 266.90/271.39 % File :CSE---1.6
% 266.90/271.39 % Problem :theBenchmark
% 266.90/271.39 % Transform :cnf
% 266.90/271.39 % Format :tptp:raw
% 266.90/271.39 % Command :java -jar mcs_scs.jar %d %s
% 266.90/271.39
% 266.90/271.39 % Result :Theorem 266.020000s
% 266.90/271.39 % Output :CNFRefutation 266.020000s
% 266.90/271.39 %-------------------------------------------
% 266.90/271.42 %--------------------------------------------------------------------------
% 266.90/271.42 % File : TOP001-2 : TPTP v8.1.2. Released v1.0.0.
% 266.90/271.42 % Domain : Topology
% 266.90/271.42 % Problem : Topology generated by a basis forms a topological space, part 1
% 266.90/271.42 % Version : [WM89] axioms : Incomplete > Reduced & Augmented > Incomplete.
% 266.90/271.42 % English :
% 266.90/271.42
% 266.90/271.42 % Refs : [WM89] Wick & McCune (1989), Automated Reasoning about Elemen
% 266.90/271.42 % Source : [WM89]
% 266.90/271.42 % Names : Lemma 1a [WM89]
% 266.90/271.42
% 266.90/271.42 % Status : Unsatisfiable
% 266.90/271.42 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v5.4.0, 0.10 v5.1.0, 0.00 v5.0.0, 0.07 v4.1.0, 0.00 v2.7.0, 0.12 v2.6.0, 0.00 v2.4.0, 0.00 v2.1.0, 0.00 v2.0.0
% 266.90/271.42 % Syntax : Number of clauses : 13 ( 3 unt; 1 nHn; 11 RR)
% 266.90/271.42 % Number of literals : 27 ( 0 equ; 14 neg)
% 266.90/271.42 % Maximal clause size : 3 ( 2 avg)
% 266.90/271.42 % Maximal term depth : 3 ( 1 avg)
% 266.90/271.42 % Number of predicates : 5 ( 5 usr; 0 prp; 2-2 aty)
% 266.90/271.42 % Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% 266.90/271.42 % Number of variables : 25 ( 0 sgn)
% 266.90/271.42 % SPC : CNF_UNS_RFO_NEQ_NHN
% 266.90/271.42
% 266.90/271.42 % Comments : The axioms in this version are known to be incomplete. To
% 266.90/271.42 % make them complete it is be necessary to add appropriate set
% 266.90/271.42 % theory axioms.
% 266.90/271.42 %--------------------------------------------------------------------------
% 266.90/271.42 %----Include Point-set topology axioms
% 266.90/271.42 % include('Axioms/TOP001-0.ax').
% 266.90/271.42 %--------------------------------------------------------------------------
% 266.90/271.42 %----Sigma (union of members).
% 266.90/271.42 cnf(union_of_members_1,axiom,
% 266.90/271.42 ( ~ element_of_set(U,union_of_members(Vf))
% 266.90/271.42 | element_of_set(U,f1(Vf,U)) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(union_of_members_2,axiom,
% 266.90/271.42 ( ~ element_of_set(U,union_of_members(Vf))
% 266.90/271.42 | element_of_collection(f1(Vf,U),Vf) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(union_of_members_3,axiom,
% 266.90/271.42 ( element_of_set(U,union_of_members(Vf))
% 266.90/271.42 | ~ element_of_set(U,Uu1)
% 266.90/271.42 | ~ element_of_collection(Uu1,Vf) ) ).
% 266.90/271.42
% 266.90/271.42 %----Basis for a topology
% 266.90/271.42 cnf(basis_for_topology_28,axiom,
% 266.90/271.42 ( ~ basis(X,Vf)
% 266.90/271.42 | equal_sets(union_of_members(Vf),X) ) ).
% 266.90/271.42
% 266.90/271.42 %----Topology generated by a basis
% 266.90/271.42 cnf(topology_generated_37,axiom,
% 266.90/271.42 ( ~ element_of_collection(U,top_of_basis(Vf))
% 266.90/271.42 | ~ element_of_set(X,U)
% 266.90/271.42 | element_of_set(X,f10(Vf,U,X)) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(topology_generated_38,axiom,
% 266.90/271.42 ( ~ element_of_collection(U,top_of_basis(Vf))
% 266.90/271.42 | ~ element_of_set(X,U)
% 266.90/271.42 | element_of_collection(f10(Vf,U,X),Vf) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(set_theory_1,axiom,
% 266.90/271.42 subset_sets(X,X) ).
% 266.90/271.42
% 266.90/271.42 cnf(set_theory_2,axiom,
% 266.90/271.42 ( ~ subset_sets(X,Y)
% 266.90/271.42 | ~ element_of_set(U,X)
% 266.90/271.42 | element_of_set(U,Y) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(set_theory_3,axiom,
% 266.90/271.42 ( ~ equal_sets(X,Y)
% 266.90/271.42 | subset_sets(X,Y) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(set_theory_4,axiom,
% 266.90/271.42 ( subset_sets(X,Y)
% 266.90/271.42 | element_of_set(in_1st_set(X,Y),X) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(set_theory_5,axiom,
% 266.90/271.42 ( subset_sets(X,Y)
% 266.90/271.42 | ~ element_of_set(in_1st_set(X,Y),Y) ) ).
% 266.90/271.42
% 266.90/271.42 cnf(lemma_1a_1,negated_conjecture,
% 266.90/271.42 basis(cx,f) ).
% 266.90/271.42
% 266.90/271.42 cnf(lemma_1a_2,negated_conjecture,
% 266.90/271.42 ~ subset_sets(union_of_members(top_of_basis(f)),cx) ).
% 266.90/271.42
% 266.90/271.42 %--------------------------------------------------------------------------
% 266.90/271.42 %-------------------------------------------
% 266.90/271.42 % Proof found
% 266.90/271.42 % SZS status Theorem for theBenchmark
% 266.90/271.42 % SZS output start Proof
% 266.90/271.44 %ClaNum:13(EqnAxiom:0)
% 266.90/271.44 %VarNum:58(SingletonVarNum:25)
% 266.90/271.44 %MaxLitNum:3
% 266.90/271.44 %MaxfuncDepth:2
% 266.90/271.44 %SharedTerms:6
% 266.90/271.44 %goalClause: 1 3
% 266.90/271.44 %singleGoalClaCount:2
% 266.90/271.44 [1]P1(a1,a2)
% 266.90/271.44 [3]~P2(f7(f3(a2)),a1)
% 266.90/271.44 [2]P2(x21,x21)
% 266.90/271.44 [4]~P3(x41,x42)+P2(x41,x42)
% 266.90/271.44 [5]~P1(x52,x51)+P3(f7(x51),x52)
% 266.90/271.44 [6]P2(x61,x62)+P4(f4(x61,x62),x61)
% 266.90/271.44 [9]~P4(x91,f7(x92))+P4(x91,f5(x92,x91))
% 266.90/271.44 [10]~P4(x102,f7(x101))+P5(f5(x101,x102),x101)
% 266.90/271.44 [11]P2(x111,x112)+~P4(f4(x111,x112),x112)
% 266.90/271.44 [7]~P2(x73,x72)+P4(x71,x72)+~P4(x71,x73)
% 266.90/271.44 [8]~P5(x83,x82)+~P4(x81,x83)+P4(x81,f7(x82))
% 266.90/271.44 [12]~P4(x121,x123)+~P5(x123,f3(x122))+P4(x121,f6(x122,x123,x121))
% 266.90/271.44 [13]~P4(x133,x132)+~P5(x132,f3(x131))+P5(f6(x131,x132,x133),x131)
% 266.90/271.44 %EqnAxiom
% 266.90/271.44
% 266.90/271.44 %-------------------------------------------
% 266.90/271.56 cnf(14,plain,
% 266.90/271.56 (~P3(f7(f3(a2)),a1)),
% 266.90/271.56 inference(scs_inference,[],[3,4])).
% 266.90/271.56 cnf(21,plain,
% 266.90/271.56 (P2(f7(a2),a1)),
% 266.90/271.56 inference(scs_inference,[],[1,5,4])).
% 266.90/271.56 cnf(25,plain,
% 266.90/271.56 (~P4(x251,x252)+P4(x251,x253)+P4(f4(x252,x253),x252)),
% 266.90/271.56 inference(scs_inference,[],[6,7])).
% 266.90/271.56 cnf(28,plain,
% 266.90/271.56 (P4(f4(f7(f3(a2)),a1),f5(f3(a2),f4(f7(f3(a2)),a1)))),
% 266.90/271.56 inference(scs_inference,[],[3,9,6])).
% 266.90/271.56 cnf(29,plain,
% 266.90/271.56 (~P4(x291,f5(x292,x293))+P4(x291,f7(x292))+~P4(x293,f7(x292))),
% 266.90/271.56 inference(scs_inference,[],[10,8])).
% 266.90/271.56 cnf(30,plain,
% 266.90/271.56 (~P4(x301,f7(a2))+P4(x301,a1)),
% 266.90/271.56 inference(scs_inference,[],[21,7])).
% 266.90/271.56 cnf(37,plain,
% 266.90/271.56 (~P4(x371,f7(x372))+P4(x371,x373)+P4(f4(f7(x372),x373),f5(x372,f4(f7(x372),x373)))),
% 266.90/271.56 inference(scs_inference,[],[25,9])).
% 266.90/271.56 cnf(182103,plain,
% 266.90/271.56 (~P4(f4(x1821031,x1821032),x1821032)+P2(x1821031,x1821032)),
% 266.90/271.56 inference(rename_variables,[],[11])).
% 266.90/271.56 cnf(182105,plain,
% 266.90/271.56 (~P4(x1821051,x1821052)+P4(f4(x1821052,x1821053),x1821052)+P4(x1821051,x1821053)),
% 266.90/271.56 inference(rename_variables,[],[25])).
% 266.90/271.56 cnf(182107,plain,
% 266.90/271.56 (~P4(x1821071,x1821072)+~P2(x1821072,x1821073)+P4(x1821071,x1821073)),
% 266.90/271.56 inference(rename_variables,[],[7])).
% 266.90/271.56 cnf(182111,plain,
% 266.90/271.56 (~P4(x1821111,x1821112)+P4(x1821111,f7(x1821113))+~P5(x1821112,x1821113)),
% 266.90/271.56 inference(rename_variables,[],[8])).
% 266.90/271.56 cnf(182113,plain,
% 266.90/271.56 (~P4(x1821131,f7(x1821132))+P5(f5(x1821132,x1821131),x1821132)),
% 266.90/271.56 inference(rename_variables,[],[10])).
% 266.90/271.56 cnf(182115,plain,
% 266.90/271.56 (~P4(x1821151,x1821152)+~P2(x1821152,x1821153)+P4(x1821151,x1821153)),
% 266.90/271.56 inference(rename_variables,[],[7])).
% 266.90/271.56 cnf(182117,plain,
% 266.90/271.56 (~P4(x1821171,x1821172)+P4(x1821171,f7(x1821173))+~P5(x1821172,x1821173)),
% 266.90/271.56 inference(rename_variables,[],[8])).
% 266.90/271.56 cnf(182119,plain,
% 266.90/271.56 (~P4(x1821191,x1821192)+P4(x1821191,f6(x1821193,x1821192,x1821191))+~P5(x1821192,f3(x1821193))),
% 266.90/271.56 inference(rename_variables,[],[12])).
% 266.90/271.56 cnf(182121,plain,
% 266.90/271.56 (~P4(x1821211,x1821212)+P5(f6(x1821213,x1821212,x1821211),x1821213)+~P5(x1821212,f3(x1821213))),
% 266.90/271.56 inference(rename_variables,[],[13])).
% 266.90/271.56 cnf(182123,plain,
% 266.90/271.56 (~P4(x1821231,x1821232)+P4(x1821231,f7(x1821233))+~P5(x1821232,x1821233)),
% 266.90/271.56 inference(rename_variables,[],[8])).
% 266.90/271.56 cnf(182125,plain,
% 266.90/271.56 (~P4(x1821251,x1821252)+P4(f4(x1821252,x1821253),x1821252)+P4(x1821251,x1821253)),
% 266.90/271.56 inference(rename_variables,[],[25])).
% 266.90/271.56 cnf(182127,plain,
% 266.90/271.56 (~P4(x1821271,x1821272)+~P2(x1821272,x1821273)+P4(x1821271,x1821273)),
% 266.90/271.56 inference(rename_variables,[],[7])).
% 266.90/271.56 cnf(182131,plain,
% 266.90/271.56 (~P4(x1821311,x1821312)+P4(x1821311,f7(x1821313))+~P5(x1821312,x1821313)),
% 266.90/271.56 inference(rename_variables,[],[8])).
% 266.90/271.56 cnf(182133,plain,
% 266.90/271.56 (~P4(x1821331,x1821332)+P4(x1821331,f6(x1821333,x1821332,x1821331))+~P5(x1821332,f3(x1821333))),
% 266.90/271.56 inference(rename_variables,[],[12])).
% 266.90/271.56 cnf(182135,plain,
% 266.90/271.56 (~P4(x1821351,x1821352)+P5(f6(x1821353,x1821352,x1821351),x1821353)+~P5(x1821352,f3(x1821353))),
% 266.90/271.56 inference(rename_variables,[],[13])).
% 266.90/271.56 cnf(182137,plain,
% 266.90/271.56 (~P4(f4(x1821371,x1821372),x1821372)+P2(x1821371,x1821372)),
% 266.90/271.56 inference(rename_variables,[],[11])).
% 266.90/271.56 cnf(182139,plain,
% 266.90/271.56 (P2(x1821391,x1821392)+~P3(x1821391,x1821392)),
% 266.90/271.56 inference(rename_variables,[],[4])).
% 266.90/271.56 cnf(182145,plain,
% 266.90/271.56 (~P4(x1821451,x1821452)+P4(f4(x1821452,x1821453),x1821452)+P4(x1821451,x1821453)),
% 266.90/271.56 inference(rename_variables,[],[25])).
% 266.90/271.56 cnf(182147,plain,
% 266.90/271.56 (~P4(x1821471,x1821472)+~P2(x1821472,x1821473)+P4(x1821471,x1821473)),
% 266.90/271.56 inference(rename_variables,[],[7])).
% 266.90/271.56 cnf(182162,plain,
% 266.90/271.56 ($false),
% 266.90/271.56 inference(scs_inference,[],[3,28,21,14,6,11,25,7,5,8,10,182107,182111,12,13,182117,182105,182115,37,182123,182119,182121,182103,4,182113,9,182125,182127,182131,182147,182133,182135,29,182137,182139,182145,30]),
% 266.90/271.56 ['proof']).
% 267.29/271.73 % SZS output end Proof
% 267.29/271.73 % Total time :266.020000s
%------------------------------------------------------------------------------