TSTP Solution File: GRA002+4 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n024.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 : 600s
% DateTime : Sat Jul 16 07:21:23 EDT 2022
% Result : Theorem 0.91s 1.13s
% Output : Refutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.08/0.14 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 02:29:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.91/1.13 # Version: 1.3
% 0.91/1.13 # SZS status Theorem
% 0.91/1.13 # SZS output start CNFRefutation
% 0.91/1.13 fof(maximal_path_length,conjecture,(complete=>(![P]:(![V1]:(![V2]:(shortest_path(V1,V2,P)=>less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))))))),input).
% 0.91/1.13 fof(c16,negated_conjecture,(~(complete=>(![P]:(![V1]:(![V2]:(shortest_path(V1,V2,P)=>less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)))))))),inference(assume_negation,status(cth),[maximal_path_length])).
% 0.91/1.13 fof(c17,negated_conjecture,(complete&(?[P]:(?[V1]:(?[V2]:(shortest_path(V1,V2,P)&~less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))))))),inference(fof_nnf,status(thm),[c16])).
% 0.91/1.13 fof(c18,negated_conjecture,(complete&(?[P]:((?[V1]:(?[V2]:shortest_path(V1,V2,P)))&~less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))))),inference(shift_quantors,status(thm),[c17])).
% 0.91/1.13 fof(c19,negated_conjecture,(complete&(?[X2]:((?[X3]:(?[X4]:shortest_path(X3,X4,X2)))&~less_or_equal(minus(length_of(X2),n1),number_of_in(triangles,graph))))),inference(variable_rename,status(thm),[c18])).
% 0.91/1.13 fof(c20,negated_conjecture,(complete&(shortest_path(skolem0002,skolem0003,skolem0001)&~less_or_equal(minus(length_of(skolem0001),n1),number_of_in(triangles,graph)))),inference(skolemize,status(esa),[c19])).
% 0.91/1.13 cnf(c23,negated_conjecture,~less_or_equal(minus(length_of(skolem0001),n1),number_of_in(triangles,graph)),inference(split_conjunct,status(thm),[c20])).
% 0.91/1.13 cnf(symmetry,axiom,X90!=X89|X89=X90,eq_axiom).
% 0.91/1.13 cnf(c22,negated_conjecture,shortest_path(skolem0002,skolem0003,skolem0001),inference(split_conjunct,status(thm),[c20])).
% 0.91/1.13 fof(shortest_path_defn,axiom,(![V1]:(![V2]:(![SP]:(shortest_path(V1,V2,SP)<=>((path(V1,V2,SP)&V1!=V2)&(![P]:(path(V1,V2,P)=>less_or_equal(length_of(SP),length_of(P))))))))),input).
% 0.91/1.13 fof(c66,axiom,(![V1]:(![V2]:(![SP]:((~shortest_path(V1,V2,SP)|((path(V1,V2,SP)&V1!=V2)&(![P]:(~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P))))))&(((~path(V1,V2,SP)|V1=V2)|(?[P]:(path(V1,V2,P)&~less_or_equal(length_of(SP),length_of(P)))))|shortest_path(V1,V2,SP)))))),inference(fof_nnf,status(thm),[shortest_path_defn])).
% 0.91/1.13 fof(c67,axiom,((![V1]:(![V2]:(![SP]:(~shortest_path(V1,V2,SP)|((path(V1,V2,SP)&V1!=V2)&(![P]:(~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P)))))))))&(![V1]:(![V2]:(![SP]:(((~path(V1,V2,SP)|V1=V2)|(?[P]:(path(V1,V2,P)&~less_or_equal(length_of(SP),length_of(P)))))|shortest_path(V1,V2,SP)))))),inference(shift_quantors,status(thm),[c66])).
% 0.91/1.13 fof(c68,axiom,((![X34]:(![X35]:(![X36]:(~shortest_path(X34,X35,X36)|((path(X34,X35,X36)&X34!=X35)&(![X37]:(~path(X34,X35,X37)|less_or_equal(length_of(X36),length_of(X37)))))))))&(![X38]:(![X39]:(![X40]:(((~path(X38,X39,X40)|X38=X39)|(?[X41]:(path(X38,X39,X41)&~less_or_equal(length_of(X40),length_of(X41)))))|shortest_path(X38,X39,X40)))))),inference(variable_rename,status(thm),[c67])).
% 0.91/1.13 fof(c70,axiom,(![X34]:(![X35]:(![X36]:(![X37]:(![X38]:(![X39]:(![X40]:((~shortest_path(X34,X35,X36)|((path(X34,X35,X36)&X34!=X35)&(~path(X34,X35,X37)|less_or_equal(length_of(X36),length_of(X37)))))&(((~path(X38,X39,X40)|X38=X39)|(path(X38,X39,skolem0006(X38,X39,X40))&~less_or_equal(length_of(X40),length_of(skolem0006(X38,X39,X40)))))|shortest_path(X38,X39,X40)))))))))),inference(shift_quantors,status(thm),[fof(c69,axiom,((![X34]:(![X35]:(![X36]:(~shortest_path(X34,X35,X36)|((path(X34,X35,X36)&X34!=X35)&(![X37]:(~path(X34,X35,X37)|less_or_equal(length_of(X36),length_of(X37)))))))))&(![X38]:(![X39]:(![X40]:(((~path(X38,X39,X40)|X38=X39)|(path(X38,X39,skolem0006(X38,X39,X40))&~less_or_equal(length_of(X40),length_of(skolem0006(X38,X39,X40)))))|shortest_path(X38,X39,X40)))))),inference(skolemize,status(esa),[c68])).])).
% 0.91/1.13 fof(c71,axiom,(![X34]:(![X35]:(![X36]:(![X37]:(![X38]:(![X39]:(![X40]:((((~shortest_path(X34,X35,X36)|path(X34,X35,X36))&(~shortest_path(X34,X35,X36)|X34!=X35))&(~shortest_path(X34,X35,X36)|(~path(X34,X35,X37)|less_or_equal(length_of(X36),length_of(X37)))))&((((~path(X38,X39,X40)|X38=X39)|path(X38,X39,skolem0006(X38,X39,X40)))|shortest_path(X38,X39,X40))&(((~path(X38,X39,X40)|X38=X39)|~less_or_equal(length_of(X40),length_of(skolem0006(X38,X39,X40))))|shortest_path(X38,X39,X40))))))))))),inference(distribute,status(thm),[c70])).
% 0.91/1.13 cnf(c72,axiom,~shortest_path(X150,X148,X149)|path(X150,X148,X149),inference(split_conjunct,status(thm),[c71])).
% 0.91/1.13 cnf(c172,plain,path(skolem0002,skolem0003,skolem0001),inference(resolution,status(thm),[c72, c22])).
% 0.91/1.13 fof(path_length_sequential_pairs,axiom,(![V1]:(![V2]:(![P]:(path(V1,V2,P)=>number_of_in(sequential_pairs,P)=minus(length_of(P),n1))))),input).
% 0.91/1.13 fof(c41,axiom,(![V1]:(![V2]:(![P]:(~path(V1,V2,P)|number_of_in(sequential_pairs,P)=minus(length_of(P),n1))))),inference(fof_nnf,status(thm),[path_length_sequential_pairs])).
% 0.91/1.13 fof(c42,axiom,(![X16]:(![X17]:(![X18]:(~path(X16,X17,X18)|number_of_in(sequential_pairs,X18)=minus(length_of(X18),n1))))),inference(variable_rename,status(thm),[c41])).
% 0.91/1.13 cnf(c43,axiom,~path(X281,X283,X282)|number_of_in(sequential_pairs,X282)=minus(length_of(X282),n1),inference(split_conjunct,status(thm),[c42])).
% 0.91/1.13 cnf(c369,plain,number_of_in(sequential_pairs,skolem0001)=minus(length_of(skolem0001),n1),inference(resolution,status(thm),[c43, c172])).
% 0.91/1.13 cnf(c371,plain,minus(length_of(skolem0001),n1)=number_of_in(sequential_pairs,skolem0001),inference(resolution,status(thm),[c369, symmetry])).
% 0.91/1.13 cnf(transitivity,axiom,X92!=X91|X91!=X93|X92=X93,eq_axiom).
% 0.91/1.13 cnf(c21,negated_conjecture,complete,inference(split_conjunct,status(thm),[c20])).
% 0.91/1.13 fof(triangles_and_sequential_pairs,plain,(complete=>(![P]:(![V1]:(![V2]:(shortest_path(V1,V2,P)=>number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))))),input).
% 0.91/1.13 fof(c24,plain,(~complete|(![P]:(![V1]:(![V2]:(~shortest_path(V1,V2,P)|number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))))),inference(fof_nnf,status(thm),[triangles_and_sequential_pairs])).
% 0.91/1.13 fof(c25,plain,(~complete|(![P]:((![V1]:(![V2]:~shortest_path(V1,V2,P)))|number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))),inference(shift_quantors,status(thm),[c24])).
% 0.91/1.13 fof(c27,plain,(![X5]:(![X6]:(![X7]:(~complete|(~shortest_path(X6,X7,X5)|number_of_in(sequential_pairs,X5)=number_of_in(triangles,X5)))))),inference(shift_quantors,status(thm),[fof(c26,plain,(~complete|(![X5]:((![X6]:(![X7]:~shortest_path(X6,X7,X5)))|number_of_in(sequential_pairs,X5)=number_of_in(triangles,X5)))),inference(variable_rename,status(thm),[c25])).])).
% 0.91/1.13 cnf(c28,plain,~complete|~shortest_path(X266,X265,X264)|number_of_in(sequential_pairs,X264)=number_of_in(triangles,X264),inference(split_conjunct,status(thm),[c27])).
% 0.91/1.13 cnf(c292,plain,~complete|number_of_in(sequential_pairs,skolem0001)=number_of_in(triangles,skolem0001),inference(resolution,status(thm),[c28, c22])).
% 0.91/1.13 cnf(c340,plain,number_of_in(sequential_pairs,skolem0001)=number_of_in(triangles,skolem0001),inference(resolution,status(thm),[c292, c21])).
% 0.91/1.13 cnf(c341,plain,X366!=number_of_in(sequential_pairs,skolem0001)|X366=number_of_in(triangles,skolem0001),inference(resolution,status(thm),[c340, transitivity])).
% 0.91/1.13 cnf(c665,plain,minus(length_of(skolem0001),n1)=number_of_in(triangles,skolem0001),inference(resolution,status(thm),[c341, c371])).
% 0.91/1.13 cnf(c677,plain,number_of_in(triangles,skolem0001)=minus(length_of(skolem0001),n1),inference(resolution,status(thm),[c665, symmetry])).
% 0.91/1.13 cnf(reflexivity,axiom,X84=X84,eq_axiom).
% 0.91/1.13 fof(graph_has_them_all,axiom,(![Things]:(![InThese]:less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)))),input).
% 0.91/1.13 fof(c29,axiom,(![X8]:(![X9]:less_or_equal(number_of_in(X8,X9),number_of_in(X8,graph)))),inference(variable_rename,status(thm),[graph_has_them_all])).
% 0.91/1.13 cnf(c30,axiom,less_or_equal(number_of_in(X155,X156),number_of_in(X155,graph)),inference(split_conjunct,status(thm),[c29])).
% 0.91/1.13 cnf(c14,plain,X254!=X253|X255!=X256|~less_or_equal(X254,X255)|less_or_equal(X253,X256),eq_axiom).
% 0.91/1.13 cnf(c247,plain,number_of_in(X487,X486)!=X488|number_of_in(X487,graph)!=X485|less_or_equal(X488,X485),inference(resolution,status(thm),[c14, c30])).
% 0.91/1.13 cnf(c1517,plain,number_of_in(X490,X491)!=X489|less_or_equal(X489,number_of_in(X490,graph)),inference(resolution,status(thm),[c247, reflexivity])).
% 0.91/1.13 cnf(c1530,plain,less_or_equal(minus(length_of(skolem0001),n1),number_of_in(triangles,graph)),inference(resolution,status(thm),[c1517, c677])).
% 0.91/1.13 cnf(c1589,plain,$false,inference(resolution,status(thm),[c1530, c23])).
% 0.91/1.13 # SZS output end CNFRefutation
% 0.91/1.13
% 0.91/1.13 # Initial clauses : 82
% 0.91/1.13 # Processed clauses : 274
% 0.91/1.13 # Factors computed : 0
% 0.91/1.13 # Resolvents computed: 1429
% 0.91/1.13 # Tautologies deleted: 3
% 0.91/1.13 # Forward subsumed : 103
% 0.91/1.13 # Backward subsumed : 6
% 0.91/1.13 # -------- CPU Time ---------
% 0.91/1.13 # User time : 0.758 s
% 0.91/1.13 # System time : 0.018 s
% 0.91/1.13 # Total time : 0.776 s
%------------------------------------------------------------------------------