%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA002+3 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:42 AM UTC 2026
% Result : Theorem 16.23s 3.77s
% Output : CNFRefutation 16.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRA002+3 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n003.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:49:07 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.23/3.77 % SZS status Theorem for theBenchmark.p
% 16.23/3.77 % SZS output start CNFRefutation for theBenchmark.p
% 16.23/3.77 fof(path_length_sequential_pairs, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X0,X1,X2) => 'number$uof$uin'('sequential$upairs',X2) = minus('length$uof'(X2),n1)))).
% 16.23/3.77 fof(sequential_pairs_and_triangles, axiom, ! [X0] : ! [X1] : ! [X2] : (((path(X1,X2,X0) & ! [X3] : ! [X4] : ((('on$upath'(X3,X0) & ('on$upath'(X4,X0) & sequential(X3,X4))) => ? [X5] : triangle(X3,X4,X5)))) => 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0)))).
% 16.23/3.77 fof(graph_has_them_all, axiom, ! [X0] : ! [X1] : 'less$uor$uequal'('number$uof$uin'(X0,X1),'number$uof$uin'(X0,graph))).
% 16.23/3.77 fof(sequential_is_triangle, lemma, (complete => ! [X0] : ! [X1] : ! [X2] : ! [X3] : ! [X4] : ((('shortest$upath'(X0,X1,X4) & (precedes(X2,X3,X4) & sequential(X2,X3))) => ? [X5] : triangle(X2,X3,X5))))).
% 16.23/3.77 fof(precedes_defn, axiom, ! [X0] : ! [X1] : ! [X2] : ((path(X1,X2,X0) => ! [X3] : ! [X4] : ((('on$upath'(X3,X0) & ('on$upath'(X4,X0) & (sequential(X3,X4) | ? [X5] : ((sequential(X3,X5) & precedes(X5,X4,X0)))))) => precedes(X3,X4,X0)))))).
% 16.23/3.78 fof(shortest_path_defn, axiom, ! [X0] : ! [X1] : ! [X2] : (('shortest$upath'(X0,X1,X2) <=> (path(X0,X1,X2) & (X0 != X1 & ! [X3] : ((path(X0,X1,X3) => 'less$uor$uequal'('length$uof'(X2),'length$uof'(X3))))))))).
% 16.23/3.78 fof(maximal_path_length, conjecture, (complete => ! [X0] : ! [X1] : ! [X2] : (('shortest$upath'(X1,X2,X0) => 'less$uor$uequal'(minus('length$uof'(X0),n1),'number$uof$uin'(triangles,graph)))))).
% 16.23/3.78 fof(negated_conjecture, negated_conjecture, ~((complete => ! [X0] : ! [X1] : ! [X2] : (('shortest$upath'(X1,X2,X0) => 'less$uor$uequal'(minus('length$uof'(X0),n1),'number$uof$uin'(triangles,graph)))))), inference(negate_conjecture, [status(cth)], [maximal_path_length])).
% 16.23/3.78 cnf(c10, plain, ~path(X0,X1,X2) | 'number$uof$uin'('sequential$upairs',X2) = minus('length$uof'(X2),n1), inference(clausification, [status(esa)], [path_length_sequential_pairs])).
% 16.23/3.78 cnf(c11, plain, ~path(X0,X1,X2) | 'on$upath'(sK13(X2),X2) | 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2), inference(clausification, [status(esa)], [sequential_pairs_and_triangles])).
% 16.23/3.78 cnf(c12, plain, ~path(X0,X1,X2) | 'on$upath'(sK14(X2),X2) | 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2), inference(clausification, [status(esa)], [sequential_pairs_and_triangles])).
% 16.23/3.78 cnf(c13, plain, ~path(X0,X1,X2) | sequential(sK13(X2),sK14(X2)) | 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2), inference(clausification, [status(esa)], [sequential_pairs_and_triangles])).
% 16.23/3.78 cnf(c14, plain, ~path(X0,X1,X2) | ~triangle(sK13(X2),sK14(X2),X3) | 'number$uof$uin'('sequential$upairs',X2) = 'number$uof$uin'(triangles,X2), inference(clausification, [status(esa)], [sequential_pairs_and_triangles])).
% 16.23/3.78 cnf(c15, plain, 'less$uor$uequal'('number$uof$uin'(X0,X1),'number$uof$uin'(X0,graph)), inference(clausification, [status(esa)], [graph_has_them_all])).
% 16.23/3.78 cnf(c16, plain, ~sequential(X0,X1) | ~complete | ~'shortest$upath'(X2,X3,X4) | triangle(X0,X1,sK23(X0,X1)) | ~precedes(X0,X1,X4), inference(clausification, [status(esa)], [sequential_is_triangle])).
% 16.23/3.78 cnf(c59, plain, ~'on$upath'(X0,X1) | precedes(X2,X0,X1) | ~'on$upath'(X2,X1) | ~path(X3,X4,X1) | ~sequential(X2,X0), inference(clausification, [status(esa)], [precedes_defn])).
% 16.23/3.78 cnf(c70, plain, ~'shortest$upath'(X0,X1,X2) | X3(X2,X0,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 16.23/3.78 cnf(c72, plain, ~X0(X1,X2,X3) | path(X2,X3,X1), inference(clausification, [status(esa)], [shortest_path_defn])).
% 16.23/3.78 cnf(c79, plain, complete, inference(clausification, [status(esa)], [negated_conjecture])).
% 16.23/3.78 cnf(c80, plain, 'shortest$upath'(sK82,sK83,sK81), inference(clausification, [status(esa)], [negated_conjecture])).
% 16.23/3.78 cnf(c81, plain, ~'less$uor$uequal'(minus('length$uof'(sK81),n1),'number$uof$uin'(triangles,graph)), inference(clausification, [status(esa)], [negated_conjecture])).
% 16.23/3.78 cnf(d0, plain, 'Ts69'(sK81,sK82,sK83), inference(resolution, [status(thm)], [c70,c80])).
% 16.23/3.78 cnf(d1, plain, path(sK82,sK83,sK81), inference(resolution, [status(thm)], [c72,d0])).
% 16.23/3.78 cnf(d2, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | 'on$upath'(sK13(sK81),sK81), inference(resolution, [status(thm)], [d1,c11])).
% 16.23/3.78 cnf(d3, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | 'on$upath'(sK14(sK81),sK81), inference(resolution, [status(thm)], [d1,c12])).
% 16.23/3.78 cnf(d4, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | sequential(sK13(sK81),sK14(sK81)), inference(resolution, [status(thm)], [d1,c13])).
% 16.23/3.78 cnf(d5, plain, triangle(X0,X1,sK23(X0,X1)) | ~sequential(X0,X1) | ~precedes(X0,X1,X2) | ~'shortest$upath'(X3,X4,X2), inference(resolution, [status(thm)], [c79,c16])).
% 16.23/3.78 cnf(d6, plain, triangle(X0,X1,sK23(X0,X1)) | ~sequential(X0,X1) | ~precedes(X0,X1,sK81), inference(resolution, [status(thm)], [d5,c80])).
% 16.23/3.78 cnf(d7, plain, ~sequential(sK13(X0),sK14(X0)) | ~precedes(sK13(X0),sK14(X0),sK81) | 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) | ~path(X1,X2,X0), inference(resolution, [status(thm)], [d6,c14])).
% 16.23/3.78 cnf(d8, plain, ~sequential(X0,X1) | ~'on$upath'(X1,sK81) | ~'on$upath'(X0,sK81) | precedes(X0,X1,sK81), inference(resolution, [status(thm)], [d1,c59])).
% 16.23/3.78 cnf(d9, plain, ~sequential(sK13(X0),sK14(X0)) | ~'on$upath'(sK14(X0),sK81) | ~'on$upath'(sK13(X0),sK81) | 'number$uof$uin'('sequential$upairs',X0) = 'number$uof$uin'(triangles,X0) | ~sequential(sK13(X0),sK14(X0)) | ~path(X1,X2,X0), inference(resolution, [status(thm)], [d8,d7])).
% 16.23/3.78 cnf(d10, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | ~path(X0,X1,sK81) | ~'on$upath'(sK13(sK81),sK81) | ~'on$upath'(sK14(sK81),sK81) | 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81), inference(resolution, [status(thm)], [d9,d4])).
% 16.23/3.78 cnf(d11, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | ~path(X0,X1,sK81) | ~'on$upath'(sK13(sK81),sK81) | 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81), inference(resolution, [status(thm)], [d10,d3])).
% 16.23/3.78 cnf(d12, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81) | ~path(X0,X1,sK81) | 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81), inference(resolution, [status(thm)], [d11,d2])).
% 16.23/3.78 cnf(d13, plain, 'number$uof$uin'('sequential$upairs',sK81) = 'number$uof$uin'(triangles,sK81), inference(resolution, [status(thm)], [d12,d1])).
% 16.23/3.78 cnf(d14, plain, 'less$uor$uequal'('number$uof$uin'('sequential$upairs',sK81),'number$uof$uin'(triangles,graph)), inference(superposition, [status(thm)], [d13,c15])).
% 16.23/3.78 cnf(d15, plain, 'number$uof$uin'('sequential$upairs',sK81) = minus('length$uof'(sK81),n1), inference(resolution, [status(thm)], [d1,c10])).
% 16.23/3.78 cnf(d16, plain, ~'less$uor$uequal'('number$uof$uin'('sequential$upairs',sK81),'number$uof$uin'(triangles,graph)), inference(demodulation, [status(thm)], [c81,d15])).
% 16.23/3.78 cnf(d17, plain, $false, inference(resolution, [status(thm)], [d16,d14])).
% 16.23/3.78 % SZS output end CNFRefutation for theBenchmark.p
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